Inhomogeneous model of an Ar–Hg direct current column discharge

Abstract

The inhomogeneous electron Boltzmann equation is solved for an Ar–Hg positive column direct current glow discharge with properties similar to the standard fluorescent lamp. The inhomogeneity arises from the ambipolar potential and requires the inclusion of the spatial gradient term in the Boltzmann equation. The electron kinetics is coupled to a collisional–radiative equilibrium model for various states of Ar and Hg subject to a reaction set with electron and heavy particle collisions. The axial electric field and space-charge potential are solved self-consistently. The calculated electron distribution function satisfies neither the local nor nonlocal approaches, but rather is found to be a function of both the electron energy and radial position. The radial dependence produces an energy flow from one part of the discharge to another, which results in nonuniform ultraviolet radiative power. Results are given for global properties of the discharge such as power per unit length and axial electric field, as well as spatially averaged quantities (densities, electron and gas temperatures, and emission powers) as a function of the wall temperature and the current. Extensive comparisons are presented with experimental data and previous homogeneous Boltzmann models of the discharge. The optimum current and fill pressures are determined and the general trends of varying the input parameters are established. There is general agreement between the present model and data, except that the calculated average electron density is larger than the measured values.