First-order effects of production on the continuum theory of spherical electrostatic probes

Abstract

The analysis of spherical Langmuir probes that are immersed in an infinite, homogeneous, slightly ionized, collision-dominated plasma is given to first order in the smallness of a pa- rameter characterizing the effects of ionization and recombination. The treatment is given as a double limit: mean free path _JVo, T_/T_}_, D_|_/D_, and the production parameter, where D is diffusion coefficient, T is temperature^ and NQ is the undisturbed ion or electron density. The first-order effects of ionization and recombination are also discussed. It is found for T_/T+ = 1 that, at negative probe potentials, the normalized ion current to the probe is increased and the electron current decreased. At positive probe potentials, on the other hand, the ion current to the probe is de- creased and the electron current increased by the effect of production. For T_/T+ > 1, the same effect is observed for negative probe potentials, but for positive probe potentials no such gen- eral statement can be made. For a 10% change in the production parameter, for example, we find that the relative change in the currents is at most slightly more than 10% (for fixed probe potential).