Kinetic theory of low-frequency cross-field instability in a weakly ionized plasma. I

A consistent kinetic theory is developed for the description of electrons under conditions of a low-frequency two-stream E×B instability in collisionally dominated, weakly ionized plasmas. Starting from the Boltzmann collision integral, a simplified kinetic equation for the electron distribution function has been derived, which takes into account strong pitch-angle scattering of electrons by neutrals, velocity dependence of the electron–neutral collision frequency, etc. Linearized equations describing small oscillations of the electron distribution function and ion density are presented. For the asymptotic case of short waves, the dispersion relation of the E×B instability has been obtained and analyzed under conditions typical for the lower ionosphere. Under certain conditions, the rigorous kinetic consideration yields substantial changes in results compared to previous theories. The general approach may be applied to other linear and nonlinear low-frequency processes in a weakly ionized plasma.