Approximate sheath solutions for a planar plasma anode

Solutions to the anode sheath problem are studied for the case where the electron temperature and plasma temperature are constant and equal. The planar geometry description of steady, low-temperature collisional plasmas permits certain simplifications to the species continuity equations whereby a single, highly nonlinear equation is obtained for the entire region disturbed by the electrode. This equation is given in terms of the electric field and a variable representing the currents. The formulation includes charged-particle production with a net current flow. Solutions are generated with a nontrivial analytic expression for the electric field. Results are described for nitrogen at moderately high densities, which at sufficiently flow currents are realistic for electron-impact ionization and two-body recombination. This case is completely described by two nondimensional groupings, which are sufficient to define the sheath and ambipolar regions. The constants A and a are evaluated using information for nitrogen at 6000 K, corresponding to degrees of ionization above 10^-6. Other practical discharge gases are also represented in the example