Diffusion regime of electron-electron collisions in weakly ionized plasmas

We consider weakly ionized plasma where the frequent elastic scattering of electrons on neutrals changes the character of electron-electron collisions entirely. This comes into play when the frequency of the electron -- neutral collisions is so large that the corresponding electron mean-free path is shorter than the closest distance between the colliding electrons. In this extreme case, the electron energy equilibration differs considerably from that in fully ionized plasma. A crucial role is now played by diffusion of electrons caused by their scattering on neutrals, and we demonstrate how a proper account of this diffusion allows one to estimate the characteristic energy equilibration time for electrons. We also present a rigorous derivation of the kinetic equation for electrons via Bogolyubov's approach based on Liouville equations for multi-particle distribution functions.