Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system

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A problem with the solution of the Vlasov equation is its tendency to become filamented/oscillatory in velocity space, which in numerical simulations can give rise to unphysical oscillations and recurrence effects. We present a three-dimensional Vlasov–Maxwell solver (three spatial and velocity dimensions, plus time), in which the Vlasov equation is Fourier transformed in velocity space and the resulting equations solved numerically. By designing absorbing outflow boundary conditions in the Fourier transformed velocity space, the highest Fourier modes in velocity space are removed from the numerical solution. This introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced. The well-posedness of the boundary conditions is proved analytically, while the stability of the numerical implementation is assessed by long-time numerical simulations. Well-known wave-modes in magnetized plasmas are shown to be reproduced by the numerical scheme.
Original languageEnglish
Pages (from-to)1508-1532
Number of pages25
JournalJournal of Computational Physics
Issue number2
Early online date17 Feb 2007
Publication statusPublished - 10 Aug 2007


  • Vlasov-Maxwell system
  • numerical method
  • Fourier method


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