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This paper is concerned with the analysis of a mathematical model arising in plasma physics, more specifically in fusion research. It directly follows, Han-Kwan (2010) [18], where the three-dimensional analysis of a Vlasov–Poisson equation with finite Larmor radius scaling was led, corresponding to the case of ions with massless electrons whose density follows a linearized Maxwell–Boltzmann law. We now consider the case of electrons in a background of fixed ions, which was only sketched in Han-Kwan (2010) [18]. Unfortunately, there is evidence that the formal limit is false in general. Nevertheless, we formally derive from the Vlasov–Poisson equation a fluid system for particular monokinetic data. We prove the local in time existence of analytic solutions and rigorously study the limit (when the inverse of the intensity of the magnetic field and the Debye length vanish) to a new anisotropic fluid system. This is achieved thanks to Cauchy–Kovalevskaya type techniques, as introduced by Caflisch (1990) [7] and Grenier (1996) [14]. We finally show that this approach fails in Sobolev regularity, due to multi-fluid instabilities.
@article{AIHPC_2013__30_6_1127_0, author = {Han-Kwan, Daniel}, title = {On the three-dimensional finite {Larmor} radius approximation: {The} case of electrons in a fixed background of ions}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1127--1157}, publisher = {Elsevier}, volume = {30}, number = {6}, year = {2013}, doi = {10.1016/j.anihpc.2012.12.012}, mrnumber = {3132419}, zbl = {1338.82055}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.12.012/} }
TY - JOUR AU - Han-Kwan, Daniel TI - On the three-dimensional finite Larmor radius approximation: The case of electrons in a fixed background of ions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 1127 EP - 1157 VL - 30 IS - 6 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.12.012/ DO - 10.1016/j.anihpc.2012.12.012 LA - en ID - AIHPC_2013__30_6_1127_0 ER -
%0 Journal Article %A Han-Kwan, Daniel %T On the three-dimensional finite Larmor radius approximation: The case of electrons in a fixed background of ions %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 1127-1157 %V 30 %N 6 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.12.012/ %R 10.1016/j.anihpc.2012.12.012 %G en %F AIHPC_2013__30_6_1127_0
Han-Kwan, Daniel. On the three-dimensional finite Larmor radius approximation: The case of electrons in a fixed background of ions. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 6, pp. 1127-1157. doi: 10.1016/j.anihpc.2012.12.012
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