Cette Note présente la dérivation de lʼapproximation de rayon de Larmor fini, en prenant en compte les collisions. Le principal sujet en est la recherche dʼune expression explicite pour la gyromoyenne de cet opérateur, ce qui revient à analyser la gyromoyenne dʼune convolution en vitesse. On note que lʼopérateur moyenné qui en résulte nʼest plus local en espace et que les propriétés physiques standards (i.e. conservation de la masse et inégalité dʼentropie) sont vérifiées seulement globalement en espace et vitesse. Cʼest un premier travail qui nous permettra dʼaborder dʼautres modèles plus réalistes pour la physique des plasmas, comme les noyaux de Fokker–Planck ou Fokker–Planck–Landau (Bostan et Caldini-Queiros (soumis pour publication) [3]).
This Note concerns the derivation of the finite Larmor radius approximation, when collisions are taken into account. We concentrate on the Boltzmann relaxation operator whose study reduces to the gyroaverage computation of velocity convolutions. We emphasize that the resulting gyroaverage collision kernel is no local in space anymore and that the standard physical properties (i.e., mass balance, entropy inequality) hold true only globally in space and velocity. This is a first step in this direction and it will allow us to handle more realistic collisional mechanisms, like the Fokker–Planck or Fokker–Planck–Landau kernels (Bostan and Caldini-Queiros (submitted for publication) [3]).
Accepté le :
Publié le :
Mihaï Bostan 1 ; Céline Caldini-Queiros 2
@article{CRMATH_2012__350_19-20_879_0,
author = {Miha{\"\i} Bostan and C\'eline Caldini-Queiros},
title = {Approximation de rayon de {Larmor} fini pour les plasmas magn\'etis\'es collisionnels},
journal = {Comptes Rendus. Math\'ematique},
pages = {879--884},
publisher = {Elsevier},
volume = {350},
number = {19-20},
year = {2012},
doi = {10.1016/j.crma.2012.09.019},
language = {fr},
}
TY - JOUR AU - Mihaï Bostan AU - Céline Caldini-Queiros TI - Approximation de rayon de Larmor fini pour les plasmas magnétisés collisionnels JO - Comptes Rendus. Mathématique PY - 2012 SP - 879 EP - 884 VL - 350 IS - 19-20 PB - Elsevier DO - 10.1016/j.crma.2012.09.019 LA - fr ID - CRMATH_2012__350_19-20_879_0 ER -
Mihaï Bostan; Céline Caldini-Queiros. Approximation de rayon de Larmor fini pour les plasmas magnétisés collisionnels. Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 879-884. doi : 10.1016/j.crma.2012.09.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.09.019/
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