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Eigenvalues of relaxed toroidal plasmas of arbitrary sharp edged cross sections. Vol. 2

Abstract

Relaxed (force-free) toroidal plasmas described by the equations cur 1 B={mu}B, and grad {mu}=O (B is the magnetic field) induces interest in nuclear fusion. Its solution is perceived to describe the gross of the reversed field pinch (RFP), spheromak configuration, current limitation in toroidal plasmas, and others. The parameter {mu} plays an important roll in relaxed states. It cannot exceed the smallest eigenvalue {mu} (min), and that for a toroidal discharge there is a maximum toroidal current which is connected to this value. The values of{mu} were calculated numerically, using the methods of collocation points, for toroids of arbitrary aspect ratio {alpha} ({alpha} = R/a, ratio of major/minor radii of tokamak) and arbitrary curved cross-sections (circle, ellipse, cassini, and D-shaped). The aim of present work is to prove the applicability of the numerical methods for calculating the eigenvalues for toroidal plasmas having sharp edged cross sections and arbitrary aspect ratio. The lowest eigenvalue {mu} (min), satisfy the boundary condition {beta} .n = O (or RB. = O) for which the toroidal flux are calculated. These are the zero field eigenvalues of the equation cur 1 b={mu}B. The poloidal magnetic field lines corresponding to different cross sections are shown by plotting  More>>
Authors:
Khalil, Sh M [1] 
  1. Plasma Physics and Nuclear Fusion Department, Nuclear Research Center, Atomic Energy Authority, Cairo, (Egypt)
Publication Date:
Mar 01, 1996
Product Type:
Miscellaneous
Report Number:
INIS-EG-002; CONF-960316-
Reference Number:
SCA: 700000; PA: AIX-28:032605; EDB-97:058842; SN: 97001766201
Resource Relation:
Conference: 6. conference of nuclear sciences and applications, Cairo (Egypt), 15-20 Mar 1996; Other Information: PBD: Mar 1996; Related Information: Is Part Of Proceedings of the sixth conference of nuclear sciences and applications. Vol. 1-4; PB: 1760 p.
Subject:
70 PLASMA PHYSICS AND FUSION; PLASMA; EIGENVALUES; ASPECT RATIO; CONFIGURATION; CROSS SECTIONS; MAGNETIC FIELDS; NUMERICAL DATA; REVERSE-FIELD PINCH; SPHEROMAK DEVICES
OSTI ID:
456153
Research Organizations:
Atomic Energy Establishment, Cairo (Egypt); Egyptian Society of Nuclear Sciences and Applications, Cairo (Egypt)
Country of Origin:
Egypt
Language:
English
Other Identifying Numbers:
Other: ON: DE97620041; TRN: EG9601758032605
Availability:
INIS; OSTI as DE97620041
Submitting Site:
INIS
Size:
pp. 252
Announcement Date:

Citation Formats

Khalil, Sh M. Eigenvalues of relaxed toroidal plasmas of arbitrary sharp edged cross sections. Vol. 2. Egypt: N. p., 1996. Web.
Khalil, Sh M. Eigenvalues of relaxed toroidal plasmas of arbitrary sharp edged cross sections. Vol. 2. Egypt.
Khalil, Sh M. 1996. "Eigenvalues of relaxed toroidal plasmas of arbitrary sharp edged cross sections. Vol. 2." Egypt.
@misc{etde_456153,
title = {Eigenvalues of relaxed toroidal plasmas of arbitrary sharp edged cross sections. Vol. 2}
author = {Khalil, Sh M}
abstractNote = {Relaxed (force-free) toroidal plasmas described by the equations cur 1 B={mu}B, and grad {mu}=O (B is the magnetic field) induces interest in nuclear fusion. Its solution is perceived to describe the gross of the reversed field pinch (RFP), spheromak configuration, current limitation in toroidal plasmas, and others. The parameter {mu} plays an important roll in relaxed states. It cannot exceed the smallest eigenvalue {mu} (min), and that for a toroidal discharge there is a maximum toroidal current which is connected to this value. The values of{mu} were calculated numerically, using the methods of collocation points, for toroids of arbitrary aspect ratio {alpha} ({alpha} = R/a, ratio of major/minor radii of tokamak) and arbitrary curved cross-sections (circle, ellipse, cassini, and D-shaped). The aim of present work is to prove the applicability of the numerical methods for calculating the eigenvalues for toroidal plasmas having sharp edged cross sections and arbitrary aspect ratio. The lowest eigenvalue {mu} (min), satisfy the boundary condition {beta} .n = O (or RB. = O) for which the toroidal flux are calculated. These are the zero field eigenvalues of the equation cur 1 b={mu}B. The poloidal magnetic field lines corresponding to different cross sections are shown by plotting the boundary condition B.n=O. The plots showed good fulfillment of the boundary condition along the whole boundaries of different cross sections. Dependence of eigenvalues {mu}a on aspect ratio {alpha} is also obtained. Several runs of the programme with various wave numbers K showed that {mu}a is very insensitive to the choice of K. 8 figs.}
place = {Egypt}
year = {1996}
month = {Mar}
}