Study of Processes at the Delay Stage of a Subnanosecond Atmospheric Pressure Discharge Developing with the Participation of Runaway Electrons

The modeling of the development of an electron avalanche initiated by an electron emitted from a micropoint on a cathode in the form of a cone 3 μm high is carried out. The avalanche development took place in nitrogen at atmospheric pressure in a uniform electric field with a strength of E = 680 kV/cm. That is, under conditions when E is much greater than the critical electric field strength E_cr required for the transition of electrons to the continuous acceleration mode according to the classical runaway criterion. The analysis was based on the experimentally obtained voltage waveforms on the discharge gas gap. Spatial distributions of electrons in the avalanche at different stages of its development and electron energy distribution functions for different numbers of electrons in the avalanche were obtained. It is shown that by the time when the number of electrons in the avalanche is in the range of 10³–10⁴, the maximum energy of electrons begins to exceed 1 keV, which can be interpreted as the beginning of the transition of individual electrons from the avalanche to the runaway mode. The beginning of the exit of individual fast electrons from the avalanche can be seen in the spatial distribution of electrons. Then these fast electrons, moving to the anode, ionize the gas and leave behind a narrow track of slow electrons. It is shown that the part of runaway electrons is very small and amounts to ~10^–5 of the total number of electrons. Thus, the gas discharge plasma mainly consists of slow electrons despite the fact that E significantly exceeds E_cr.