General moment system for plasma physics based on minimum entropy principle

Jessy  Mallet; Stéphane Brull; Bruno  Dubroca

doi:10.3934/krm.2015.8.533

Article Contents

2015, Volume 8, Issue 3: 533-558. Doi: 10.3934/krm.2015.8.533

This issue Previous Article Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature Next Article Stability of a superposition of shock waves with contact discontinuities for the Jin-Xin relaxation system

General moment system for plasma physics based on minimum entropy principle

1.
Univ. Bordeaux, CELIA, UMR 5107, F- 33400 TALENCE
2.
Université de Bordeaux 1, 351, cours de la Libération, 33405 TALENCE Cedex

Received: May 31, 2014

Revised: March 31, 2015

Published: August 2015

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Abstract

In plasma physics domain, the electrons transport can be described from kinetic and hydrodynamical models. Both methods present disadvantages and thus cannot be considered in practical computations for Inertial Confinement Fusion (ICF). That is why we propose in this paper a new model which is intermediate between these two descriptions. More precisely, the derivation of such models is based on an angular closure in the phase space and retains only the energy of particles as a kinetic variable. The closure of the moment system is obtained from a minimum entropy principle. The resulting continuous model is proved to satisfy fundamental properties. Moreover the model is discretized w.r.t the energy variable and the semi-discretized scheme is shown to satisfy conservation properties and entropy decay.

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Mathematics Subject Classification: 35Q84, 35Q83, 65Z05.

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