%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 }