Comptes Rendus
A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations
[Un nouveau modèle paraxial asymptotique pour approcher le système dʼéquations de Vlasov–Maxwell]
Comptes Rendus. Mécanique, Volume 340 (2012) no. 10, pp. 706-714.

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 :
Accepté le :
Publié le :
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
@article{CRMECA_2012__340_10_706_0,
     author = {Franck Assous and J. Chaskalovic},
     title = {A new paraxial asymptotic model for the relativistic {Vlasov{\textendash}Maxwell} equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {706--714},
     publisher = {Elsevier},
     volume = {340},
     number = {10},
     year = {2012},
     doi = {10.1016/j.crme.2012.09.002},
     language = {en},
}
TY  - JOUR
AU  - Franck Assous
AU  - J. Chaskalovic
TI  - A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations
JO  - Comptes Rendus. Mécanique
PY  - 2012
SP  - 706
EP  - 714
VL  - 340
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2012.09.002
LA  - en
ID  - CRMECA_2012__340_10_706_0
ER  - 
%0 Journal Article
%A Franck Assous
%A J. Chaskalovic
%T A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations
%J Comptes Rendus. Mécanique
%D 2012
%P 706-714
%V 340
%N 10
%I Elsevier
%R 10.1016/j.crme.2012.09.002
%G en
%F CRMECA_2012__340_10_706_0
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

Cité par Sources :

Commentaires - Politique