# A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma

## Abstract

A two-fluid, neoclassical theory of the interaction of a single magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. The plasmas typically found in large hot tokamaks lie in the so-called weak neoclassical flow-damping regime in which the neoclassical ion stress tensor is not the dominant term in the ion parallel equation of motion. Nevertheless, flow-damping in such plasmas dominates ion perpendicular viscosity, and is largely responsible for determining the phase velocity of a freely rotating island chain (which is in the ion diamagnetic direction relative to the local **E** × **B** frame at the rational surface). The critical vacuum island width required to lock the island chain is mostly determined by the ion neoclassical poloidal flow damping rate at the rational surface. The stabilizing effect of the average field-line curvature, as well as the destabilizing effect of the perturbed bootstrap current, is the same for a freely rotating, a non-uniformly rotating, and a locked island chain. The destabilizing effect of the error-field averages to zero when the chain is rotating and only manifests itself when the chain locks. The perturbed ion polarization current has a small destabilizing effect on a freely rotating islandmore »

- Authors:

- Univ. of Texas, Austin, TX (United States). Dept. of Physics, Inst. for Fusion Studies

- Publication Date:

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

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

- OSTI Identifier:
- 1540170

- Alternate Identifier(s):
- OSTI ID: 1431393

- Grant/Contract Number:
- FG02-04ER-54742

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 4; 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

```
Fitzpatrick, Richard. A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma. United States: N. p., 2018.
Web. doi:10.1063/1.5022685.
```

```
Fitzpatrick, Richard. A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma. United States. doi:10.1063/1.5022685.
```

```
Fitzpatrick, Richard. Thu .
"A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma". United States. doi:10.1063/1.5022685. https://www.osti.gov/servlets/purl/1540170.
```

```
@article{osti_1540170,
```

title = {A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma},

author = {Fitzpatrick, Richard},

abstractNote = {A two-fluid, neoclassical theory of the interaction of a single magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. The plasmas typically found in large hot tokamaks lie in the so-called weak neoclassical flow-damping regime in which the neoclassical ion stress tensor is not the dominant term in the ion parallel equation of motion. Nevertheless, flow-damping in such plasmas dominates ion perpendicular viscosity, and is largely responsible for determining the phase velocity of a freely rotating island chain (which is in the ion diamagnetic direction relative to the local E × B frame at the rational surface). The critical vacuum island width required to lock the island chain is mostly determined by the ion neoclassical poloidal flow damping rate at the rational surface. The stabilizing effect of the average field-line curvature, as well as the destabilizing effect of the perturbed bootstrap current, is the same for a freely rotating, a non-uniformly rotating, and a locked island chain. The destabilizing effect of the error-field averages to zero when the chain is rotating and only manifests itself when the chain locks. The perturbed ion polarization current has a small destabilizing effect on a freely rotating island chain, but a large destabilizing effect on both a non-uniformly rotating and a locked island chain. Finally, this behavior may account for the experimentally observed fact that locked island chains are much more unstable than corresponding freely rotating chains.},

doi = {10.1063/1.5022685},

journal = {Physics of Plasmas},

number = 4,

volume = 25,

place = {United States},

year = {2018},

month = {4}

}

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