Comptes Rendus
A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations
Comptes Rendus. Mécanique, Volume 340 (2012) no. 10, pp. 706-714.

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.

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.

Received:
Accepted:
Published online:
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

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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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/

[1] J.D. Lawson The Physics of Charged Particle Beams, Clarendon Press, Oxford, 1988

[2] C.K. Birdsall; A.B. Langdon Plasmas Physics via Computer Simulation, McGraw–Hill, New York, 1985

[3] F. Assous; P. Degond; J. Segre A particle-tracking method for 3D electromagnetic PIC codes on unstructured meshes, Comput. Phys. Comm., Volume 72 (1992), pp. 105-114

[4] F. Assous; P. Degond; E. Heintzé; P.A. Raviart; J. Segré On a finite element method for solving the three-dimensional Maxwell equations, J. Comput. Phys., Volume 109 (1993) no. 2, pp. 222-237

[5] M.A. Mostrom; D. Mitrovich; D.R. Welch The ARCTIC charged particle beam propagation code, J. Comput. Phys., Volume 128 (1996) no. 2, pp. 489-497

[6] P. Degond; P.-A. Raviart On the paraxial approximation of the stationary Vlasov–Maxwell, Math. Models Methods Appl. Sci., Volume 3 (1993) no. 4, pp. 513-562

[7] P.A. Raviart; E. Sonnendrucker A hierarchy of approximate models for the Maxwell equations, Numer. Math., Volume 73 (1996) no. 3, pp. 329-372

[8] G. Laval; S. Mas-Gallic; P.-A. Raviart Paraxial approximation of ultrarelativistic intense beams, Numer. Math., Volume 69 (1994) no. 1, pp. 33-60

[9] F. Assous; F. Tsipis A PIC method for solving a paraxial model of highly relativistic beams, J. Comput. Appl. Math., Volume 227 (2009) no. 1, pp. 136-146

[10] F. Assous, J. Chaskalovic, A paraxial approach for electromagnetic PIC codes in highly relativistic beams, in preparation.

[11] F. Assous; J. Chaskalovic Data mining techniques for scientific computing: Application to asymptotic paraxial approximations to model ultra relativistic particles, J. Comput. Phys., Volume 230 (2011), pp. 4811-4827

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