Kinetic Theory of Plasmas
Abstract
In this work, we propose to derive the multicomponent plasma conservation equations of mass, momentum, and energy, as well as the expressions for the associated multicomponent transport fluxes and coefficients. The multicomponent Navier-Stokes regime is reached for the heavy particles and is coupled to first-order drift-diffusion equations for the electrons. We deal here with first-order equations for electrons, thus one order beyond the expansion commonly investigated in the literature. The derivation relies on kinetic theory and is based on the ansatz that the particles of the plasma are inert and only possess translational degrees of freedom. The electromagnetic field influence is accounted for. In Section 2, we introduce the Boltzmann equation, derive the H-theorem and the Maxwell transfer equations. In Section 3, we express the Boltzmann equation in the heavy-particle velocity frame. This step is essential to establish a formalism where the electrons follow the bulk movement of the plasma. Then, we define the reference quantities of the system in order to derive the scaling of the Boltzmann equation from a dimensional analysis. The multiscale aspect occurs in both the streaming operator and collision operator of the Boltzmann equation. We use a Chapman-Enskog method to derive macroscopic conservation equations. The system is examined at successive orders of approximation, each corresponding to a physical time scale. For that purpose, scalar products and linearized collision operators are introduced. The global expressions for the macroscopic fluid equations are then provided up to Navier-Stokes equations for the heavy particles and first-order drift-diffusion equations for the electrons.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 2009
- Accession Number
- ADA567760
Entities
People
- B. Graille
- M. Massot
- T. E. Magin