Hydrodynamic limit of WignerPoisson kinetic theory: Revisited
Abstract
In this paper, we revisit the hydrodynamic limit of the Langmuir wave dispersion relation based on the WignerPoisson model in connection with that obtained directly from the original Lindhard dielectric function based on the randomphaseapproximation. It is observed that the (fourthorder) expansion of the exact Lindhard dielectric constant correctly reduces to the hydrodynamic dispersion relation with an additional term of fourthorder, beside that caused by the quantum diffraction effect. It is also revealed that the generalized Lindhard dielectric theory accounts for the recently discovered ShuklaEliasson attractive potential (SEAP). However, the expansion of the exact Lindhard static dielectric function leads to a k{sup 4} term of different magnitude than that obtained from the linearized quantum hydrodynamics model. It is shown that a correction factor of 1/9 should be included in the term arising from the quantum Bohm potential of the momentum balance equation in fluid model in order for a correct plasma dielectric response treatment. Finally, it is observed that the longrange oscillatory screening potential (Friedel oscillations) of type cos(2k{sub F}r)/r{sup 3}, which is a consequence of the divergence of the dielectric function at point k = 2k{sub F} in a quantum plasma, arises due to the finiteness of the Fermiwavenumber and ismore »
 Authors:
 Faculty of Sciences, Department of Physics, Azarbaijan Shahid Madani University, 51745406 Tabriz (Iran, Islamic Republic of)
 (Germany)
 Publication Date:
 OSTI Identifier:
 22408056
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOHM CRITERION; DIELECTRIC MATERIALS; DIFFRACTION; DISPERSION RELATIONS; ELECTRON DENSITY; FLOW MODELS; HYDRODYNAMICS; LANDAU DAMPING; METALS; NEUTRON STARS; OSCILLATIONS; PERMITTIVITY; QUANTUM PLASMA; RANDOM PHASE APPROXIMATION; SEMICONDUCTOR MATERIALS; WAVELENGTHS; WHITE DWARF STARS
Citation Formats
AkbariMoghanjoughi, M., and International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Ruhr University Bochum, D44780 Bochum. Hydrodynamic limit of WignerPoisson kinetic theory: Revisited. United States: N. p., 2015.
Web. doi:10.1063/1.4907167.
AkbariMoghanjoughi, M., & International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Ruhr University Bochum, D44780 Bochum. Hydrodynamic limit of WignerPoisson kinetic theory: Revisited. United States. doi:10.1063/1.4907167.
AkbariMoghanjoughi, M., and International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Ruhr University Bochum, D44780 Bochum. 2015.
"Hydrodynamic limit of WignerPoisson kinetic theory: Revisited". United States.
doi:10.1063/1.4907167.
@article{osti_22408056,
title = {Hydrodynamic limit of WignerPoisson kinetic theory: Revisited},
author = {AkbariMoghanjoughi, M. and International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Ruhr University Bochum, D44780 Bochum},
abstractNote = {In this paper, we revisit the hydrodynamic limit of the Langmuir wave dispersion relation based on the WignerPoisson model in connection with that obtained directly from the original Lindhard dielectric function based on the randomphaseapproximation. It is observed that the (fourthorder) expansion of the exact Lindhard dielectric constant correctly reduces to the hydrodynamic dispersion relation with an additional term of fourthorder, beside that caused by the quantum diffraction effect. It is also revealed that the generalized Lindhard dielectric theory accounts for the recently discovered ShuklaEliasson attractive potential (SEAP). However, the expansion of the exact Lindhard static dielectric function leads to a k{sup 4} term of different magnitude than that obtained from the linearized quantum hydrodynamics model. It is shown that a correction factor of 1/9 should be included in the term arising from the quantum Bohm potential of the momentum balance equation in fluid model in order for a correct plasma dielectric response treatment. Finally, it is observed that the longrange oscillatory screening potential (Friedel oscillations) of type cos(2k{sub F}r)/r{sup 3}, which is a consequence of the divergence of the dielectric function at point k = 2k{sub F} in a quantum plasma, arises due to the finiteness of the Fermiwavenumber and is smeared out in the limit of very high electron numberdensities, typical of white dwarfs and neutron stars. In the very low electron numberdensity regime, typical of semiconductors and metals, where the Friedel oscillation wavelength becomes much larger compared to the interparticle distances, the SEAP appears with a much deeper potential valley. It is remarked that the fourthorder approximate Lindhard dielectric constant approaches that of the linearized quantum hydrodynamic in the limit if very high electron numberdensity. By evaluation of the imaginary part of the Lindhard dielectric function, it is shown that the Landaudamping region in ωk plane increases dramatically by increase of the electron numberdensity.},
doi = {10.1063/1.4907167},
journal = {Physics of Plasmas},
number = 2,
volume = 22,
place = {United States},
year = 2015,
month = 2
}

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