Theory of a spherical electrostatic probe in a continuum plasma: Analytical models

A simple physical model of the charge distribution surrounding a biased spherical probe in a quiescent plasma, suggested by the theory of Su and Lam, is used to rederive the probe current-voltage characteristic. The result is compared with that of a slightly different version due to Kiel and with the exact numerical results of Baum and Chapkis. It is shown that if the ratio of the probe radius to the Debye length of the plasma is greater than or of the order of unity, the model calculation is in excellent agreement with the exact results when the dimensionless probe voltage φ*p,=‖eφp/kT‖ in standard notation, is greater than 10, for both thick and thin sheaths. The comparison also provides an assessment of the importance of various additional validity criteria encountered in analytical treatments of the problem.