<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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 the numerical 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.</p></abstract>

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 the numerical 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.

Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena

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 7 rue René Descartes, 67084 Strasbourg Cedex, France

International Journal of Applied Mathematics and Computer Science

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...

Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena

Pubblicato online: 11 ott 2007

Pagine: 361 - 374

DOI: https://doi.org/10.2478/v10006-007-0030-3

Parole chiave
Vlasov-Darwin model, Vlasov-Poisswell model, semi-Lagrangian methods, low-frequency electromagnetic phenomena

This content is open access.

Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena

Pubblicato online: 11 ott 2007

Pagine: 361 - 374

DOI: https://doi.org/10.2478/v10006-007-0030-3

Parole chiaveVlasov-Darwin model, Vlasov-Poisswell model, semi-Lagrangian methods, low-frequency electromagnetic phenomena

This content is open access.

Parole chiave
Vlasov-Darwin model, Vlasov-Poisswell model, semi-Lagrangian methods, low-frequency electromagnetic phenomena