Radial distributions of charged-particle densities and electric field strength in the positive column

A model is presented for the radial distribution of ion and electron densities and electric field strength in the positive column of a dc discharge for a plasma consisting of a singly charged positive-ion species, electrons, and neutral species. The set of equations involved consists of the particle- and momentum-conservation equations for the ions and electrons and Poisson’s equation. Utilizing this single set of equations and appropriate assumptions, the model has been solved, through suitable numerical techniques, for various gas pressures $p_0$ and tube radii R. These calculations show the development of both the electric field in the ‘‘bulk’’ of the positive column and the sheath field ‘‘near’’ the discharge wall. The results also demonstrate the existence of a nonzero difference between the ion and electron densities at the discharge axis, with an increase in this difference for decreasing $p_0$R. The importance of including the various terms in the momentum-conservation equations of both the ions and electrons when solving the model has been investigated. The model can be used to calculate the radial properties of positive-column discharges for conditions ranging from the ambipolar diffusion limit to the free-diffusion limit.