A hierarchy of reduced models to approximate Vlasov–Maxwell equations for slow time variations

Franck Assous; Yevgeni Furman

doi:10.5802/crmeca.50

Note

A hierarchy of reduced models to approximate Vlasov–Maxwell equations for slow time variations
[Une hiérarchie de modèles asymptotiques paraxiaux pour approcher les équations de Vlasov–Maxwell non relativistes]

Franck Assous ¹ ; Yevgeni Furman ¹

¹ Department of Mathematics, Ariel University, 40700, Ariel, Israel

Comptes Rendus. Mécanique, Volume 348 (2020) no. 12, pp. 969-981.

Résumé
Abstract

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 $η$ , 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.

We introduce a new family of paraxial asymptotic models that approximate the Vlasov–Maxwell equations in non-relativistic cases. This formulation is $n$ th order accurate in a parameter $η$ , 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.

Reçu le : 2020-02-26
Révisé le : 2020-09-04
Accepté le : 2020-09-21
Publié le : 2021-01-19

DOI : 10.5802/crmeca.50

Keywords: Vlasov–Maxwell equations, Asymptotic analysis, Paraxial model, Reduced models, Non-relativistic
Mot clés : Équations de Vlasov–Maxwell, Analyse asymptotique, Modèle paraxial, Modèles réduits, Non relativiste

Affiliations des auteurs :

Franck Assous ¹ ; Yevgeni Furman ¹

¹ Department of Mathematics, Ariel University, 40700, Ariel, Israel

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     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},
}

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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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