# Dielectric function for the Balescu-Lenard-Poisson kinetic equations

## Abstract

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 relationmore »

- Authors:

- Publication Date:

- Research Org.:
- Air Force Geophysics Laboratory, Hanscom Air Force Base, Bedford, Massachusetts 01731

- OSTI Identifier:
- 6295117

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Fluids; (United States)

- Additional Journal Information:
- Journal Volume: 29:1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COLLISIONAL PLASMA; DIELECTRIC PROPERTIES; ELECTRON-ELECTRON COLLISIONS; ELECTRON-ION COLLISIONS; ANALYTICAL SOLUTION; DAMPING; DISPERSION RELATIONS; ELECTROSTATICS; KINETIC EQUATIONS; NUMERICAL SOLUTION; PLASMA WAVES; PROPAGATOR; THERMAL EQUILIBRIUM; COLLISIONS; ELECTRICAL PROPERTIES; ELECTRON COLLISIONS; EQUATIONS; EQUILIBRIUM; ION COLLISIONS; 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. doi:10.1063/1.865986.

```
Jasperse, J R, & Basu, B.
```*Dielectric function for the Balescu-Lenard-Poisson kinetic equations*. United States. https://doi.org/10.1063/1.865986

```
Jasperse, J R, and Basu, B. Wed .
"Dielectric function for the Balescu-Lenard-Poisson kinetic equations". United States. https://doi.org/10.1063/1.865986.
```

```
@article{osti_6295117,
```

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 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.},

doi = {10.1063/1.865986},

url = {https://www.osti.gov/biblio/6295117},
journal = {Phys. Fluids; (United States)},

number = ,

volume = 29:1,

place = {United States},

year = {1986},

month = {1}

}