Sheath-Convection Effects with Flush-Mounted Electrostatic Probes

Abstract

Theoretical expressions are derived for the ion current to a planar flush-mounted probe which arises from the convection of ions from a moving plasma into the probe sheath. The two situations considered are those where the sheath is either very large or is small compared with the boundary layer. It is found that sheath effects, with an accompanying lack of true current saturation with increasing probe bias, can be expected to intrude when the parameter REα2χ2 > (X/l)1/4. (RE = electric Reynold's number, α = ratio of Debye length to probe length [X], χ = potential of probe normalized with respect to the electron energy, and l = the distance of the probe from the leading edge of the surface into which it is mounted.) For values of REα2χ2(l/X)2 which exceed unity, the formula[Formula: see text](where ne = plasma electron density, u∞ = free stream flow velocity, V = probe bias, μ∞ = free stream ion mobility, e = electronic charge, and ε0 = permittivity of free space) is derived. At lower values of REα2χ2(l/X)2 theoretical considerations which take compression and cooling effects into account show that the above relation should still be approximately correct down to values of [Formula: see text]. The relation shows good agreement with the recent results presented by Scharfman and Bredfeldt under conditions where they report the conventional diffusion theory to be in error by up to one order of magnitude, and moreover to predict an incorrect variation of current with electron density and probe bias.