On the three-dimensional finite Larmor radius approximation: The case of electrons in a fixed background of ions
Daniel Han-Kwan
École Normale Supérieure, Département de Mathématiques et Applications, 45 rue dʼUlm, 75230 Paris Cedex 05, France
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Abstract
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.
Cite this article
Daniel Han-Kwan, On the three-dimensional finite Larmor radius approximation: The case of electrons in a fixed background of ions. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 6, pp. 1127–1157
DOI 10.1016/J.ANIHPC.2012.12.012