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Title: Dielectric function for the Balescu-Lenard-Poisson kinetic equations

Abstract

By using the propagator expansion method applied to an electron-ion plasma near thermal equilibrium, a closed-form solution is found for the high frequency, collisional dielectric function in the electrostatic approximation to the first order in the plasma parameter when the Balescu-Lenard collision operator is used to describe electron-electron and electron-ion collisions. The Balescu-Lenard dielectric function is shown to be an entire function of the complex frequency variable w. Since an exact solution for the collisional propagtor for the Balescu-Lenard problem is probably impossible, these results illustrate the usefulness of the propagator expansion method as a way of obtaining the dielectric function for collisional plasmas. A comparison is made between the Balescu-Lenard result for the plasma conductivity as the wave vector K approaches 0 and the Guernsey result, obtained by Oberman, Ron, and Dawson. By solving the Balescu-Lenard dispersion relation in the long wavelength approximation, a formula is obtained for the total damping rate for Langmuir waves, which is the sum of the collisionless (Landau) part and the collisional part. A numerical solution of the Balescu-Lenard dispersion relation was also performed, and the analytical and numerical results for the damping rates are compared at long wavelengths. Comparisons of the Balescu-Lenard dampingmore » rate to the quantum-mechanical result are made.« less

Authors:
;
Publication Date:
Research Org.:
Air Force Geophysics Lab., Hanscom AFB, MA (USA)
OSTI Identifier:
5791861
Report Number(s):
AD-A-164764/3/XAB; AFGL-TR-86-0033
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COLLISIONAL PLASMA; DIELECTRIC PROPERTIES; KINETIC EQUATIONS; DAMPING; ELECTRON-ELECTRON COLLISIONS; ELECTRON-ION COLLISIONS; ELECTROSTATICS; EXPANSION; NUMERICAL ANALYSIS; COLLISIONS; ELECTRICAL PROPERTIES; ELECTRON COLLISIONS; EQUATIONS; ION COLLISIONS; MATHEMATICS; PHYSICAL PROPERTIES; PLASMA; 700105* - Fusion Energy- Plasma Research- Plasma Kinetics-Theoretical- (-1987)

Citation Formats

Jasperse, J R, and Basu, B. Dielectric function for the Balescu-Lenard-Poisson kinetic equations. United States: N. p., 1986. Web.
Jasperse, J R, & Basu, B. Dielectric function for the Balescu-Lenard-Poisson kinetic equations. United States.
Jasperse, J R, and Basu, B. Wed . "Dielectric function for the Balescu-Lenard-Poisson kinetic equations". United States.
@article{osti_5791861,
title = {Dielectric function for the Balescu-Lenard-Poisson kinetic equations},
author = {Jasperse, J R and Basu, B},
abstractNote = {By using the propagator expansion method applied to an electron-ion plasma near thermal equilibrium, a closed-form solution is found for the high frequency, collisional dielectric function in the electrostatic approximation to the first order in the plasma parameter when the Balescu-Lenard collision operator is used to describe electron-electron and electron-ion collisions. The Balescu-Lenard dielectric function is shown to be an entire function of the complex frequency variable w. Since an exact solution for the collisional propagtor for the Balescu-Lenard problem is probably impossible, these results illustrate the usefulness of the propagator expansion method as a way of obtaining the dielectric function for collisional plasmas. A comparison is made between the Balescu-Lenard result for the plasma conductivity as the wave vector K approaches 0 and the Guernsey result, obtained by Oberman, Ron, and Dawson. By solving the Balescu-Lenard dispersion relation in the long wavelength approximation, a formula is obtained for the total damping rate for Langmuir waves, which is the sum of the collisionless (Landau) part and the collisional part. A numerical solution of the Balescu-Lenard dispersion relation was also performed, and the analytical and numerical results for the damping rates are compared at long wavelengths. Comparisons of the Balescu-Lenard damping rate to the quantum-mechanical result are made.},
doi = {},
url = {https://www.osti.gov/biblio/5791861}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1986},
month = {1}
}

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