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.

Evaluating competing perspectives towards undeclared work: some lessons from Bulgaria

When explaining and tackling the undeclared economy in Central and Eastern Europe, participants have been conventionally viewed as rational economic actors. They engage in undeclared work when the benefits outweigh the costs. Participation is thus deterred by increasing the sanctions and/or probability of being caught. Recently, however, an alternative social actor approach has emerged which views participants as engaging in undeclared work when their norms, values and beliefs (i.e., citizen morale) do not align with the laws and regulations (i.e., state morale). Here, therefore, initiatives to develop greater symmetry between civic and state morale are pursued. To evaluate the validity and effectiveness of these competing explanations and policy approaches, 2,004 face-to-face interviews conducted in Bulgaria in late 2015 are reported. Logit marginal effects regression analysis reveals no association between participation in undeclared work and the perceived level of penalties and risk of detection, but a strong significant association with the level of asymmetry between citizen and state morale; the greater the asymmetry, the higher is the likelihood of participation in undeclared work. The paper concludes by discussing the implications for explaining and tackling undeclared work