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

## TL;DR

This paper models streamer propagation in dielectric liquids using an RC-circuit approach, revealing how capacitance and conductivity influence streamer behavior, potential, and branching dynamics.

## Contribution

It introduces a novel RC-model for streamer channels that accounts for capacitance and resistance, providing insights into propagation speed and breakdown phenomena.

## Key findings

- Capacitance increase reduces streamer potential and affects propagation.
- Conductivity influences the frequency of channel breakdowns.
- Branching increases capacitance and decreases potential, affecting streamer dynamics.

## Abstract

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.