Modelling finite cylinder electronegative discharges

A model for a finite length cylindrical electronegative (EN) plasma is constructed by obtaining an approximate solution when negative ions exist over the entire plasma, but with ion flux to the walls dominating internal recombination flux. The profiles obtained in this manner are useful for making calculations even when the recombination flux competes with the diffusion flux for ion loss. The result is that there is an approximately parabolic profile in the smaller dimension (radius or axial length) with a flat central region and a similar edge profile in the larger dimension. The results are extended to include plasmas in which the electronegative region does not occupy the entire cylinder by introducing a single length scale that defines a smaller EN cylinder embedded in the larger plasma. Single types of positively and negatively charged ions and electrons are assumed to be the principal charged species. The plasma thus formed is embedded in a full model of an attaching feedstock gas with all relevant species and reaction rates included. The complete model can be considered as a generalized global model which includes one additional spatial parameter and one additional equation. The resulting equations are readily solved as in previous global models. The results are compared with experiments in an oxygen discharge, obtaining reasonably good agreement for the measurable parameters.