Analytical formulation of ionization source term for discharge models in argon, helium, nitrogen, and silane

Simple analytical representations of the ionization source terms in argon, helium, nitrogen, and silane dc glow discharges for steady-state and quasisteady-state conditions are presented. These analytical forms express well the highly nonequilibrium nature of the ionization in the cathode fall and negative glow regions which cannot be described by a Townsend ionization coefficient depending on the local value of the reduced electric field. These source terms can be easily incorporated into fluid models of gas discharges.