Boltzmann equation and Monte Carlo analysis of the spatiotemporal electron relaxation in nonisothermal plasmas

D. Loffhagen, R. Winkler, Z. Donkó

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The spatiotemporal relaxation of electrons in spatially one-dimensional plasmas acted upon by electric fields is investigated on the basis of the space- and time-dependent electron Boltzmann equation. The relaxation process is treated using the two-term approximation of an expansion of the electron velocity distribution function in Legendre polynomials. To verify the complex Boltzmann equation approach by a completely independent kinetic method, results for inhomogeneous column-anode plasmas of glow discharges between plane electrodes are compared with corresponding ones obtained by Monte Carlo simulations. The spatiotemporal electron relaxation.in argon plasmas, subjected to a space-independent electric field and maintained by a time-independent inflow of electrons at the cathode side of the plasma region, is considered. Starting from steady state at a given electric field, the relaxation process is initiated by a pulse-like change of the electric field strength and is traced until the spatially structured, time-independent state associated to the changed field is reached. The behaviour of the velocity distribution function and macroscopic quantities of the electrons in space and time is analyzed for enlarged and reduced electric field strengths typical of the column region of glow discharges. In particular, the spatiotemporal reformation of plasma structures has been found to progress in two phases, i.e., existing structures in the distribution are driven to merge in wide plasma region first, followed by a formation phase of new spatial structures which are induced by the cathode-sided inflow of electrons. The results for the macroscopic quantities and the isotropic distribution functions obtained by Boltzmann and Monte Carlo calculations agree very well during the spatiotemporal transient process as well as in the new steady state finally reached.

Original languageEnglish
Pages (from-to)189-200
Number of pages12
JournalEPJ Applied Physics
Volume18
Issue number3
Publication statusPublished - Jun 2002

Fingerprint

Boltzmann equation
Plasmas
Electrons
Electric fields
electrons
Distribution functions
distribution functions
Glow discharges
electric field strength
Relaxation processes
Velocity distribution
glow discharges
electric fields
Cathodes
velocity distribution
cathodes
Legendre functions
Argon
argon plasma
Anodes

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Boltzmann equation and Monte Carlo analysis of the spatiotemporal electron relaxation in nonisothermal plasmas. / Loffhagen, D.; Winkler, R.; Donkó, Z.

In: EPJ Applied Physics, Vol. 18, No. 3, 06.2002, p. 189-200.

Research output: Contribution to journalArticle

@article{27d4b7fc643c4a6e9d7ba61e0312d864,
title = "Boltzmann equation and Monte Carlo analysis of the spatiotemporal electron relaxation in nonisothermal plasmas",
abstract = "The spatiotemporal relaxation of electrons in spatially one-dimensional plasmas acted upon by electric fields is investigated on the basis of the space- and time-dependent electron Boltzmann equation. The relaxation process is treated using the two-term approximation of an expansion of the electron velocity distribution function in Legendre polynomials. To verify the complex Boltzmann equation approach by a completely independent kinetic method, results for inhomogeneous column-anode plasmas of glow discharges between plane electrodes are compared with corresponding ones obtained by Monte Carlo simulations. The spatiotemporal electron relaxation.in argon plasmas, subjected to a space-independent electric field and maintained by a time-independent inflow of electrons at the cathode side of the plasma region, is considered. Starting from steady state at a given electric field, the relaxation process is initiated by a pulse-like change of the electric field strength and is traced until the spatially structured, time-independent state associated to the changed field is reached. The behaviour of the velocity distribution function and macroscopic quantities of the electrons in space and time is analyzed for enlarged and reduced electric field strengths typical of the column region of glow discharges. In particular, the spatiotemporal reformation of plasma structures has been found to progress in two phases, i.e., existing structures in the distribution are driven to merge in wide plasma region first, followed by a formation phase of new spatial structures which are induced by the cathode-sided inflow of electrons. The results for the macroscopic quantities and the isotropic distribution functions obtained by Boltzmann and Monte Carlo calculations agree very well during the spatiotemporal transient process as well as in the new steady state finally reached.",
author = "D. Loffhagen and R. Winkler and Z. Donk{\'o}",
year = "2002",
month = "6",
language = "English",
volume = "18",
pages = "189--200",
journal = "EPJ Applied Physics",
issn = "1286-0042",
publisher = "EDP Sciences",
number = "3",

