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.
%0 Journal Article
%1 Besse_2007
%A Besse, Nicolas
%A Mauser, Norbert
%A Sonnendrücker, Eric
%D 2007
%J International Journal of Applied Mathematics and Computer Science
%K electromagnetic plasma simulation vlasov
%N 3
%P 361--374
%R 10.2478/v10006-007-0030-3
%T Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena
%U http://dx.doi.org/10.2478/v10006-007-0030-3
%V 17
%X 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.
@article{Besse_2007,
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.},
added-at = {2012-04-11T14:04:10.000+0200},
author = {Besse, Nicolas and Mauser, Norbert and Sonnendrücker, Eric},
biburl = {https://www.bibsonomy.org/bibtex/2fba19b1d73df55950477fb61e070f823/pkilian},
doi = {10.2478/v10006-007-0030-3},
interhash = {edd87a9c515001a7ba392c7e0b6ba62a},
intrahash = {fba19b1d73df55950477fb61e070f823},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {electromagnetic plasma simulation vlasov},
month = oct,
number = 3,
pages = {361--374},
timestamp = {2012-04-11T14:04:11.000+0200},
title = {Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena},
url = {http://dx.doi.org/10.2478/v10006-007-0030-3},
volume = 17,
year = 2007
}