On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas

Hans Schamel, Bengt Eliasson

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional (3D) Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes the holes become of cnoidal wave type and the electron density is shown to be described by a phi(x)^{1/2} rather than a phi(x) expansion, where phi(x) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of phi(x) and the nonlinear dispersion relation, which describes their phase velocity.
LanguageEnglish
Article number052114
Number of pages7
JournalPhysics of Plasmas
Volume23
Issue number5
DOIs
Publication statusPublished - 19 May 2016

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Fermi-Dirac statistics
collisionless plasmas
wave propagation
plane waves
trapping
electrostatics
cnoidal waves
electrostatic waves
quantum statistics
electrons
phase velocity
distribution functions
analogs
expansion
propagation
coefficients
excitation

Keywords

  • electron trapping
  • Fermi-Dirac distribution
  • electrostatic wave

Cite this

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abstract = "Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional (3D) Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes the holes become of cnoidal wave type and the electron density is shown to be described by a phi(x)^{1/2} rather than a phi(x) expansion, where phi(x) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of phi(x) and the nonlinear dispersion relation, which describes their phase velocity.",
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AU - Eliasson, Bengt

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N2 - Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional (3D) Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes the holes become of cnoidal wave type and the electron density is shown to be described by a phi(x)^{1/2} rather than a phi(x) expansion, where phi(x) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of phi(x) and the nonlinear dispersion relation, which describes their phase velocity.

AB - Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional (3D) Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes the holes become of cnoidal wave type and the electron density is shown to be described by a phi(x)^{1/2} rather than a phi(x) expansion, where phi(x) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of phi(x) and the nonlinear dispersion relation, which describes their phase velocity.

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