Continuum theory of spherical electrostatic probes in a stationary, moderately ionized plasma

Abstract

A theory is developed for spherical electrostatic probes in a stationary, collision-dominated plasma in which the ratio of charge-charge to charge-neutral collision frequencies may range between zero and unity. The former limit corresponds to the usual “weakly ionized” condition of earlier probe analyses, while for non-zero values of this ratio, transport coefficients must be assumed to vary with position in the plasma. Electron temperature variation is allowed for through the consideration of electron energy conservation and transport. Quasilinearization is used to solve the equations numerically, and an orthonormalization technique is developed to overcome the “ill-conditioning” problem which often occurs in the solution of linear two-point boundary value problems. Plasma property profiles in the vicinity of the probe, for several values of collision frequency ratio and a wide range of probe potentials, are investigated. A few representative current-voltage characteristics are calculated. The effects of including variable transport coefficients in the formulation are discussed. It is found that including charge-charge collisions increases the effective positive bias of an electron-attracting probe, and of a probe at plasma potential, and more effectively shields an electron-retarding probe of low potential. For more strongly retarding probes, this trend reverses and shielding is decreased (although very slightly). For strongly retarding probes, there is no apparent difference between the behavior of weakly and moderately ionized gases. A systematic procedure is developed by which experimentally obtained probe characteristics may be interpreted.