{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T21:35:42Z","timestamp":1766180142417},"reference-count":26,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,10,1]]},"abstract":"<jats:title>Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.2478\/v10006-007-0030-3","type":"journal-article","created":{"date-parts":[[2007,10,12]],"date-time":"2007-10-12T14:22:52Z","timestamp":1192198972000},"page":"361-374","source":"Crossref","is-referenced-by-count":13,"title":["Numerical Approximation of Self-Consistent Vlasov Models for Low-Frequency Electromagnetic Phenomena"],"prefix":"10.61822","volume":"17","author":[{"given":"Nicolas","family":"Besse","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Norbert","family":"Mauser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric","family":"Sonnendr\u00fccker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s00023-005-0207-y","article-title":"The Darwin approximation of the relativistic Vlasov-Maxwell system","volume":"2","author":"S. 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