# Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

## Abstract

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period, is used to describe steady-state nonlinear oscillations in plasma.

- Authors:

- Institute of Advanced Studies (Austria)
- Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation)
- Peoples' Friendship University of Russia (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22047394

- Resource Type:
- Journal Article

- Journal Name:
- Plasma Physics Reports

- Additional Journal Information:
- Journal Volume: 38; Journal Issue: 6; Other Information: Copyright (c) 2012 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-780X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; COLD PLASMA; DECAY; MAGNETIC FIELDS; MODULATION; NONLINEAR PROBLEMS; OSCILLATIONS; PLASMA WAVES; STEADY-STATE CONDITIONS

### Citation Formats

```
Dorofeenko, V. G., Krasovitskiy, V. B., and Turikov, V. A.
```*Nonlinear modulation of an extraordinary wave under the conditions of parametric decay*. United States: N. p., 2012.
Web. doi:10.1134/S1063780X12050030.

```
Dorofeenko, V. G., Krasovitskiy, V. B., & Turikov, V. A.
```*Nonlinear modulation of an extraordinary wave under the conditions of parametric decay*. United States. doi:10.1134/S1063780X12050030.

```
Dorofeenko, V. G., Krasovitskiy, V. B., and Turikov, V. A. Fri .
"Nonlinear modulation of an extraordinary wave under the conditions of parametric decay". United States. doi:10.1134/S1063780X12050030.
```

```
@article{osti_22047394,
```

title = {Nonlinear modulation of an extraordinary wave under the conditions of parametric decay},

author = {Dorofeenko, V. G. and Krasovitskiy, V. B. and Turikov, V. A.},

abstractNote = {A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period, is used to describe steady-state nonlinear oscillations in plasma.},

doi = {10.1134/S1063780X12050030},

journal = {Plasma Physics Reports},

issn = {1063-780X},

number = 6,

volume = 38,

place = {United States},

year = {2012},

month = {6}

}