On the critical charge required for positive leader inception in long air gaps

The amount of the electric charge injected by the streamer corona bursts during the stage of leader inception determines the energy deposited to thermalize the corona stem into a leader segment. This paper is aimed at investigating the critical charge required for positive leader inception in air by using a thermo-hydrodynamic model with a detailed kinetic scheme. In order to simplify the analysis and to speed up the simulation, a reduced kinetic scheme for air is proposed. Numerical comparisons show that the reduced scheme can obtain almost the same results as the previous comprehensive kinetic scheme but with only half of the number of species and reactions. The thermo-hydrodynamic model with the reduced kinetics is then used to solve the radial dynamics of a single stem heated by current pulses typical of streamer corona bursts. The critical charge necessary for the direct transition of a first streamer corona into a leader under electrodes with large curvature radius is estimated between 0.08 and 0.5 µ C per stem. Furthermore, the simulation shows that the gas heating of corona stem formed from electrodes with small curvature radius is mainly determined by the total accumulated charge injected by previous streamer corona bursts and the length of the dark periods in between the current pulses. The shape and the number of the corona current pulses in the discharge also play a role and their effects are discussed. It is suggested that the transition into a leader is triggered when a secondary streamer burst is initiated after the gas temperature is increased by the heating of previous streamers to about 1200 K. In addition, it is found that the heating produced by the charge injected by previous streamer corona bursts can be neglected if the dark period to the next burst is larger than few hundreds of µ s for a corona stem with moderate initial stem radius. This indicates that the critical charge criterion obtained from laboratory experiments does not hold to evaluate the inception of positive leaders under conditions when long dark periods are present.