Nonequilibrium Continuum Theory of Spherical Electrostatic Probes at Large Debye Number

Abstract

Continuum theory is used to describe the steady spherically symmetric state of an unbounded expanse of slightly ionized gas about a perfectly catalytic conductor. Far from the sphere the gas is in chemical equilibrium, but at finite distances finite-rate ionization and recombination may occur according to a direct one-step reversible reaction in which either a neutral or an electron (the negative-charge carrier) participates as the third body in the recombination process. The limit of large Debye number appropriate to the use of small electrostatic probes in slightly ionized gases (where the Debye number is the ratio of the Debye length to the probe radius) is examined. In this limit the case of nearly frozen chemistry near the sphere is of greatest practical interest; modification of current collected from the value given by Su and Lam, owing to incipient reaction effects, is determined for negative potential bias applied at the probe.