Streamer to leader transition criteria for propagation of long sparks and lightning leaders

Certain models have been dedicated to analyze the breakdown of long spark gaps and the lightning attachment process based on the mechanism of leader propagation. One of the most important processes on the mechanism of leader is the transition between streamers to leader. The streamer to leader transition is characterized by a rapid increase in the electron density and gas temperature, which is a consequence of the onset of thermal-ionization instability. To simplify the complexity of the physical process lightning attachment and long spark gaps models assumed that a minimum charge of 1μC is necessary to thermalize a leader channel, independently of the electric field and atmospheric conditions as temperature, pressure and humidity. In this paper an approach that takes into account the continuity equations and the gas temperature balance equation is used to investigate the minimum charge required to start the streamer to leader transition. The obtained results are compared with the minimum charge criteria used for long spark gaps and lightning attachment modeling. Simulation shows that the required charge to thermalize a leader depends on the vibrational energy relaxation. Results also indicate that only a small part of the energy input, transferred by electrons to gas molecules in the stem, contributes immediately to the temperature rise.