A continuum theory of electrostatic probes in a slightly ionized gas

A systematic continuum theory based on the method of matched asymptotic expansions is developed to deal with electrostatic probes in a slightly ionized gas. To the first approximation of thin space charge sheath, the sheath solution is shown to become common to the geometries considered, i.e. plane, cylindrically and spherically symmetric probe surfaces: the main interest lies in the last geometry. The second-order approximation strongly affects the last two geometries. Detailed numerical calculations are presented to illustrate the effects of a finite ratio of the Debye length to the characteristic body dimension; including a contraction of the sheath region and enhancement of the electric field from the asymptotic (first-order approximation) values.