  Propagation of positive streamers in dielectric liquids, modeled by the
electron avalanche mechanism, is simulated in a needle-plane gap. The streamer
is modeled as an RC-circuit where the channel is a resistor and the extremities
of the streamer have a capacitance towards the plane. The addition of the
RC-model introduces a time constant to the propagation model. Increase in
capacitance as a streamer branch propagates reduces its potential, while
conduction through the streamer channel increases its potential, as a function
of the time constant of the RC-system. Streamer branching also increases the
capacitance and decreases the potential of the branches. If the electric field
within the streamer channel exceeds a threshold, a breakdown occurs in the
channel, and the potential of the streamer is equalized with the needle
electrode. This is interpreted as a re-illumination. According to this model, a
low conductive streamer branch can propagate some distance before its potential
is reduced to below the propagation threshold, and then the RC time constant
controls the streamer propagation speed. Channel breakdowns, or
re-illuminations, are less frequent when the channels are conductive and more
frequent for more branched streamers.
