# Symmetries of a reduced fluid-gyrokinetic system

## Abstract

Symmetries of a fluid-gyrokinetic model are investigated using Lie group techniques. Specifically, the nonlinear system constructed by Zocco & Schekochihin (Phys. Plasmas, vol. 18, 2011, 102309), which combines nonlinear fluid equations with a drift-kinetic description of parallel electron dynamics, is studied. Significantly, this model is fully gyrokinetic, allowing for arbitrary$$k_{\bot }\unicode[STIX]{x1D70C}_{i}$$, where$$k_{\bot }$$is the perpendicular wave vector of the fluctuations and$$\unicode[STIX]{x1D70C}_{i}$$the ion gyroradius. The model includes integral operators corresponding to gyroaveraging as well as the moment equations relating fluid variables to the kinetic distribution function. A large variety of exact symmetries is uncovered, some of which have unexpected form. Using these results, new nonlinear solutions are constructed, including a helical generalization of the Chapman–Kendall solution for a collapsing current sheet.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Texas, Austin, TX (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Oak Ridge Associated Univ., Oak Ridge, TN (United States)

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

- OSTI Identifier:
- 1538936

- DOE Contract Number:
- FG02-04ER54742; FG02-91ER54109; SC0014664

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Plasma Physics

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 2; Journal ID: ISSN 0022-3778

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Physics

### Citation Formats

```
White, R. L., Hazeltine, R. D., and Loureiro, N. F.
```*Symmetries of a reduced fluid-gyrokinetic system*. United States: N. p., 2018.
Web. doi:10.1017/s0022377818000247.

```
White, R. L., Hazeltine, R. D., & Loureiro, N. F.
```*Symmetries of a reduced fluid-gyrokinetic system*. United States. doi:10.1017/s0022377818000247.

```
White, R. L., Hazeltine, R. D., and Loureiro, N. F. Wed .
"Symmetries of a reduced fluid-gyrokinetic system". United States. doi:10.1017/s0022377818000247.
```

```
@article{osti_1538936,
```

title = {Symmetries of a reduced fluid-gyrokinetic system},

author = {White, R. L. and Hazeltine, R. D. and Loureiro, N. F.},

abstractNote = {Symmetries of a fluid-gyrokinetic model are investigated using Lie group techniques. Specifically, the nonlinear system constructed by Zocco & Schekochihin (Phys. Plasmas, vol. 18, 2011, 102309), which combines nonlinear fluid equations with a drift-kinetic description of parallel electron dynamics, is studied. Significantly, this model is fully gyrokinetic, allowing for arbitrary$k_{\bot }\unicode[STIX]{x1D70C}_{i}$, where$k_{\bot }$is the perpendicular wave vector of the fluctuations and$\unicode[STIX]{x1D70C}_{i}$the ion gyroradius. The model includes integral operators corresponding to gyroaveraging as well as the moment equations relating fluid variables to the kinetic distribution function. A large variety of exact symmetries is uncovered, some of which have unexpected form. Using these results, new nonlinear solutions are constructed, including a helical generalization of the Chapman–Kendall solution for a collapsing current sheet.},

doi = {10.1017/s0022377818000247},

journal = {Journal of Plasma Physics},

issn = {0022-3778},

number = 2,

volume = 84,

place = {United States},

year = {2018},

month = {3}

}