Modeling of low-pressure gas discharges

In the first part of this paper, the ionization-balance and excitation-balance equations for low-pressure self-sustained rare-gas discharges are used to derive the scaling relationship that
E/P
is a constant for a constant
I P^{3}R^{2}
product. Comparison with experiment shows that this is a fair to good approximation for argon, neon, and helium discharges over a wide range of conditions. In the second part, the inclusion of two electron energy-conservation equations, based on the Vriens two-temperature model for the electron-energy distribution function, provides a simple and accurate method of predicting discharge parameters from first principles. Predicted values of
E/P
and excited-state density as a function of electron density and current in helium show very good agreement with experiment.