Diffusion regime of electron-electron collisions in weakly ionized plasmas

We consider weakly ionized plasma where frequent elastic scattering of electrons on neutrals changes the individual acts and the rate of electron–electron collisions significantly. In this case, the kinetics of electron thermalization is very different from that in fully ionized plasma. The colliding electrons do not move freely. They, instead, diffuse because of fast scattering on neutrals. We demonstrate how a proper account of this diffusion enables one to estimate the characteristic time of electron thermalization. We also present a rigorous derivation of the kinetic equation for electrons by using Bogolyubov's method based on Liouville equations for multi-particle distribution functions.