Wall emission dominated discharge channel

Abstract

The diffusion of ions and electron through a uniform neutral gas was treated with complete wall emission-absorption boundary conditions. Volumetric ionization and recombination processes were ignored. In the limit of the small ratio of Debye length to channel width (ε→0), the problem splits into three regions: anode sheath, cathode sheath, and quasi-neutral region. The solution is obtained in closed form in each of the three regions and matched in the overlap domains. The unusual feature of this problem is that the boundary conditions are coupled to the solution in a transcendental manner requiring iteration in order to achieve a consistent solution. The degree of surface coverage is an important parameter in determining emission and absorption rates. The results show that ion densities are elevated (above quasi-neutral levels) in the anode and cathode sheaths tending to enhance electron emission. The quasi-neutral density at each electrode is the geometric mean of the true charged particle densities at the boundary. Electrical current between the electrodes increases linearly, then saturates sharply with increasing voltage between the electrodes.