Self-consistent model for the nonequilibrium cathode region

We present a theoretical study and a numerical simulation of the formation and development of the cathode region (cathode-fall and negative-glow ones) in CO₂ and N₂ discharges from the inception of the discharge to its stationary state. The model is a self-consistent one: the distribution of the electric field is found from the charge carriers and the hydrodynamic moment equations (density, velocity, energy) are solved by a sophisticated flux-corrected transport method. The ionization and excitation source terms are calculated using an electron-energy distribution function which takes into account the electron-density gradient and the local electric field. The results show that this choice is more realistic in representing the spatiotemporal evolution of the cathode region. Our theoretical results are compared with the experimental ones obtained by other authors and a good agreement is observed concerning the current intensity and the spatial distribution of light in the cathode region in N₂.