We introduce a new family of paraxial asymptotic models that approximate the Vlasov–Maxwell equations in non-relativistic cases. This formulation is th order accurate in a parameter , which denotes the ratio between the characteristic velocity of the beam and the speed of light. This family of models is interesting, first because it is simpler than the complete Vlasov–Maxwell equation and then because it allows us to choose the model complexity according to the expected accuracy.
On introduit une nouvelle famille de modèles asymptotiques paraxiaux pour approcher le système d’équations de Vlasov–Maxwell dans le cas non relativiste. Cette formulation est précise à un ordre n (que l’on peut choisir) par rapport à un paramètre , qui désigne le quotient de la vitesse caractéristique du faisceau par celle de la lumière. L’intéret de cette famille de modèle est, d’une part, qu’elle est plus simple que le système complet des équations de Vlasov–Maxwell, tout en permettant, d’autre part, de choisir le degré de complexité du modèle, en fonction de la précison désirée.
Revised:
Accepted:
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Mot clés : Équations de Vlasov–Maxwell, Analyse asymptotique, Modèle paraxial, Modèles réduits, Non relativiste
Franck Assous 1; Yevgeni Furman 1
@article{CRMECA_2020__348_12_969_0, author = {Franck Assous and Yevgeni Furman}, title = {A hierarchy of reduced models to approximate {Vlasov{\textendash}Maxwell} equations for slow time variations}, journal = {Comptes Rendus. M\'ecanique}, pages = {969--981}, publisher = {Acad\'emie des sciences, Paris}, volume = {348}, number = {12}, year = {2020}, doi = {10.5802/crmeca.50}, language = {en}, }
TY - JOUR AU - Franck Assous AU - Yevgeni Furman TI - A hierarchy of reduced models to approximate Vlasov–Maxwell equations for slow time variations JO - Comptes Rendus. Mécanique PY - 2020 SP - 969 EP - 981 VL - 348 IS - 12 PB - Académie des sciences, Paris DO - 10.5802/crmeca.50 LA - en ID - CRMECA_2020__348_12_969_0 ER -
%0 Journal Article %A Franck Assous %A Yevgeni Furman %T A hierarchy of reduced models to approximate Vlasov–Maxwell equations for slow time variations %J Comptes Rendus. Mécanique %D 2020 %P 969-981 %V 348 %N 12 %I Académie des sciences, Paris %R 10.5802/crmeca.50 %G en %F CRMECA_2020__348_12_969_0
Franck Assous; Yevgeni Furman. A hierarchy of reduced models to approximate Vlasov–Maxwell equations for slow time variations. Comptes Rendus. Mécanique, Volume 348 (2020) no. 12, pp. 969-981. doi : 10.5802/crmeca.50. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.50/
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