Transport coefficients of plasmas and disparate mass binary gases

We investigate the dynamics of an inhomogeneous disparate mass binary gas or plasma at various scales. The scaling of the cross collision terms follows that derived in [11] in the homogeneous case, and is combined with a scaling of the transport terms of the Boltzmann (or Fokker-Planck) equation which is not the same for the light and heavy particle. Then, a Chapman-Enskog procedure is applied. At the heavy particle (or ion) kinetic scale, this approach leads to a system consisting of a kinetic equation for the heavy particle coupled with massless compressible Navier-Stokes equations for the light particle. At the hydrodynamic/diffusion scale, it leads to a system of coupled compressible Navier-Stokes equations, in which the light particle mass has again being set to zero. In particular, the obtained model is very close to the conventional hydrodynamic model of plasma physics.