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

G. J. Boyle, M. Casey, R. D. White, Robert Carman

Research output: Contribution to conferenceAbstractResearch

Abstract

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.

Conference

ConferenceThe 20th Gaseous Electronics Meeting
Abbreviated titleGEM
CountryAustralia
CityTownsville
Period21/06/1824/06/18
Internet address

Fingerprint

xenon
energy distribution
distribution functions
electron energy
electric fields
electric potential
Maxwell-Boltzmann density function
electrons
gases
plasma jets
waveforms
room temperature
pulses
energy

Keywords

  • plasma physics
  • Atomic processes

Cite this

Boyle, G. J., Casey, M., White, R. D., & Carman, R. (2018). Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td. Session J. Abstract from The 20th Gaseous Electronics Meeting, Townsville, Australia.
Boyle, G. J. ; Casey, M. ; White, R. D. ; Carman, Robert. / Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td. Abstract from The 20th Gaseous Electronics Meeting, Townsville, Australia.1 p.
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title = "Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td",
abstract = "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.",
keywords = "plasma physics, Atomic processes",
author = "Boyle, {G. J.} and M. Casey and White, {R. D.} and Robert Carman",
year = "2018",
month = "6",
day = "24",
language = "English",
pages = "Session J",
note = "The 20th Gaseous Electronics Meeting, GEM ; Conference date: 21-06-2018 Through 24-06-2018",
url = "https://www.jcu.edu.au/gemxx/program",

}

Boyle, GJ, Casey, M, White, RD & Carman, R 2018, 'Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td' The 20th Gaseous Electronics Meeting, Townsville, Australia, 21/06/18 - 24/06/18, pp. Session J.

Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td. / Boyle, G. J.; Casey, M.; White, R. D.; Carman, Robert.

2018. Session J Abstract from The 20th Gaseous Electronics Meeting, Townsville, Australia.

Research output: Contribution to conferenceAbstractResearch

TY - CONF

T1 - Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td

AU - Boyle, G. J.

AU - Casey, M.

AU - White, R. D.

AU - Carman, Robert

PY - 2018/6/24

Y1 - 2018/6/24

N2 - 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.

AB - 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.

KW - plasma physics

KW - Atomic processes

UR - https://www.jcu.edu.au/gemxx

M3 - Abstract

SP - Session J

ER -

Boyle GJ, Casey M, White RD, Carman R. Thermalisation time of electron energy distribution functions in Xenon for electric fields in the range 1Td<E/N<1000Td. 2018. Abstract from The 20th Gaseous Electronics Meeting, Townsville, Australia.