Nonisothermal Theory of an Electrostatic Probe in a Weakly Ionized Gas

The isothermal assumption for electrons is removed from the continuum theory of the electrostatic probe. Asymptotic analyses based upon small Debye length are developed for both cold and warm ions with an appropriate electron energy equation. The structure of the asymptotic expansion is essentially changed from that of the isothermal theory. In particular, the current-voltage characteristic is expressed as a series in which the leading term, obtained under quasineutral approximation, is of the order of unity and the subsequent terms are small in the asymptotic sense. The results may be used to explain the discrepancies between the isothermal theory and some experimental results of Little and Waymouth.