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It is widely accepted that the simplified streamer breakdown criterion $$ \int_0^{{x_c}} {\bar \alpha (x)} {\text{ }} \cdot {\text{ }} = {\text{ }}K $$ (1) where \( {\bar \alpha } \) is the effective coefficient of ionization, x is a coordinate along an electric field line and K is a dimensionless number representing various secondary ionization process, can well be used to calculate breakdown voltages in many gases subjected to homogeneous or weakly inhomogeneous field distributions. For field distributions of this kind, x c is either identical with the gap distance ( g) or a critical electron avalanche length, which is defined by a position within the gap, where \( \overline \alpha \leqslant 0 \). Though K is often taken to be 18 for calculating onset of breakdown ( thus taken to be the natural logarithm of a critical number Ncrit of about 108, assumed as a number of electrons produced by ionization in a critical avalanche), it has been shown by A. Pedersen et. al.1 and W.S. Zaengl et. al.2 that K for SF6 and synthetic air is much lower.

A time-dependent, hydrodynamic, model of partial discharges in voids in dielectrics is presented. The partial discharge is regarded as a space charge dominated electron avalanche. The model incorporates the relevant collisional and radiative processes in the void and at its boundary, and the field distortion due to the presence of space charge and void surface charges. Also the coupling with the external circuit is taken into account. Model simulations show that, as a result of field quenching, the associated charge versus applied field shows saturation above a certain threshold. The threshold field depends on geometry and initial electron number, but is higher than the inception values usually quoted. The saturation charge may deviate by a factor of 2–10 from values obtained with simplified models.

The conditions for production of a secondary-emission microwave discharge in systems with a large distance between the walls (cavity resonators, waveguides, etc.) and in free space are analyzed. The traditional theory of a resonance discharge is shown to be invalid for these cases and a new method is proposed for determining the thresholds for the discharge. The discussion takes into account the contribution to the discharge current from electrons emitted at all phases of the field. The theoretical calculations are compared with experimental results.