The ion flux from a thermal plasma to a surface

On the basis of a continuum multi-fluid description of a plasma, a theory is developed of an ionization layer between a plasma in ionization (Saha) equilibrium and the space-charge sheath near a surface of a cathode or of an insulating wall. The crucial parameter determining the character of the solution is the ratio of the recombination length to the mean free path ion-neutral species; if this ratio is large, then the developed theory is consistent with a conventional diffusion approach. Numerical and asymptotic solutions of a stated problem are obtained. It is found that the problem is solvable only if the degree of ionization does not exceed a certain value, which varies between approximately 0.6 and 1. Beyond this value, the equation of the pressure balance cannot be satisfied and the plasma as a whole in the considered layer cannot stay in static equilibrium. A simple approximate formula for the ion flux is obtained.