A numerical investigation on electron runaway threshold at the initial stage of atmospheric streamer development

Pre-ionization caused by runaway electrons is an important mechanism for negative streamer development. The aim of this paper is to investigate the runaway criteria and overvoltage threshold of electrons at the initial stage of streamer development in air, with the self-developed 3D particle-in-cell with Monte Carlo Collision code. First, numerical simulations are performed with fixed number of electrons to study the runaway criteria in nonrelativistic cases. This method takes the stochastic fluctuations of collisions into account and solves the major shortcomings of theoretical approach. The simulated critical electric field is less than that of the theoretical approach, and the amplitude of the difference increases with electron energy, due to the "tunneling effect" caused by the stochastic fluctuations of collisions. Then, simulations of negative streamers at various applied voltages are performed to investigate the overvoltage threshold. A more intuitive method, searching energetic electrons in front of the negative streamer head, which corresponds to the nature of runaway electrons, is applied to determine the generation of runaway electrons. Electrons that escaped a certain distance ahead of the streamer can be observed at 30 kV. Thus, the overvoltage threshold for runaway electrons can be roughly estimated as 3.3 in our simulations, which is about three times less than the previously published one. At last, with the redefined overvoltage threshold, the figure of regions of breakdown development for various mechanisms depending upon the overvoltage in air is updated.