Figure 1: A cross section of a planar discharge cell: it consist of a metal anode, a gas layer, a high-ohmic cathode, and another metal contact. The subscripts g and s refer to the gas and semiconductor regions. electrons and positive ions with particle densities n e and $_{n$_{i}$}$: which are coupled to Poisson’s equation for the electric field in electrostatic approximation: Here, Φ is the electric potential, E is the electric field in the gas discharge, e is the elementary charge, and ε 0 is the dielectric constant. The vector fields Γ$_{e}$ and Γ i are the particle flux densities, that in simplest approximation are described by drift only. (In general, particle diffusion D$_{e,i}$ ∇ n$_{e,i}$ could be included.) The drift velocities are assumed to depend linearly on the local electric field with mobilities µ$_{e}$ ≫ $_{µ$_{i}$}$: hence the total electric current in the discharge is Two types of ionization processes are taken into account: the α process of electron impact ionization in the bulk of the gas, and the γ process of electron emission by ion impact onto the cathode. In a local field approximation, the α process determines the source terms in the continuity equations (1.5) and ∂$_{t}$n e + ∇ · Γ$_{e}$ = S$_{e}$ , (1.5) ∂$_{t}$n$_{i}$ + ∇ · Γ i = S$_{i}$ , (1.6) ∇ · E = e ε 0 ( n$_{i}$ − n e ) , E = −∇ Φ . (1.7) Γ$_{e}$ = − µ e n $_{e}$E , Γ i = µ$_{i}$n$_{i}$ E , (1.8) J = ϵ 0 ∂$_{t}$ E + e ( Γ i − Γ$_{e}$ ) = ϵ 0 ∂$_{t}$ E + e ( µ$_{i}$n$_{i}$ + µ e n e ) E . (1.9) 5