Asymptotic Theory of Spherical Electrostatic Probes in a Slightly Ionized, Collision-Dominated Gas

The problem of an electrostatic probe in a dense, slightly ionized gas is treated by techniques of asymptotic analysis. In particular, the asymptotic limits ρp = rp/λd → ∞ and ε = T+/T− → 0 are treated in considerable detail. (rp, λd, T−, T+ are probe radius, Debye length, electron, and ion temperature, respectively.) Sample integral curves for electrostatic potential, ion and electron density are given. Probe characteristic curves for three values of ε (finite and small) and ρp (large) are also given. It is noted that these characteristics do not saturate for large probe potential because the influence of the probe is felt to very great distances from the probe; the shielding due to the space-charge sheath is incomplete.