Unipolar Flow of Charge Carriers in a Dense Gas with and without Consideration of Diffusion

Abstract

Abstract The basic equations for the unipolar, stationary, one-dimensional flow of charge carriers in a dense gas, characterized by mobility and diffusion coefficient, can be integrated numerically. The discharge gap generally has a finite length; as far as in the end cross-section either density of particles and intensity of electric field tend towards infinity, or the density of particles becomes zero. Which of these two cases occurs depends on the current density of the discharge and on the intensity of the electric field in the initial cross-section. The notions mobility and diffusion coefficient will lose their applicability close to a pole like singularity as well as in a "dilution to zero", so that from a certain cross-section onwards the continuation of discharge is determined by modified equations. It is shown that in case the diffusion component of the current density is neglected, the integrals of the basic equations change fundamentally. Neglecting the diffusion is inadmissible. This is finally a consequence of the relationship between mobility and diffusion coefficient, as expressed by the Einstein-relation.