An Avalanche-to-Streamer Transition Criterion for Overstressed Breakdown on a Rising Slope

The Meek–Raether criterion underpins much of the current physical understanding of gas breakdown. The classical kinetic approach estimates the moment of transition from Townsend’s avalanche to a streamer discharge and has very often been used as a means of explaining experimental breakdown results. The Meek–Raether criterion holds great predictive power for the design of gas insulated systems, owing to its reasonable accuracy that has withstood the test of time. However, with the advent of pulsed power technology which often involves fast-rising and nonstandard waveshapes applied to complex (nonuniform) electrode topologies, the limitations of the method have been made increasingly apparent. In this work, the avalanche-to-streamer transition criterion has been theoretically revisited for fast-rising pulsed breakdown, particularly for overstressed breakdown occurring on a rising voltage slope. Based on the simplified transport of a Gaussian-distributed electron density, mathematical analyses unveil the time-dependent nature of the electron growth rates and their dependence on the voltage slope. Explicit expressions for the breakdown voltage and formative breakdown time, under the assumption of no statistical time lag, as a function of the rate-of-rise have further been derived for the limiting case of a nonattaching and nondiffusive gas. From this, it was found that electron diffusion may be an important consideration for pulsed breakdown, and an approximate condition separating the diffusion-dominated regime and where diffusion can be neglected is suggested. The novel analytical approach is also shown to be capable of recreating the upward shift of Paschen’s curve with increasing rate of voltage rise, validated against both simulation and experimental data. Furthermore, the predicted field-time breakdown scaling relationship is also shown to describe observed experimental trends well; as do its predictions for the streamer initiation time compared with hydrodynamic simulations. The results may be significant for future development of gas insulated power and pulsed power equipment and advance the fundamental understanding of fast transient breakdown processes.