Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Finite Larmor radius approximation for collisional magnetic confinement. Part II: the Fokker-Planck-Landau equation

Authors: Mihai Bostan and Céline Caldini-Queiros
Journal: Quart. Appl. Math. 72 (2014), 513-548
MSC (2010): Primary 35Q75, 78A35, 82D10
DOI: https://doi.org/10.1090/S0033-569X-2014-01357-4
Published electronically: June 9, 2014
MathSciNet review: 3237562
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Abstract: This paper is devoted to the finite Larmor radius approximation of the Fokker-Planck-Landau equation, which plays a major role in plasma physics. We obtain a completely explicit form for the gyroaverage of the Fokker-Planck-Landau kernel, accounting for diffusion and convolution with respect to both velocity and (perpendicular) position coordinates. We show that the new collision operator enjoys the usual physical properties; the averaged kernel balances the mass, momentum, and kinetic energy and dissipates the entropy, globally in velocity and perpendicular position coordinates.

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Mihai Bostan
Affiliation: Laboratoire d’Analyse, Topologie, Probabilités LATP, Centre de Mathématiques et Informatique CMI, UMR CNRS 7353, 39 rue Frédéric Joliot Curie, 13453 Marseille Cedex 13 France
Email: bostan@cmi.univ-mrs.fr

Céline Caldini-Queiros
Affiliation: Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex France
Email: celine.caldini-queiros@univ-fcomte.fr

DOI: https://doi.org/10.1090/S0033-569X-2014-01357-4
Received by editor(s): July 4, 2012
Received by editor(s) in revised form: December 15, 2012
Published electronically: June 9, 2014
Article copyright: © Copyright 2014 Brown University

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