On the accuracy and limitations of fluid models of the cathode region of dc glow discharges

This paper compares the performance and limitations of different models of the cathode region of cold-cathode low-pressure dc glow discharges: (i) we review known modelling approaches, (ii) develop our own simulation codes based on these approaches, (iii) perform calculations using these codes for reference sets of discharge conditions, which allows a critical comparison of the models and (iv) for a further check of the simulation results we carry out Langmuir probe measurements of electron densities in abnormal Ar glow discharges. The theoretical approaches include fluid models both neglecting and including the electron energy balance equation, as well as hybrid models, which combine the fluid treatment of slow plasma species with the kinetic simulation of fast electrons. We also test the effect of the choice of the ionization source term in fluid models. We find that the electron densities calculated from the fluid models are far (several orders of magnitude) below the experimental values even if the electron energy equation is considered in the calculations. This weakness of fluid models clearly points out the importance of an accurate calculation of the ionization source term, which can only be accomplished by a kinetic approach under the conditions of highly nonlocal electron transport in the cathode region of glow discharges. In hybrid models Monte Carlo simulation is used for this purpose, and indeed, this approach gives electron densities comparable to our experimental data.