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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 ( process), secondary electron emission from
the cathode ( 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 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.