Highly negative electric probes in a flowing continuum plasma

Abstract

The general problem of an electric probe in a flowing continuum plasma is solved using perturbation theory, together with the method of matched asymptotic expansions. The small parameter used is the inverse of the dimensionless probe potential. The lowest order results yield a quasineutral region in which the ion concentration is constant, and an ion sheath region in which the electron density is zero. The electric potential and the electric field are zero at the edge of the sheath region. The remaining problem consists of solving the sheath equations. A solution is found for spherical and cylindrical probes in the case that the sheath is thin compared with the radius of the probe, but thick compared with the viscous boundary layer. For sheaths that are not thin compared with the probe radius, an iterative method of solution is proposed. The results are presented as a one-parameter family of curves. It is shown that there exists a limiting current, which obtains when the ion density around the probe remains essentially equal to the freestream value. The theoretical results obtained are in fair agreement with available experimental data. Attention is given to other theoretical results, as well as to various improvements neededmore » for further progress.« less