The transition from Townsend to glow discharge is investigated numerically in one space dimension in full parameter space within the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons (α process), secondary electron emission from the cathode (γ process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the current that fits our numerical data very well. Depending on the two determining parameters γ 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 unexpected intermediate "mixed" behavior. Our work shows the same qualitative dependence of U = U (I, pd) for fixed γ as the old experiments by Pokrovskaya-Soboleva and Klyarfeld. Furthermore, the analysis lays the basis for understanding the complex spatio-temporal patterns in short planar barrier discharge systems.52. 80.-s, 05.45.-a, 51.50.+v, 47.54.+r

A short gas-discharge layer sandwiched with a semiconductor layer between planar electrodes shows a variety of spatiotemporal patterns. We focus on the spontaneous temporal oscillations that occur while a dc voltage is applied and while the system stays spatially homogeneous; the results for these oscillations apply equally to a planar discharge in series with any resistor with capacitance. We define the minimal model, identify its independent dimensionless parameters, and then present the results of the full time-dependent numerical solutions of the model as well as of a linear stability analysis of the stationary state. Full numerical solutions and the results of the stability analysis agree very well. The stability analysis is then used for calculating bifurcation diagrams. We find semiquantitative agreement with experiment for the diagram of bifurcations from stationary to oscillating solutions as well as for amplitude and frequency of the developing limit cycle oscillations.

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A system very similar to a dielectric barrier discharge, but with a simple stationary DC voltage, can be realized by sandwiching a gas discharge and a high-ohmic semiconductor layer between two planar electrodes. In experiments this system forms spatiotemporal and temporal patterns spontaneously, quite similarly to e.g., Rayleigh-Bénard convection. Here it is modeled with a simple discharge model with space charge effects, and the semiconductor is approximated as a linear conductor. In previous work, this model has reproduced the phase transition from homogeneous stationary to homogeneous oscillating states semiquantitatively. In the present work, the formation of spatial patterns is investigated through linear stability analysis and through numerical simulations of the initial value problem; the methods agree well. They show the onset of spatiotemporal patterns for high semiconductor resistance. The parameter dependence of temporal or spatiotemporal pattern formation is discussed in detail.