# Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

## Abstract

A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeitmore »

- Authors:

- Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies
- Univ. of California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
- Max Planck fur Plasmaphysik, Garching (Germany)
- Univ. of Wisconsin-Madison, Madison, WI (United States)

- Publication Date:

- Research Org.:
- Univ. of Texas, Austin, TX (United States)

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

- OSTI Identifier:
- 1272650

- Alternate Identifier(s):
- OSTI ID: 1272651; OSTI ID: 1326679

- Grant/Contract Number:
- FG02-04ER54742

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- New Journal of Physics

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 7; Journal ID: ISSN 1367-2630

- Publisher:
- IOP Publishing

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; gyrokinetics; pseudospectra; non-modal; plasma turbulence; Landau damping; Hermite polynomials

### Citation Formats

```
Hatch, D. R., Jenko, F., Navarro, A. Banon, Bratanov, V., Terry, P. W., and Pueschel, M. J.
```*Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra*. United States: N. p., 2016.
Web. doi:10.1088/1367-2630/18/7/075018.

```
Hatch, D. R., Jenko, F., Navarro, A. Banon, Bratanov, V., Terry, P. W., & Pueschel, M. J.
```*Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra*. United States. doi:10.1088/1367-2630/18/7/075018.

```
Hatch, D. R., Jenko, F., Navarro, A. Banon, Bratanov, V., Terry, P. W., and Pueschel, M. J. Tue .
"Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra". United States.
doi:10.1088/1367-2630/18/7/075018.
```

```
@article{osti_1272650,
```

title = {Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra},

author = {Hatch, D. R. and Jenko, F. and Navarro, A. Banon and Bratanov, V. and Terry, P. W. and Pueschel, M. J.},

abstractNote = {A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.},

doi = {10.1088/1367-2630/18/7/075018},

journal = {New Journal of Physics},

number = 7,

volume = 18,

place = {United States},

year = {Tue Jul 26 00:00:00 EDT 2016},

month = {Tue Jul 26 00:00:00 EDT 2016}

}

*Citation information provided by*

Web of Science

Web of Science