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2007 | 17 | 3 | 361-374
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Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena

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We present a new numerical method to solve the Vlasov-Darwin and Vlasov-Poisswell systems which are approximations of the Vlasov-Maxwell equation in the asymptotic limit of the infinite speed of light. These systems model low-frequency electromagnetic phenomena in plasmas, and thus "light waves" are somewhat supressed, which in turn allows thenumerical discretization to dispense with the Courant-Friedrichs-Lewy condition on the time step. We construct a numerical scheme based on semi-Lagrangian methods and time splitting techniques. We develop a four-dimensional phase space algorithm for the distribution function while the electromagnetic field is solved on a two-dimensional Cartesian grid. Finally, we present two nontrivial test cases: (a) the wave Landau damping and (b) the electromagnetic beam-plasma instability. For these cases our numerical scheme works very well and is in agreement with analytic kinetic theory.
Opis fizyczny
  • Laboratoire de Physique des Milieux Ionisés et Applications & Institut de Mathématiques Elie Cartan, Université Henri Poincaré Nancy-I, BP 239 54506 Vandoeuvre-lès-Nancy Cedex, France
  • Wolfgang Pauli Institute c/o Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Wien, Austria
  • Institut de Recherche Mathématique Avancée, UMR 7501 CNRS/ULP, rue René Descartes, 67084 Strasbourg Cedex, France
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