Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena

Nicolas Besse, Norbert J. Mauser, Eric Sonnendrücker

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish
Pages (from-to)361-374
Number of pages14
JournalInternational Journal of Applied Mathematics and Computer Science
Issue number3
StatePublished - 1 Oct 2007
Externally publishedYes


  • Low-frequency electromagnetic phenomena
  • Semi-Lagrangian methods
  • Vlasov-Darwin model
  • Vlasov-Poisswell model


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