Modeling the propagation of streamers in liquids - The Townsend-Meek criterion and a novel model for photoionization

Conducting channels forms when a dielectric liquid is subjected to high electric stress. These channels are know as streamers, and if allowed the time to form and propagate, they can lead to an electrical breakdown. Sintef has developed a numerical model for the propagation of streamers, which is based on the Townsend-Meek criterion, and is focused on impact ionization by electrons accelerated in an electric field. The model is able to correctly predict many aspects of streamer propagation, but propagation voltage is a bit too high, the degree of streamer branching is somewhat low, and the model fails to replicate the transition to the fast fourth mode streamer. In an attempt to improve the streamer model the both the Townsend-Meek criterion and a model for photoionization is explored. The most important parameter in the Townsend Meek criterion is the Meek constant $Q_|c|$. Currently, Qc = 23 is used by the model. Calculations done with data available in literature suggest that this value is too high, and that the definition used to calculate the Meek constant needs to be clarified. The photoionization model assumes a high radiation peak from molecules relaxing from the lowest electronically excited state to the ground state. The radiation originates within the streamer channel. The ionization rate is calculated by assuming an ionization cross section that is dependent on the magnitude of the electric field. A transition in speed is found when the electric field has reduced the ionization potential of the molecules to the energy of the lowest excited state