# Quasilinear theory of general electromagnetic fluctuations in unmagnetized plasmas

## Abstract

The general quasilinear Fokker-Planck kinetic equation for the plasma particle distribution functions in unmagnetized plasmas is derived, making no restrictions on the frequency of the electromagnetic fluctuations. The derived kinetic particle equation complements our earlier study of the general fluctuation's kinetic equation. For collective plasma eigenmodes and gyrotropic particle distribution functions, the two coupled kinetic equations describe the self-consistent dynamical evolution of the plasma. The limit of weakly damped collective modes correctly reproduces the well-known textbook kinetic particle equation with longitudinal Langmuir and ion-acoustic fluctuations, demonstrating, in particular, the resonant nature of parallel momentum diffusion of particles. In the limit of aperiodic modes, the Fokker-Planck equation contains the nonresonant diffusion of particles in momentum and the parallel and perpendicular momentum drag coefficients. As an application these drag and diffusion coefficients are calculated for extragalactic cosmic ray particles propagating in the unmagnetized intergalactic medium. Whereas for all cosmic rays, the perpendicular momentum diffusion in intergalactic aperiodic fluctuations is negligibly small; cosmic ray protons with energies below 10{sup 5 }GeV are affected by the plasma drag.

- Authors:

- Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany)
- (Germany)
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
- (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22303612

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COSMIC RADIATION; DIFFUSION; DISTRIBUTION FUNCTIONS; FLUCTUATIONS; FOKKER-PLANCK EQUATION; KINETIC EQUATIONS; PLASMA; QUASILINEAR PROBLEMS

### Citation Formats

```
Schlickeiser, R., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu, Research Department Plasmas with Complex Interactions, Ruhr-Universität Bochum, D-44780 Bochum, Yoon, P. H., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu, and School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701.
```*Quasilinear theory of general electromagnetic fluctuations in unmagnetized plasmas*. United States: N. p., 2014.
Web. doi:10.1063/1.4893147.

```
Schlickeiser, R., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu, Research Department Plasmas with Complex Interactions, Ruhr-Universität Bochum, D-44780 Bochum, Yoon, P. H., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu, & School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701.
```*Quasilinear theory of general electromagnetic fluctuations in unmagnetized plasmas*. United States. doi:10.1063/1.4893147.

```
Schlickeiser, R., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu, Research Department Plasmas with Complex Interactions, Ruhr-Universität Bochum, D-44780 Bochum, Yoon, P. H., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu, and School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701. Mon .
"Quasilinear theory of general electromagnetic fluctuations in unmagnetized plasmas". United States. doi:10.1063/1.4893147.
```

```
@article{osti_22303612,
```

title = {Quasilinear theory of general electromagnetic fluctuations in unmagnetized plasmas},

author = {Schlickeiser, R., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu and Research Department Plasmas with Complex Interactions, Ruhr-Universität Bochum, D-44780 Bochum and Yoon, P. H., E-mail: rsch@tp4.rub.de, E-mail: yoonp@umd.edu and School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701},

abstractNote = {The general quasilinear Fokker-Planck kinetic equation for the plasma particle distribution functions in unmagnetized plasmas is derived, making no restrictions on the frequency of the electromagnetic fluctuations. The derived kinetic particle equation complements our earlier study of the general fluctuation's kinetic equation. For collective plasma eigenmodes and gyrotropic particle distribution functions, the two coupled kinetic equations describe the self-consistent dynamical evolution of the plasma. The limit of weakly damped collective modes correctly reproduces the well-known textbook kinetic particle equation with longitudinal Langmuir and ion-acoustic fluctuations, demonstrating, in particular, the resonant nature of parallel momentum diffusion of particles. In the limit of aperiodic modes, the Fokker-Planck equation contains the nonresonant diffusion of particles in momentum and the parallel and perpendicular momentum drag coefficients. As an application these drag and diffusion coefficients are calculated for extragalactic cosmic ray particles propagating in the unmagnetized intergalactic medium. Whereas for all cosmic rays, the perpendicular momentum diffusion in intergalactic aperiodic fluctuations is negligibly small; cosmic ray protons with energies below 10{sup 5 }GeV are affected by the plasma drag.},

doi = {10.1063/1.4893147},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 9,

volume = 21,

place = {United States},

year = {2014},

month = {9}

}