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

Abstract

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.

Two-dimensional hybrid model for a glow discharge: comparison with fluid and kinetic (particle) models, reliability and accuracy

“…After all fast electrons within MCC cycle have escaped from the volume or converted to the slow electrons, the ionization events data is interpolated into the grid points in order to determine the ionization rate profile. The ionization source profile is weighted to the actual value using the equation [11,17] S i,e = j (1 + 1/γ)∆x…”

“…L x = 1 cm and L y = 1 cm. We used constant transport coefficient for slow electrons, µ e = 3 × 10 5 cm 2 s −1 V and D e = µ e T e , where T e = 1 eV [17]. Ions are assumed to be in thermal equilibrium with background gas, T i = T g = 0.025 eV .…”

“…We compared our 1D simulation results (electron density, electric field and ionization source profile) in figure 2 with results of Ref. [17]. For electrons and ions zero density boundary conditions are used on the anode, zero gradient for ions and secondary electron emission condition for electrons on the cathode.…”

Particle in Cell/Monte Carlo Collision Method for Simulation of RF Glow Discharges: Effect of Super Particle Weighting

“…In such cases, it is useful to apply the kinetic model, which may involve either direct solution of the kinetic Boltzmann equation or particle method. Finally, in a hybrid model, a combination of particle and fluid models, slow electrons and ions are treated as fluids, whereas fast electrons are described by the particle method, employing Monte Carlo method for collisions [6]. This method has speed advantage of fluid and accuracy of particle methods.…”

Uniqueness Theorem for the Non-Local Ionization Source in Glow Discharge and Hollow Cathode

“…In a hybrid model ions and slow electrons are described in terms of drift and diffusion, but fast electrons are described with the aid of the boltzmann equations or simulated with MonteCarlo methods [6][7][8]. It was shown [9] that hybrid models describe a density of plasma in a glow discharge much better, though they are more complicated.…”