Dielectric function for the Balescu-Lenard-Poisson kinetic equations

Journal Article · Wed Jan 01 04:00:00 EST 1986 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.865986· OSTI ID:6295117

Jasperse, J R; Basu, B

By using the propagator expansion method applied to an electon-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 (Phys. Fluids 3, 52 (1960); Ann. Phys. (N.Y.) 3, 390 (1960)) 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 ..omega... Since an exact solution for the collisional propagator 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 ..-->.. 0 and the Guernsey result, obtained by Oberman, Ron, and Dawson (Phys. Fluids 5, 1514 (1962)). By solving the Balescu-Lenard dispersion relation in the long wavelength approximation, a formula is obtained for the total damping rate for Langmuir waves GAMMA/sub k/, which is the sum of the collisionless (Landau) part ..gamma../sup L//sub k/ and the collisional part ..gamma../sup ..nu..//sub k/. A numerical solution of the Balescu-Lenard dispersion relation has also been 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 obtained by Dubois, Gilinsky, and Kivelson (Phys. Rev. Lett. 8, 419 (1962)) and to other results are also made.

• Research Organization: Air Force Geophysics Laboratory, Hanscom Air Force Base, Bedford, Massachusetts 01731
• OSTI ID: 6295117
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 29:1; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105* -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
ANALYTICAL SOLUTION
COLLISIONAL PLASMA
COLLISIONS
DAMPING
DIELECTRIC PROPERTIES
DISPERSION RELATIONS
ELECTRICAL PROPERTIES
ELECTRON COLLISIONS
ELECTRON-ELECTRON COLLISIONS
ELECTRON-ION COLLISIONS
ELECTROSTATICS
EQUATIONS
EQUILIBRIUM
ION COLLISIONS
KINETIC EQUATIONS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
PLASMA
PLASMA WAVES
PROPAGATOR
THERMAL EQUILIBRIUM