}

TY - JOUR

T1 - Boltzmann equation and Monte Carlo analysis of the spatiotemporal electron relaxation in nonisothermal plasmas

AU - Loffhagen, D.

AU - Winkler, R.

AU - Donkó, Z.

PY - 2002/6

Y1 - 2002/6

N2 - The spatiotemporal relaxation of electrons in spatially one-dimensional plasmas acted upon by electric fields is investigated on the basis of the space- and time-dependent electron Boltzmann equation. The relaxation process is treated using the two-term approximation of an expansion of the electron velocity distribution function in Legendre polynomials. To verify the complex Boltzmann equation approach by a completely independent kinetic method, results for inhomogeneous column-anode plasmas of glow discharges between plane electrodes are compared with corresponding ones obtained by Monte Carlo simulations. The spatiotemporal electron relaxation.in argon plasmas, subjected to a space-independent electric field and maintained by a time-independent inflow of electrons at the cathode side of the plasma region, is considered. Starting from steady state at a given electric field, the relaxation process is initiated by a pulse-like change of the electric field strength and is traced until the spatially structured, time-independent state associated to the changed field is reached. The behaviour of the velocity distribution function and macroscopic quantities of the electrons in space and time is analyzed for enlarged and reduced electric field strengths typical of the column region of glow discharges. In particular, the spatiotemporal reformation of plasma structures has been found to progress in two phases, i.e., existing structures in the distribution are driven to merge in wide plasma region first, followed by a formation phase of new spatial structures which are induced by the cathode-sided inflow of electrons. The results for the macroscopic quantities and the isotropic distribution functions obtained by Boltzmann and Monte Carlo calculations agree very well during the spatiotemporal transient process as well as in the new steady state finally reached.

AB - The spatiotemporal relaxation of electrons in spatially one-dimensional plasmas acted upon by electric fields is investigated on the basis of the space- and time-dependent electron Boltzmann equation. The relaxation process is treated using the two-term approximation of an expansion of the electron velocity distribution function in Legendre polynomials. To verify the complex Boltzmann equation approach by a completely independent kinetic method, results for inhomogeneous column-anode plasmas of glow discharges between plane electrodes are compared with corresponding ones obtained by Monte Carlo simulations. The spatiotemporal electron relaxation.in argon plasmas, subjected to a space-independent electric field and maintained by a time-independent inflow of electrons at the cathode side of the plasma region, is considered. Starting from steady state at a given electric field, the relaxation process is initiated by a pulse-like change of the electric field strength and is traced until the spatially structured, time-independent state associated to the changed field is reached. The behaviour of the velocity distribution function and macroscopic quantities of the electrons in space and time is analyzed for enlarged and reduced electric field strengths typical of the column region of glow discharges. In particular, the spatiotemporal reformation of plasma structures has been found to progress in two phases, i.e., existing structures in the distribution are driven to merge in wide plasma region first, followed by a formation phase of new spatial structures which are induced by the cathode-sided inflow of electrons. The results for the macroscopic quantities and the isotropic distribution functions obtained by Boltzmann and Monte Carlo calculations agree very well during the spatiotemporal transient process as well as in the new steady state finally reached.

UR - http://www.scopus.com/inward/record.url?scp=0036608923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036608923&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036608923

VL - 18

SP - 189

EP - 200

JO - EPJ Applied Physics

JF - EPJ Applied Physics

SN - 1286-0042

IS - 3

ER -