Streamer inception thresholds derived from a statistical electron transport model

The aim of this article is to review a statistical description of electron transport in gases based on transport parameter theory, and to derive expressions for streamer inception thresholds in quasi-homogeneous electrical fields within this description. The critical average number of electrons n(crit) required to induce avalanche-to-streamer transition is derived for arbitrary gases as a function of the gap electric field and the relevant gas parameters. The model is then evaluated for synthetic air. Significant deviations from the traditional approximation n(crit, cl) = 10(8) are found for small gaps (d < 1 mm). Moreover, the minimal necessary number of electrons for avalanche-to-streamer transition is found to scale approximately with the inverse of gas pressure. The application of the adapted streamer inception criterion to the calculation of the partial discharge inception voltage for twisted enamelled wires, where discharges are incepted in gaps with d << 1 mm, is discussed. Our results support the conclusion that space charges generated by sub-critical avalanche processes play a determining role for streamer onset in such configurations, i.e. that their partial discharge inception cannot be reliably quantified by applying the streamer criterion in the Laplacian electrode field. Finally, the streamer inception probability is compared to the deterministic streamer inception criterion. In particular, the problem of non-exponential growth in the early stages of the electron avalanche development is argued to be properly addressed within the applied statistical interpretation of transport parameters.