KINETIC THEORY OF PLASMAS: TRANSLATIONAL ENERGY

Abstract

In the present study, 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 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 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, emphasizing the role of the 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 corresponding to a physical timescale. 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 operators 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 thermodynamics are proved to be satisfied by deriving a total energy equation and an entropy equation. Moreover, the purely convective system of equations is shown to be hyperbolic.