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

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Besse N., Mauser N. J., Sonnendrücker E.

International Journal of Applied Mathematics and Computer Science

2007

tom 17

nr 3

361-374

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.

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 Besse N.

1 Mauser N. J.

1 Sonnendrücker E.

1 2007

Wyniki wyszukiwania

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