# Parametric instability in a collisional dusty plasma

## Abstract

The present work investigates the parametric instability of parallel propagating circularly polarized Alfven (pump) waves in a collisional dusty plasma. It is demonstrated that the relative drift between the charged dust and the electrons and ions gives rise to the Hall effect resulting in the modified pump wave characteristics. Although the linearized fluid equations with periodic coefficients are difficult to solve analytically, it is shown that a linear transformation can remove the periodic dependence. The resulting linearized equations with constant coefficients are used to derive an algebraic dispersion relation. The growth rate of the parametric instability is a sensitive function of the amplitude of the pump wave as well as to the ratio of the pump and the dust-cyclotron frequencies. The instability is insensitive to the plasma-beta parameter. The possible application of the result in the astrophysical context is discussed.

- Authors:

- Department of Physics, Macquarie University, Sydney NSW 2109 (Australia)
- (Australia)

- Publication Date:

- OSTI Identifier:
- 20974965

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 5; Other Information: DOI: 10.1063/1.2730495; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; AMPLITUDES; COLLISIONS; CYCLOTRON FREQUENCY; DISPERSION RELATIONS; DUSTS; ELECTRONS; HALL EFFECT; IONS; MAGNETOHYDRODYNAMICS; PARAMETRIC INSTABILITIES; PERIODICITY; PLASMA; PLASMA FLUID EQUATIONS; PUMPS

### Citation Formats

```
Pandey, B. P., Vladimirov, S. V., and School of Physics, University of Sydney, Sydney NSW 2006.
```*Parametric instability in a collisional dusty plasma*. United States: N. p., 2007.
Web. doi:10.1063/1.2730495.

```
Pandey, B. P., Vladimirov, S. V., & School of Physics, University of Sydney, Sydney NSW 2006.
```*Parametric instability in a collisional dusty plasma*. United States. doi:10.1063/1.2730495.

```
Pandey, B. P., Vladimirov, S. V., and School of Physics, University of Sydney, Sydney NSW 2006. Tue .
"Parametric instability in a collisional dusty plasma". United States.
doi:10.1063/1.2730495.
```

```
@article{osti_20974965,
```

title = {Parametric instability in a collisional dusty plasma},

author = {Pandey, B. P. and Vladimirov, S. V. and School of Physics, University of Sydney, Sydney NSW 2006},

abstractNote = {The present work investigates the parametric instability of parallel propagating circularly polarized Alfven (pump) waves in a collisional dusty plasma. It is demonstrated that the relative drift between the charged dust and the electrons and ions gives rise to the Hall effect resulting in the modified pump wave characteristics. Although the linearized fluid equations with periodic coefficients are difficult to solve analytically, it is shown that a linear transformation can remove the periodic dependence. The resulting linearized equations with constant coefficients are used to derive an algebraic dispersion relation. The growth rate of the parametric instability is a sensitive function of the amplitude of the pump wave as well as to the ratio of the pump and the dust-cyclotron frequencies. The instability is insensitive to the plasma-beta parameter. The possible application of the result in the astrophysical context is discussed.},

doi = {10.1063/1.2730495},

journal = {Physics of Plasmas},

number = 5,

volume = 14,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}