7 research outputs found
Kinetic Theory of Plasmas: Translational Energy
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