Flows of a Weakly Ionized Gas between Parallel Cold Walls

Abstract

Ambipolar diffusion between parallel cold walls in the weakly ionized gas which flows in the direction parallel to walls is investigated theoretically. The whole region is divided into three ones: the linear, non-linear and sheath regions where the linear diffusion equations, the continuum equations contaning inertia terms and the collisionless equations are used respectively. Solutions are patched and the Bohm's criterion is used to match the nonlinear and sheath regions. The thickness of the non-linear region is O (α 1/4 ). The density of electrons and ions decreases to a fraction of O (α 1/2 ) at the sheath edge. And the potential drop between the center and the walls is \(O\left(-\frac{1}{2}\frac{kT_{e}}{e}\ln\alpha^{-1}\right)\). (α∼ l i 2 / L 2 , l i is the mean free path of ions and 2 L is the distance between walls).