## Saturation scalings of toroidal ion temperature gradient turbulence

## Abstract

The emerging understanding of instability-driven plasma-turbulence saturation in terms of energy transfer to stable modes in the same scale range as the instability is employed to derive a saturation theory for the toroidal branch of ion temperature gradient turbulence that provides the scaling of turbulence and zonal flow levels for all physical parameters. The theory is based on the eigenmode decomposition of a nonlinear fluid model, which is subjected to a statistical closure and simplified via an ordering expansion consistent with zonal-flow catalyzed energy transfer from the unstable mode to the stable mode at large scale. Solution of the closed energy balance equations yields a turbulence level that is proportional to the ratio of the zonal flow damping rate and the inverse of the triplet correlation time of the zonal-flow catalyzed wavenumber triplet interaction. The zonal flow energy is proportional to the ratio of the growth rate and the inverse triplet correlation time. The saturation scalings are applied to the ion heat flux, showing that it has a factor proportional to the quasilinear heat flux and a correction factor that includes the inverse of the triplet correlation time and a reduction due to the stable mode.

- Authors:

- University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

- Publication Date:

- Research Org.:
- Univ. of Wisconsin, Madison, WI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1540133

- Grant/Contract Number:
- FG02-89ER53291; FG02-93ER54222; FG02-99ER54546

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 1; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Physics

### Citation Formats

```
Terry, P. W., Faber, B. J., Hegna, C. C., Mirnov, V. V., Pueschel, M. J., and Whelan, G. G. Saturation scalings of toroidal ion temperature gradient turbulence. United States: N. p., 2018.
Web. doi:10.1063/1.5007062.
```

```
Terry, P. W., Faber, B. J., Hegna, C. C., Mirnov, V. V., Pueschel, M. J., & Whelan, G. G. Saturation scalings of toroidal ion temperature gradient turbulence. United States. doi:10.1063/1.5007062.
```

```
Terry, P. W., Faber, B. J., Hegna, C. C., Mirnov, V. V., Pueschel, M. J., and Whelan, G. G. Mon .
"Saturation scalings of toroidal ion temperature gradient turbulence". United States. doi:10.1063/1.5007062. https://www.osti.gov/servlets/purl/1540133.
```

```
@article{osti_1540133,
```

title = {Saturation scalings of toroidal ion temperature gradient turbulence},

author = {Terry, P. W. and Faber, B. J. and Hegna, C. C. and Mirnov, V. V. and Pueschel, M. J. and Whelan, G. G.},

abstractNote = {The emerging understanding of instability-driven plasma-turbulence saturation in terms of energy transfer to stable modes in the same scale range as the instability is employed to derive a saturation theory for the toroidal branch of ion temperature gradient turbulence that provides the scaling of turbulence and zonal flow levels for all physical parameters. The theory is based on the eigenmode decomposition of a nonlinear fluid model, which is subjected to a statistical closure and simplified via an ordering expansion consistent with zonal-flow catalyzed energy transfer from the unstable mode to the stable mode at large scale. Solution of the closed energy balance equations yields a turbulence level that is proportional to the ratio of the zonal flow damping rate and the inverse of the triplet correlation time of the zonal-flow catalyzed wavenumber triplet interaction. The zonal flow energy is proportional to the ratio of the growth rate and the inverse triplet correlation time. The saturation scalings are applied to the ion heat flux, showing that it has a factor proportional to the quasilinear heat flux and a correction factor that includes the inverse of the triplet correlation time and a reduction due to the stable mode.},

doi = {10.1063/1.5007062},

journal = {Physics of Plasmas},

number = 1,

volume = 25,

place = {United States},

year = {2018},

month = {1}

}