A nonlocal transport model of the self-consistent potential distribution in a plasma sheath with charge transfer collisions.

The relationship between the potential distribution, ion flux and thickness of a plasma sheath is given by the solution to Poisson's equation. The space charge term in Poisson's equation depends on the ion drift velocity, which is determined by collision processes and the potential distribution. A functional relationship between the drift velocity, the potential distribution and the collision cross section was recently derived for charge transfer collisions, and is used here to solve Poisson's equation self-consistently. The results may be used to estimate the ion flux from measurements of the sheath thickness and voltage drop, or to estimate the sheath thickness from measurements of the ion flux and voltage drop. We also present an excellent one parameter approximation to the numerically determined potential distribution.