Approximate Analytical Method of Streamer Discharge: Solutions

Based on the simplified mathematical model of streamer discharge proposed in the previous work, this article first obtains the closed-form analytical solution of the electron number density in the streamer head as a function of position, which includes three types of streamers (stable streamer, avalanche, and spark streamer). Among these, the stable streamer and the spark streamer could not be described analytically in the past, while the avalanche type is consistent with Townsend’s theoretical model. Second, this article presents the polarity effect of the stable streamer, as well as the two types and conditions for streamer extinction. Finally, the closed-form analytical solution of the streamer head position changing with time is derived, whose characteristic parameters are the same as those in the spatial domain. The above results provide a unified and simplified approximate analysis method of streamer discharge.