A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations

Franck Assous; J. Chaskalovic

doi:10.1016/j.crme.2012.09.002

A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations
[Un nouveau modèle paraxial asymptotique pour approcher le système dʼéquations de Vlasov–Maxwell]

Franck Assous ¹ ; J. Chaskalovic ²

¹ Computer Science and Mathematics Department, Ariel University Center & Bar-Ilan University, 40700 Ariel, Israel
² DALEMBERT, University Pierre and Marie Curie, 4, place Jussieu, 75005 Paris, France

Comptes Rendus. Mécanique, Volume 340 (2012) no. 10, pp. 706-714.

Résumé
Abstract

On propose un nouveau modèle paraxial asymptotique pour approcher le système dʼéquations de Vlasov–Maxwell. Cette formulation est précise à lʼordre quatre par rapport à un paramètre η désignant le quotient de la vitesse transverse caractéristique du faisceau par rapport à celle de la lumière. Lʼintéret de ce modèle est quʼil est plus simple que le système complet des équations de Vlasov–Maxwell, tout en étant une approximation suffisamment précise. Ce nouveau modèle devrait conduire à une méthode numérique fiable, rapide et facile à implementer.

We introduce a new paraxial asymptotic model to approximate the Vlasov–Maxwell equations. This formulation is fourth order accurate in a parameter η which denotes the ratio between the transverse characteristic velocity of the beam and the speed of light. The model is interesting because it is simpler than the complete Vlasov–Maxwell equations, and is an accurate approximation of them. This model should give an accurate, fast and easy to implement numerical method of solution.

Reçu le : 2012-06-17
Accepté le : 2012-09-06
Publié le : 2012-09-28

DOI : 10.1016/j.crme.2012.09.002

Keywords: Computational fluid mechanics, Vlasov–Maxwell equations, Asymptotic analysis, Paraxial model
Mot clés : Mécanique des fluides numérique, Équations de Vlasov–Maxwell, Analyse asymptotique, Modèle paraxial

Affiliations des auteurs :

Franck Assous ¹ ; J. Chaskalovic ²

¹ Computer Science and Mathematics Department, Ariel University Center & Bar-Ilan University, 40700 Ariel, Israel
² DALEMBERT, University Pierre and Marie Curie, 4, place Jussieu, 75005 Paris, France

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     title = {A new paraxial asymptotic model for the relativistic {Vlasov{\textendash}Maxwell} equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {706--714},
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     number = {10},
     year = {2012},
     doi = {10.1016/j.crme.2012.09.002},
     language = {en},
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Franck Assous; J. Chaskalovic. A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations. Comptes Rendus. Mécanique, Volume 340 (2012) no. 10, pp. 706-714. doi : 10.1016/j.crme.2012.09.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.09.002/

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