# Phenomenological theory of the kink instability in a slender plasma column

## Abstract

In this paper we are concerned with the kink instability of a current-carrying plasma column whose radius a is much smaller than its length L. In the limit a<<L, one can consider the column as a thin filament whose kinking can be adequately described simply by a two dimensional 2D displacement vector, {xi}{sub x}={xi}{sub x}(z,t); {xi}{sub y}={xi}{sub y}(z,t). Details of the internal structure of the column such as the radial distribution of the current, density, and axial flow can be lumped into some phenomenological parameters. This approach is particularly efficient in the problems with nonideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and with a substantial axial flow. With the sheath BC imposed at one of the endplates, we find instability in the domain well below the classical Kruskal-Shafranov limit. The presence of an axial flow causes the onset of rotation of the kink and strong axial 'skewness' of the eigenfunction, with the perturbation amplitude increasing in the flow direction. The limitations of the phenomenological approach are analyzed and are related to the steepness with which the plasma resistivity increases at the plasma boundary with vacuum.

- Authors:

- Lawrence Livermore National Laboratory, Livermore, California 94551 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20782540

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 3; Other Information: DOI: 10.1063/1.2180667; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; ASYMMETRY; BOUNDARY CONDITIONS; CHARGED-PARTICLE TRANSPORT; CURRENT DENSITY; DISTURBANCES; EIGENFUNCTIONS; EIGENVALUES; ELECTRIC CURRENTS; ELECTRODES; KINK INSTABILITY; PLASMA; PLASMA DENSITY; PLASMA SHEATH; ROTATION; SPATIAL DISTRIBUTION; STATISTICS; TWO-DIMENSIONAL CALCULATIONS; VECTORS

### Citation Formats

```
Ryutov, D.D., Furno, I., Intrator, T.P., Abbate, S., Madziwa-Nussinov, T., and Los Alamos National Laboratory, Los Alamos, New Mexico 87545.
```*Phenomenological theory of the kink instability in a slender plasma column*. United States: N. p., 2006.
Web. doi:10.1063/1.2180667.

```
Ryutov, D.D., Furno, I., Intrator, T.P., Abbate, S., Madziwa-Nussinov, T., & Los Alamos National Laboratory, Los Alamos, New Mexico 87545.
```*Phenomenological theory of the kink instability in a slender plasma column*. United States. doi:10.1063/1.2180667.

```
Ryutov, D.D., Furno, I., Intrator, T.P., Abbate, S., Madziwa-Nussinov, T., and Los Alamos National Laboratory, Los Alamos, New Mexico 87545. Wed .
"Phenomenological theory of the kink instability in a slender plasma column". United States.
doi:10.1063/1.2180667.
```

```
@article{osti_20782540,
```

title = {Phenomenological theory of the kink instability in a slender plasma column},

author = {Ryutov, D.D. and Furno, I. and Intrator, T.P. and Abbate, S. and Madziwa-Nussinov, T. and Los Alamos National Laboratory, Los Alamos, New Mexico 87545},

abstractNote = {In this paper we are concerned with the kink instability of a current-carrying plasma column whose radius a is much smaller than its length L. In the limit a<<L, one can consider the column as a thin filament whose kinking can be adequately described simply by a two dimensional 2D displacement vector, {xi}{sub x}={xi}{sub x}(z,t); {xi}{sub y}={xi}{sub y}(z,t). Details of the internal structure of the column such as the radial distribution of the current, density, and axial flow can be lumped into some phenomenological parameters. This approach is particularly efficient in the problems with nonideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and with a substantial axial flow. With the sheath BC imposed at one of the endplates, we find instability in the domain well below the classical Kruskal-Shafranov limit. The presence of an axial flow causes the onset of rotation of the kink and strong axial 'skewness' of the eigenfunction, with the perturbation amplitude increasing in the flow direction. The limitations of the phenomenological approach are analyzed and are related to the steepness with which the plasma resistivity increases at the plasma boundary with vacuum.},

doi = {10.1063/1.2180667},

journal = {Physics of Plasmas},

number = 3,

volume = 13,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}