Two-Fluid Theory of the Positive Column of a Gas Discharge

Abstract

The transition from inertia-limited flow to mobility-limited flow of ions to the walls of the positive column of a planar gas discharge is analyzed from a hydrodynamic point of view. The analysis is based on the assumption that the electrons and ions in the positive column behave as inviscid fluids with different temperatures. The resultant formulation is valid for gas pressures from the free-fall limit to the continuum limit, including the high-field sheaths at the walls as well as the almost field-free plasma at the center of the discharge. Numerical results for the characteristic value, wall field, wall potential, and ion energy at the wall are given for many different pressures and central Debye lengths, and it is shown that the results are identical to those of Allis and Rose in the continuum limit and very close to those of Self in the free-fall limit.