A self-consistent model of the cathode-fall of glow discharges

The strong spatial variation of the electric field intensity in the vicinity of the cathode of a gas discharge requires the use of microscopic methods to describe the non-equilibrium behavior of the electron dynamics in this region. The authors developed a model of the cathode fall using a one-dimensional Monte-Carlo code, which allows one to obtain the spatial distribution of rate coefficients, and the electron drift velocity for a given electric field intensity in the cathode-fall. The results of this calculation are used to find the charged particle density distribution in this region and consequently, by means of Poisson's equation, the electric field intensity, which generally is different from the initially assumed one. In order to obtain a self-consistent solution for the cathode-fall, the described computational process is repeated until a sufficient conformity between subsequently calculated electric field profiles is reached. This iterative procedure gives a solution for the thickness of the cathode fall layer, the electric field profile in this boundary layer, and the particle density and current density distributions in the discharge