# Statistical simulation of the magnetorotational dynamo

## Abstract

We analyze turbulence and dynamo induced by the magnetorotational instability (MRI) using quasi-linear statistical simulation methods. We find that homogenous turbulence is unstable to a large scale dynamo instability, which saturates to an inhomogenous equilibrium with a very strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the quasi-linear model exhibits the same qualitative scaling of angular momentum transport with Pm as fully nonlinear turbulence. This demonstrates the relationship of recent convergence problems to the large scale dynamo and suggests possible methods for studying astrophysically relevant regimes at very low or high Pm.

- Authors:

- PPPL

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

- Contributing Org.:
- Princeton Plasma Physics Laboratory

- OSTI Identifier:
- 1182199

- Report Number(s):
- PPPL-5060

- DOE Contract Number:
- DE-AC02-09CH11466

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review letters

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; MRI instability; magnetic Prandtl number (Pm)

### Citation Formats

```
Squire, J., and Bhattacharjee, A.
```*Statistical simulation of the magnetorotational dynamo*. United States: N. p., 2014.
Web.

```
Squire, J., & Bhattacharjee, A.
```*Statistical simulation of the magnetorotational dynamo*. United States.

```
Squire, J., and Bhattacharjee, A. Fri .
"Statistical simulation of the magnetorotational dynamo". United States.
doi:. https://www.osti.gov/servlets/purl/1182199.
```

```
@article{osti_1182199,
```

title = {Statistical simulation of the magnetorotational dynamo},

author = {Squire, J. and Bhattacharjee, A.},

abstractNote = {We analyze turbulence and dynamo induced by the magnetorotational instability (MRI) using quasi-linear statistical simulation methods. We find that homogenous turbulence is unstable to a large scale dynamo instability, which saturates to an inhomogenous equilibrium with a very strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the quasi-linear model exhibits the same qualitative scaling of angular momentum transport with Pm as fully nonlinear turbulence. This demonstrates the relationship of recent convergence problems to the large scale dynamo and suggests possible methods for studying astrophysically relevant regimes at very low or high Pm.},

doi = {},

journal = {Physical Review letters},

number = ,

volume = ,

place = {United States},

year = {Fri Aug 01 00:00:00 EDT 2014},

month = {Fri Aug 01 00:00:00 EDT 2014}

}

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