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hal-00185109, version 1

Kinetic Theory of Plasmas: Translational Energy

Benjamin Graille () 1, Thierry Magin (Auteur à contacter de préférence) 2, Marc Massot () 3

Mathematical Models and Methods in Applied Sciences 19, 04 (2009) 527-599

Résumé : In the present contribution, we derive from kinetic theory a unified fluid model for multicomponent plasmas by accounting for the electromagnetic field influence. We deal with a possible thermal nonequilibrium of the translational energy of the particles, neglecting their internal energy and the reactive collisions. Given the strong disparity of mass between the electrons and heavy particles, such as molecules, atoms, and ions, we conduct a dimensional analysis of the Boltzmann equation. We then generalize the Chapman-Enskog method, emphasizing the role of a multiscale perturbation parameter on the collisional operator, the streaming operator, and the collisional invariants of the Boltzmann equation. The system is examined at successive orders of approximation, each of which corresponding to a physical time scale. The multicomponent Navier-Stokes regime is reached for the heavy particles, which follow a hyperbolic scaling, and is coupled to first order drift-diffusion equations for the electrons, which follow a parabolic scaling. The transport coefficients exhibit an anisotropic behavior when the magnetic field is strong enough. We also give a complete description of the Kolesnikov effect, i.e., the crossed contributions to the mass and energy transport fluxes coupling the electrons and heavy particles. Finally, the first and second principles of thermodynamics are proved to be satisfied by deriving a total energy equation and an entropy equation. Moreover, the system of equations is shown to be conservative and the purely convective system hyperbolic, thus leading to a well-defined structure.

  • 1 :  Laboratoire de Mathématiques d'Orsay (LM-Orsay)
  • CNRS : UMR8628 – Université Paris XI - Paris Sud
  • 2 :  Center for Turbulence Research (CTR)
  • Stanford University
  • 3 :  Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C)
  • CNRS : UPR288 – Ecole Centrale Paris
  • Domaine : Physique/Physique/Physique des plasmas
    Physique/Mécanique/Mécanique des fluides
    Sciences de l'ingénieur/Mécanique/Mécanique des fluides
    Mathématiques/Equations aux dérivées partielles
    Sciences de l'ingénieur/Milieux fluides et réactifs
    Sciences de l'ingénieur/Plasmas
  • Mots-clés : Kinetic theory – plasmas in thermal nonequilibrium – conservation equations – multicomponent transport properties.
  • Commentaire : Preprint of an article accepted for publication in Mathematical Models and Methods in Applied Sciences © [2007] [copyright World Scientific Publishing Company] [http://www.worldscinet.com/m3as/m3as.shtml] Subject of a NASA Technical Memorandum NASA/TM—2008–214578 - June 2008
 
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  • Soumis le : Lundi 5 Novembre 2007, 14:02:32
  • Dernière modification le : Mardi 26 Mai 2009, 14:52:24