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Title: 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:
; ; ; ;  [1];  [2]
  1. Lawrence Livermore National Laboratory, Livermore, California 94551 (United States)
  2. (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}
}
  • When one deals with a plasma column whose radius a is much smaller than its length L, one can think of it as of a thin filament whose kink instability can be adequately described simply by a 2D displacement vector, {xi}{sub x} = {xi}{sub s}(z,t); {xi}{sub y} = {xi}{sub y}(z,t). Details of the internal structure of the column such as the current, density, and axial flow velocity distribution would be lumped into some phenomenological parameters. This approach is particularly efficient in the problems with non-ideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and withmore » a substantial axial flow. With the sheath BC imposed at one of the end-plates, 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. We consider the limitations of the phenomenological approach and find that they are related to the steepness with which the plasma resistivity increases at the plasma boundary with vacuum.« less
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  • An experimental investigation of the kink instability is presented in a linear plasma column where one end is line-tied to the plasma source, and the other end is not line-tied and therefore free to slide over the surface of the end-plate. This latter boundary condition is a result of plasma sheath resistance that insulates, at least partially, the plasma from the end-plate. The helical m = 1 kink mode is observed to grow when the plasma current exceeds a threshold and, close to the criticality, is characterized by an axial mode structure with maximum displacement at the free axial boundary.more » Azimuthal rotation of the mode is observed such that the helically kinked column always screws into the free axial boundary. The kink mode structure, rotation frequency and instability threshold are accurately reproduced by a recent kink theory [D. D. Ryutov, et al., Phys. Plasmas 13, 032105 (2006)], which includes axial plasma flow and one end of the plasma column that is free to move due to a perfect non-line-tying boundary condition which is experimentally verified. A brief review of the kink theory and its predictions for the boundary conditions relevant in the present experiments are presented.« less
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