# The general dielectric tensor for bi-kappa magnetized plasmas

## Abstract

In this paper, we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation, and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.

- Authors:

- Instituto de Física, UFRGS, 91501-970 Porto Alegre, RS (Brazil)

- Publication Date:

- OSTI Identifier:
- 22598971

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANISOTROPY; DIELECTRIC MATERIALS; DIELECTRIC TENSOR; DISTRIBUTION; DISTRIBUTION FUNCTIONS; ELECTROMAGNETIC RADIATION; PARTICLES; PLASMA; POLARIZATION; VELOCITY

### Citation Formats

```
Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, Ziebell, L. F., E-mail: luiz.ziebell@ufrgs.br, and Meneses, A. R., E-mail: anemeneses@gmail.com.
```*The general dielectric tensor for bi-kappa magnetized plasmas*. United States: N. p., 2016.
Web. doi:10.1063/1.4953430.

```
Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, Ziebell, L. F., E-mail: luiz.ziebell@ufrgs.br, & Meneses, A. R., E-mail: anemeneses@gmail.com.
```*The general dielectric tensor for bi-kappa magnetized plasmas*. United States. doi:10.1063/1.4953430.

```
Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, Ziebell, L. F., E-mail: luiz.ziebell@ufrgs.br, and Meneses, A. R., E-mail: anemeneses@gmail.com. Wed .
"The general dielectric tensor for bi-kappa magnetized plasmas". United States.
doi:10.1063/1.4953430.
```

```
@article{osti_22598971,
```

title = {The general dielectric tensor for bi-kappa magnetized plasmas},

author = {Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br and Ziebell, L. F., E-mail: luiz.ziebell@ufrgs.br and Meneses, A. R., E-mail: anemeneses@gmail.com},

abstractNote = {In this paper, we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation, and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.},

doi = {10.1063/1.4953430},

journal = {Physics of Plasmas},

number = 6,

volume = 23,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}