Non-local model of hollow cathode and glow discharge - theory calculations and experiment comparison

General form of the non-local equation for an ionization source in glow discharge and hollow cathode 3D-simulation is formulated. It is a fundamental equation in a hollow cathode theory, which allows to make up a complete set of field equations for a self-consistent problem in a stationary glow discharge and a hollow cathode. It enables to describe adequately the region of negative glow and the hollow cathode effect. Here you can see first attempts to compare calculation results of electrical dependences (pressure - voltage) and experimental data, - under conditions of gradual appearance of the hollow cathode effect.Comment: 4 pages, 2 figure

Transition from Townsend to glow discharge: subcritical, mixed or supercritical

The full parameter space of the transition from Townsend to glow discharge is investigated numerically in one space dimension in the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons ($\alpha$ process), secondary electron emission from the cathode ($\gamma$ process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the total current that fits our numerical data very well. Depending on $\gamma$ and system size pd, the transition from Townsend to glow discharge can show the textbook subcritical behavior, but for smaller values of pd, we also find supercritical or some intermediate ``mixed'' behavior. The analysis in particular lays the basis for understanding the complex spatio-temporal patterns in planar barrier discharge systems.Comment: 12 pages, 10 figures, submitted to Phys. Rev.

A smooth transition approach between the Vlasov-Poisson and the Euler-Poisson system

In the present work, we extend a novel numerical algorithm which was constructed for the solution of gas dynamics problems \cite{degond1, degond3} to the solution of the Vlasov-Poisson equation in combination with the Euler-Poisson system. The new method is designed for computing the solution of plasma problems which require a localized resolution of the kinetic scale. The main idea relies on the introduction of buffer zones which realize a smooth transition between the kinetic and the fluid regions. The buffer zone is drawn around the kinetic regions by introducing a cut-off function. We numerically validate the presented method and demonstrate its performances