Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td

The time taken for an electron swarm to reach its equilibrium (or thermalise) with an instantaneously applied electric field (E/N) is very short, typically less than 10-9s for most medium and high-pressure plasmas (p=0.01-5bar). Thus, to undertake numerical modelling of the temporal evolution of plasmas driven by relatively slow time-varying voltage waveforms (>>10-9s), a steady-state Boltzmann code is usually sufficient to deduce the electron energy distribution function (EEDF) and the requisite electron swarm parameters as a function of E/N. Recently, however, plasmas driven by fast transient voltage pulses (e.g. risetimes >100V.ns-1, 1-10ns duration) are being rapidly developed, as reviewed in [1]. It is not yet clear whether the EEDFs in these fast transient plasmas deviate significantly from “thermalised” due to the very rapidly varying E/N. To investigate this issue, we have calculated the time taken for electrons to become thermalised for a given E/N, over a range of fields applicable to most medium-high pressure plasma discharges, and for a variety of gases (Xe, Kr, Ar, Ne, He, N2). We have numerically solved the multi-term, spatially-homogenous Boltzmann equation, subject to a constant electric field, to follow the EEDF as it evolves from an initial room-temperature Maxwellian distribution toward thesteady-state. Transport quantities such as mean energy <> and drift velocity We were calculated at each time, and the <> was used to define thermalisation time th. Key results for Xenon are shown in fig.1. Our preliminary results for Xe and other gases suggest that th can be comparable with the voltage pulserisetimes for fast discharges [1], suggesting the EEDFs may not be fully thermalised.