Nonequilibrium positive column revisited

The paper presents a fluid modeling of the nonequilibrium, dc-positive column of cylindrical gas discharges, by using a robust numerical code that describes the transport of electrons and positive ions, over a broad domain of pressures p≃100 mtorr-10 torr and discharge currents I_dc≃5-200 mA. 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, and adopts adequate boundary conditions for the particle fluxes at the wall. The electron transport parameters and rate coefficients are calculated using the local mean energy approximation in articulation with a two-term Boltzmann solver. For coherence, the electron transport equations and boundary conditions are deduced in the same two-term approximation framework, which induces some specific features when writing the mean energy transport equations. The model equations are integrated from the discharge axis to the wall, passing through the space-charge sheath and monitoring the charge separation within it. An eigenvalue formulation is adopted to find a univocal solution to the particle and energy balance equations. The model is solved for pure helium dc discharges, as an application example. The results obtained allow a systematic study of the discharge energy deposition and sheath formation, leading to a general criterion defining the transition region in pressure between nonlocal and local regimes.