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

Nicolas Besse; Norbert J. mauser; Eric Sonnendrücker

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 3, page 361-374
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Besse, Nicolas, J. mauser, Norbert, and Sonnendrücker, Eric. "Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena." International Journal of Applied Mathematics and Computer Science 17.3 (2007): 361-374. <http://eudml.org/doc/207843>.

@article{Besse2007,
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 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.},
author = {Besse, Nicolas, J. mauser, Norbert, Sonnendrücker, Eric},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {low-frequency electromagnetic phenomena; semi-Lagrangian methods; Vlasov-Poisswell model; Vlasov-Darwin model; Vlasov equation; Landau damping; beam-plasma instability},
language = {eng},
number = {3},
pages = {361-374},
title = {Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena},
url = {http://eudml.org/doc/207843},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Besse, Nicolas
AU - J. mauser, Norbert
AU - Sonnendrücker, Eric
TI - Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 3
SP - 361
EP - 374
AB - 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.
LA - eng
KW - low-frequency electromagnetic phenomena; semi-Lagrangian methods; Vlasov-Poisswell model; Vlasov-Darwin model; Vlasov equation; Landau damping; beam-plasma instability
UR - http://eudml.org/doc/207843
ER -

References

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