On the ambipolar diffusion and other asymptotic limits of weakly ionized plasma flows

This paper reviews several different models of weakly ionized plasma flows, where charged particles are scattered in a background flow of neutral particles. A multispecies diffusion model is derived from either a kinetic model or a multifluid model (which is the Maxwellian closure of the kinetic model). This derivation is purely formal (in the sense that only the Hilbert or Chapman-Enskog expansions are established). An even simpler model, the so-called ambipolar diffusion model is derived from the multispecies diffusion model. This latter derivation is based on energy estimates and on a form of maximum principle which is established by writing the multispecies diffusion system in terms of the so-called Slotboom variables.