1. Kinetic theory of plasmas
- Author
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Thierry Magin, Marc Massot, Benjamin Graille, Center for Turbulence Research [Stanford] (CTR), Stanford University, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, Papers presented during the AVT-162 RTO AVT/VKI Lecture Series held at the von Karman Institute, Rhode St. Genèse, Belgium., CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris Saclay (COmUE), and The authors acknowledge support from two scientific departments of CNRS (French Center for Scientific Research): MPPU (Mathématiques, Physique, Planète et Univers) and ST2I (Sciences et Technologies de l'Information et de l'Ingénierie), through a 2007-2008 PEPS project entitled: ``Analyse et simulation de problèmes multi-échelles : applications aux plasmas froids, à la combustion et aux écoulements diphasiques'.
- Subjects
Electromagnetic field ,Physics ,plasmas in thermal nonequilibrium ,Internal energy ,82C40, 76X05, 41A60 ,[SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment ,[SPI.PLASMA]Engineering Sciences [physics]/Plasmas ,Non-equilibrium thermodynamics ,Electron ,01 natural sciences ,Boltzmann equation ,[SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph] ,010305 fluids & plasmas ,Magnetic field ,Classical mechanics ,[PHYS.PHYS.PHYS-PLASM-PH]Physics [physics]/Physics [physics]/Plasma Physics [physics.plasm-ph] ,0103 physical sciences ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,conservation equations ,multicomponent transport properties ,[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] ,Kinetic theory ,010306 general physics ,Boltzmann's entropy formula ,Scaling - Abstract
International audience; In the present study, we derive from kinetic theory a unified fluid model for multi- component 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 reactive collisions. Given the strong disparity of mass between the electrons and heavy particles, such as molecules, atoms, and ions, we conduct a dimen- sional analysis of the Boltzmann equation and introduce a scaling based on a multiscale perturbation parameter equal to the square root of the ratio of the electron mass to a characteristic heavy-particle mass. We then generalize the Chapman-Enskog method, em- phasizing the role of the perturbation parameter on the collisional operator, the streaming operator, and the collisional invariants of the Boltzmann equation. The system is exam- ined at successive orders of approximation, each corresponding to a physical time scale. At the highest approximation order investigated, the multicomponent Navier-Stokes regime is reached for the heavy particles and is coupled to first-order drift-diffusion equations for the electrons. The transport coefficients are then calculated in terms of bracket opera- tors whose mathematical structure allows for positivity properties to be determined and Onsager's reciprocal relations to hold. 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 laws of ther- modynamics are proved to be satisfied by deriving a total energy equation and an entropy equation.