Numerical modelling of the electron energy distribution functionin the electric field of a nanosecond pulsed discharge

Abstract

A numerical code is developed and used to model an unsteady electronenergy distribution function (EEDF) in the electric field of ananosecond repetitive discharge propagating as a fast ionization wave(FIW) of negative polarity. The EEDF in a FIW is shown to form as aresult of the interaction between two oppositely directed electronfluxes along the energy axis. On the one hand, high-energy electronsoriginating in the breakdown front give rise to a decreasing power-lawelectron energy distribution: high-energy electrons loseenergy in inelastic collisions in the weak field region behind thefront, thereby producing the downward electron flux along the energyaxis. On the other hand, near the thresholds for inelastic processes,the formation of the EEDF is strongly affected by the electric field,which heats the electron component and thus increases the energy of thecold electrons. The time required for the EEDF to relax to a quasisteadyfunction is governed by the time scales of both the upward and downwardelectron fluxes along the energy axis. The spatially non-local processesthat increase the mean electron energy ahead of the front of the strongelectric fields are also found to have a significant effect on the shapeof the resulting EEDF.