Fluid modelling of the positive column of direct-current glow discharges

This paper presents a tutorial on the fluid modelling of the positive column of direct-current cylindrical glow discharges. The model writes the continuity and momentum-transfer equations for electrons and ions, coupled with Poisson's equation and the electron mean energy transport equations. The model is solved for helium at pressures p ≃ 0.1–10 Torr, gas temperature T g = 500 K, discharge currents I dc = 5–200 mA, and tube radius R = 1 cm. The electron transport parameters and rate coefficients are calculated using the local mean energy approximation in articulation with a two-term Boltzmann solver. Model equations are integrated from the discharge axis to the wall, passing through the space-charge sheath and monitoring the charge separation within it. The results obtained allow a systematic characterization of discharge energy deposition and space-charge sheath formation, as a function of pressure and axial current. A general good agreement is found between model results and experimental measurements available in the literature.