Phenomenological theory of the kink instability in a slender plasma column
Abstract
In this paper we are concerned with the kink instability of a currentcarrying 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 KruskalShafranov 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; CHARGEDPARTICLE TRANSPORT; CURRENT DENSITY; DISTURBANCES; EIGENFUNCTIONS; EIGENVALUES; ELECTRIC CURRENTS; ELECTRODES; KINK INSTABILITY; PLASMA; PLASMA DENSITY; PLASMA SHEATH; ROTATION; SPATIAL DISTRIBUTION; STATISTICS; TWODIMENSIONAL CALCULATIONS; VECTORS
Citation Formats
Ryutov, D.D., Furno, I., Intrator, T.P., Abbate, S., MadziwaNussinov, 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., MadziwaNussinov, 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., MadziwaNussinov, 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 MadziwaNussinov, T. and Los Alamos National Laboratory, Los Alamos, New Mexico 87545},
abstractNote = {In this paper we are concerned with the kink instability of a currentcarrying 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 KruskalShafranov 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 nonideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and withmore »

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