# Numerical simulation of laminar plasma dynamos in a cylindrical von Karman flow

## Abstract

The results of a numerical study of the magnetic dynamo effect in cylindrical von Karman plasma flow are presented with parameters relevant to the Madison Plasma Couette Experiment. This experiment is designed to investigate a broad class of phenomena in flowing plasmas. In a plasma, the magnetic Prandtl number Pm can be of order unity (i.e., the fluid Reynolds number Re is comparable to the magnetic Reynolds number Rm). This is in contrast to liquid metal experiments, where Pm is small (so, Re>>Rm) and the flows are always turbulent. We explore dynamo action through simulations using the extended magnetohydrodynamic NIMROD code for an isothermal and compressible plasma model. We also study two-fluid effects in simulations by including the Hall term in Ohm's law. We find that the counter-rotating von Karman flow results in sustained dynamo action and the self-generation of magnetic field when the magnetic Reynolds number exceeds a critical value. For the plasma parameters of the experiment, this field saturates at an amplitude corresponding to a new stable equilibrium (a laminar dynamo). We show that compressibility in the plasma results in an increase of the critical magnetic Reynolds number, while inclusion of the Hall term in Ohm's law changesmore »

- Authors:

- University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706 (United States)
- University of New Hampshire, 8 College Road, Durham, New Hampshire 03824 (United States)

- Publication Date:

- OSTI Identifier:
- 21537270

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 3; Other Information: DOI: 10.1063/1.3559472; (c) 2011 American Institute of Physics; Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPUTERIZED SIMULATION; COUETTE FLOW; LAMINAR FLOW; MAGNETIC REYNOLDS NUMBER; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA SIMULATION; PRANDTL NUMBER; DIMENSIONLESS NUMBERS; FLUID FLOW; FLUID MECHANICS; HYDRODYNAMICS; MECHANICS; REYNOLDS NUMBER; SIMULATION; VISCOUS FLOW

### Citation Formats

```
Khalzov, I. V., Brown, B. P., Schnack, D. D., Forest, C. B., and Ebrahimi, F.
```*Numerical simulation of laminar plasma dynamos in a cylindrical von Karman flow*. United States: N. p., 2011.
Web. doi:10.1063/1.3559472.

```
Khalzov, I. V., Brown, B. P., Schnack, D. D., Forest, C. B., & Ebrahimi, F.
```*Numerical simulation of laminar plasma dynamos in a cylindrical von Karman flow*. United States. doi:10.1063/1.3559472.

```
Khalzov, I. V., Brown, B. P., Schnack, D. D., Forest, C. B., and Ebrahimi, F. Tue .
"Numerical simulation of laminar plasma dynamos in a cylindrical von Karman flow". United States. doi:10.1063/1.3559472.
```

```
@article{osti_21537270,
```

title = {Numerical simulation of laminar plasma dynamos in a cylindrical von Karman flow},

author = {Khalzov, I. V. and Brown, B. P. and Schnack, D. D. and Forest, C. B. and Ebrahimi, F.},

abstractNote = {The results of a numerical study of the magnetic dynamo effect in cylindrical von Karman plasma flow are presented with parameters relevant to the Madison Plasma Couette Experiment. This experiment is designed to investigate a broad class of phenomena in flowing plasmas. In a plasma, the magnetic Prandtl number Pm can be of order unity (i.e., the fluid Reynolds number Re is comparable to the magnetic Reynolds number Rm). This is in contrast to liquid metal experiments, where Pm is small (so, Re>>Rm) and the flows are always turbulent. We explore dynamo action through simulations using the extended magnetohydrodynamic NIMROD code for an isothermal and compressible plasma model. We also study two-fluid effects in simulations by including the Hall term in Ohm's law. We find that the counter-rotating von Karman flow results in sustained dynamo action and the self-generation of magnetic field when the magnetic Reynolds number exceeds a critical value. For the plasma parameters of the experiment, this field saturates at an amplitude corresponding to a new stable equilibrium (a laminar dynamo). We show that compressibility in the plasma results in an increase of the critical magnetic Reynolds number, while inclusion of the Hall term in Ohm's law changes the amplitude of the saturated dynamo field but not the critical value for the onset of dynamo action.},

doi = {10.1063/1.3559472},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 3,

volume = 18,

place = {United States},

year = {2011},

month = {3}

}