Theory of Ion Collection by a Stationary Electrostatic Probe

Abstract

The operation of a spherical electrostatic probe in a weakly ionized, collision‐dominated gas, such as the D region of the ionosphere, is examined theoretically. A plasma consisting of one type of positive ion, one type of negative ion (or electrons), and a neutral gas is assumed to surround the (stationary) probe. The equations governing the collection of positive ions by a negatively biased probe are developed from a continuum theory after Su and Lam (1963) and are solved numerically. For highly negative probes a method is found to solve the equations in their exact form. Current‐voltage characteristics for probes of moderate size in comparison with the Debye length are presented graphically. It is shown that the current to the probe varies approximately as the 0.6 power of the probe voltage, which varies slowly with the ratio of probe radius to Debye length. The current also varies approximately as the 0.75 power of the positive ion concentration for D‐region conditions. These conclusions show the importance of including space charge in the theory and agree rather well with those of Balmain's (1966) simplified analysis. A considerable improvement is obtained over the results of Su and Lam for the regime of interest.