Analytical Solutions for a Continuum Parallel-Plate Electrostatic Probe

摘要

The theory for the flow of a weakly ionized gas through a parallel-plate, continuum, electrostatic probe is developed. The flow is separated into three distinct regions: (a) the inviscid, neutral core where electron conduction maintains the continuity of current between the two plates; (b) the viscous, quasi-neutral boundary layer in which the charged particle flow is similar to ambipolar diffusion; and (c) the one-dimensional, collision dominated, space-charge sheath. Analytical solutions, matched at the boundary of each region, are presented for the electron temperature in equilibrium with the gas temperature and for the electron temperature constant at its free-stream value. A criterion is given which may be used to determine whether electron thermal equilibrium exists through the boundary layer. It is shown that the sheath voltage drop comprises approximately 60 percent of the total plate voltage drop. The results also show a very well defined saturation current for the double probe and that this current is controlled by ion diffusion through the boundary layer. Expressions are developed from the solutions which allow the use of experimental data to determine the free-stream electron density and temperature. (Author)