# Theory of critical balance in plasma turbulence

## Abstract

Critical balance, a statement of the approximate equality of a timescale of motion parallel to the magnetic field with a timescale of turbulent motion perpendicular to the field, is analyzed from a statistical description of the relative motion of two particles consistent with two-point correlation in a nonlinear gyrokinetic system with collisions. Critical balance is understood from a premise that the fastest time to any spatial scale that encounters decorrelated motions sets an overall correlation time for both perpendicular and parallel scales. For a regime of weak collisionality, this leads to the approximate equality of the parallel streaming time and the perpendicular turbulent correlation time, which is a standard statement of critical balance. These two timescales are only approximately equal because of effects in parallel streaming dynamics and collisions, the former producing deviations tied to variations of perpendicular and parallel wavenumbers. Finally, analysis of a collisional regime shows that critical balance also applies in that limit with a modified relation between parallel and perpendicular spatial scales.

- Authors:

- Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics

- Publication Date:

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

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

- OSTI Identifier:
- 1540238

- Grant/Contract Number:
- [FG02-89ER53291]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- [ Journal Volume: 25; Journal Issue: 9]; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; physics

### Citation Formats

```
Terry, P. W. Theory of critical balance in plasma turbulence. United States: N. p., 2018.
Web. doi:10.1063/1.5041754.
```

```
Terry, P. W. Theory of critical balance in plasma turbulence. United States. doi:10.1063/1.5041754.
```

```
Terry, P. W. Wed .
"Theory of critical balance in plasma turbulence". United States. doi:10.1063/1.5041754. https://www.osti.gov/servlets/purl/1540238.
```

```
@article{osti_1540238,
```

title = {Theory of critical balance in plasma turbulence},

author = {Terry, P. W.},

abstractNote = {Critical balance, a statement of the approximate equality of a timescale of motion parallel to the magnetic field with a timescale of turbulent motion perpendicular to the field, is analyzed from a statistical description of the relative motion of two particles consistent with two-point correlation in a nonlinear gyrokinetic system with collisions. Critical balance is understood from a premise that the fastest time to any spatial scale that encounters decorrelated motions sets an overall correlation time for both perpendicular and parallel scales. For a regime of weak collisionality, this leads to the approximate equality of the parallel streaming time and the perpendicular turbulent correlation time, which is a standard statement of critical balance. These two timescales are only approximately equal because of effects in parallel streaming dynamics and collisions, the former producing deviations tied to variations of perpendicular and parallel wavenumbers. Finally, analysis of a collisional regime shows that critical balance also applies in that limit with a modified relation between parallel and perpendicular spatial scales.},

doi = {10.1063/1.5041754},

journal = {Physics of Plasmas},

number = [9],

volume = [25],

place = {United States},

year = {2018},

month = {9}

}

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