# Nonlinear damping of zonal flows

## Abstract

The modulatonal instability theory for the generation of large-scale (zonal) modes by drift modes has been extended to the second order including the effects of finite amplitude zonal flows, ϕ{sub q}. The nonlinear (second-order) sidebands are included in the perturbative expansion to derive the nonlinear equation for the evolution of ϕ{sub q}. It is shown that effects of finite ϕ{sub q} reduce the growth rate of zonal flow with a possibility of oscillatory regimes at a later stage.

- Authors:

- University of Saskatchewan, Department of Physics and Engineering Physics (Canada)
- Instituto Superior Técnico, Instituto de Plasmas e Fusão Nuclear (Portugal)

- Publication Date:

- OSTI Identifier:
- 22614094

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Plasma Physics Reports; Journal Volume: 42; Journal Issue: 8; Other Information: Copyright (c) 2016 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; DAMPING; EQUATIONS; NONLINEAR PROBLEMS; PLASMA INSTABILITY

### Citation Formats

```
Koshkarov, O., E-mail: koshkarov.alexandr@usask.ca, Smolyakov, A. I., and Mendonca, J. T.
```*Nonlinear damping of zonal flows*. United States: N. p., 2016.
Web. doi:10.1134/S1063780X16080067.

```
Koshkarov, O., E-mail: koshkarov.alexandr@usask.ca, Smolyakov, A. I., & Mendonca, J. T.
```*Nonlinear damping of zonal flows*. United States. doi:10.1134/S1063780X16080067.

```
Koshkarov, O., E-mail: koshkarov.alexandr@usask.ca, Smolyakov, A. I., and Mendonca, J. T. Mon .
"Nonlinear damping of zonal flows". United States.
doi:10.1134/S1063780X16080067.
```

```
@article{osti_22614094,
```

title = {Nonlinear damping of zonal flows},

author = {Koshkarov, O., E-mail: koshkarov.alexandr@usask.ca and Smolyakov, A. I. and Mendonca, J. T.},

abstractNote = {The modulatonal instability theory for the generation of large-scale (zonal) modes by drift modes has been extended to the second order including the effects of finite amplitude zonal flows, ϕ{sub q}. The nonlinear (second-order) sidebands are included in the perturbative expansion to derive the nonlinear equation for the evolution of ϕ{sub q}. It is shown that effects of finite ϕ{sub q} reduce the growth rate of zonal flow with a possibility of oscillatory regimes at a later stage.},

doi = {10.1134/S1063780X16080067},

journal = {Plasma Physics Reports},

number = 8,

volume = 42,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}

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