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

A numerical code is developed and used to model an unsteady electron energy distribution function (EEDF) in the electric field of a nanosecond repetitive discharge propagating as a fast ionization wave (FIW) of negative polarity. The EEDF in a FIW is shown to form as a result of the interaction between two oppositely directed electron fluxes along the energy axis. On the one hand, high-energy electrons originating in the breakdown front give rise to a decreasing power-law electron energy distribution: high-energy electrons lose energy in inelastic collisions in the weak field region behind the front, thereby producing the downward electron flux along the energy axis. 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 the cold electrons. The time required for the EEDF to relax to a quasisteady function is governed by the time scales of both the upward and downward electron fluxes along the energy axis. The spatially non-local processes that increase the mean electron energy ahead of the front of the strong electric fields are also found to have a significant effect on the shape of the resulting EEDF.