# 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

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topBesse, 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 -

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