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Propagation of positive streamers in dielectric liquids, modeled by theelectron avalanche mechanism, is simulated in a needle-plane gap. The streameris modeled as an RC-circuit where the channel is a resistor and the extremitiesof the streamer have a capacitance towards the plane. The addition of theRC-model introduces a time constant to the propagation model. Increase incapacitance as a streamer branch propagates reduces its potential, whileconduction through the streamer channel increases its potential, as a functionof the time constant of the RC-system. Streamer branching also increases thecapacitance and decreases the potential of the branches. If the electric fieldwithin the streamer channel exceeds a threshold, a breakdown occurs in thechannel, and the potential of the streamer is equalized with the needleelectrode. This is interpreted as a re-illumination. According to this model, alow conductive streamer branch can propagate some distance before its potentialis reduced to below the propagation threshold, and then the RC time constantcontrols the streamer propagation speed. Channel breakdowns, orre-illuminations, are less frequent when the channels are conductive and morefrequent for more branched streamers.

Conductivity and capacitance of streamers in avalanche model for streamer propagation in dielectric liquids