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

Abstract

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.

Energy efficiency in nanoscale synthesis using nanosecond plasmas

“…The time evolution of the EEDF of nanosecond discharges has been modeled for the case of a fast ionization wave at 4 torr and shows the development of a significant high-energy tail41. The corresponding time profile of < ε > closely follows that of the reduced electric field E / N , where E is the electric field and N is the gas density, with a lag of 0.5 ns.…”

Effect of explosive emission on runaway electron generation

“…In order to describe the FIW propagation, the phenomenon of runaway electrons (RAEs) is considered. [4][5][6][7][8][9][10][11][12][13][14][15] These RAEs efficiently generate secondary electrons and ions, which produce gas pre-ionization during their propagation toward the anode. In addition, secondary electrons participate in ionization processes, forming plasma that could result in the shorting of the cathode-anode (CA) gap.…”

Studying the Electron Energy Distribution Function (EEDF) and Electron Transport Coefficients in SF6 – He Gas Mixtures by Solving the Boltzmann Equation

“…The higher values of E/N lead to the extension of the EEDF curves towards higher energy tail. This behavior can be attributed to the electric field that heats up the electrons and thus the energy of cold electrons increases [11]. Subsequently, the mean electron energy depends on the ratio of E/N as well as on the electron transport coefficients.…”