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electrons and positive ions with particle densities n e and $_{n$_{i}$}$: 

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which are coupled to Poisson’s equation for the electric field in electrostatic approximation: 

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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 

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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 

