On the macroscopic dynamics induced by a model wave-particle collision operator |
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Authors: | P. Degond José L. López P.F. Peyrard |
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Affiliation: | (1) Mathématiques pour l'Industrie et la Physique, UMR CNRS 5640, URF MIG, Université Paul Sabatier, 118, route de Narbonne, F-31062 Toulouse cedex, France , FR;(2) Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, E-18071 Granada, Spain , ES;(3) DERTS / CERT ONERA, 2, Avenue Edouard Belin, BP 4025, F-31055 Toulouse cedex, France , FR |
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Abstract: | The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation. In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling. Received June 16, 1997 |
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Keywords: | AMS Subject classification:41A60 35Q20 76P05 |
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