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Title: High beta flux-conserving tokamaks

Abstract

Numerical and analytic studies have shown that plasmas subject to external heating will naturally seek high beta equilibria whose characteristics are determined by flux conservation. These equilibria can be characterized by broad pressure profiles and plasma currents peaked toward the plasma surface. They possess the same q profiles as the low beta equilibria from which the heating commences, and consequently have reasonable stability properties against local MHD modes. These equilibria are naturally noncircular and tend to approximate a D-shape with moderate elongation of roughly one and one-half. The technological requirements for sustaining such equilibria are not extreme. Their confinement characteristics are such that one can contemplate attaining ignition conditions in moderate-size plasmas. The one remaining factor which must be analyzed is the stability of these equilibria to MHD modes. In this regard, there is no reason to suspect difficulty at moderate beta. However, since these equilibria have the capability of attaining arbitrarily high beta as far as the equilibrium of the plasma is concerned, it is important to investigate the limitations imposed on maximum attainable beta by MHD stability theory.

Authors:
Publication Date:
Research Org.:
Oak Ridge National Lab., Tenn. (USA)
OSTI Identifier:
7344460
Report Number(s):
ORNL/TM-5429
TRN: 76-018644
DOE Contract Number:
W-7405-ENG-26
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; TOKAMAK DEVICES; BETA RATIO; MAGNETIC FLUX; EQUILIBRIUM; HIGH-BETA PLASMA; MAGNETOHYDRODYNAMICS; PLASMA MACROINSTABILITIES; CLOSED PLASMA DEVICES; FLUID MECHANICS; HYDRODYNAMICS; INSTABILITY; MECHANICS; PLASMA; PLASMA INSTABILITY; THERMONUCLEAR DEVICES; 700101* - Fusion Energy- Plasma Research- Confinement, Heating, & Production

Citation Formats

Clarke, J.F.. High beta flux-conserving tokamaks. United States: N. p., 1976. Web. doi:10.2172/7344460.
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Clarke, J.F.. High beta flux-conserving tokamaks. United States. doi:10.2172/7344460.
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Clarke, J.F.. Tue . "High beta flux-conserving tokamaks". United States. doi:10.2172/7344460. https://www.osti.gov/servlets/purl/7344460.
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@article{osti_7344460,
title = {High beta flux-conserving tokamaks},
author = {Clarke, J.F.},
abstractNote = {Numerical and analytic studies have shown that plasmas subject to external heating will naturally seek high beta equilibria whose characteristics are determined by flux conservation. These equilibria can be characterized by broad pressure profiles and plasma currents peaked toward the plasma surface. They possess the same q profiles as the low beta equilibria from which the heating commences, and consequently have reasonable stability properties against local MHD modes. These equilibria are naturally noncircular and tend to approximate a D-shape with moderate elongation of roughly one and one-half. The technological requirements for sustaining such equilibria are not extreme. Their confinement characteristics are such that one can contemplate attaining ignition conditions in moderate-size plasmas. The one remaining factor which must be analyzed is the stability of these equilibria to MHD modes. In this regard, there is no reason to suspect difficulty at moderate beta. However, since these equilibria have the capability of attaining arbitrarily high beta as far as the equilibrium of the plasma is concerned, it is important to investigate the limitations imposed on maximum attainable beta by MHD stability theory.},
doi = {10.2172/7344460},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Jun 01 00:00:00 EDT 1976},
month = {Tue Jun 01 00:00:00 EDT 1976}
}
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Technical Report:
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DOI:  10.2172/7344460
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  • ;
    Using Grad's theory of generalized differential equations, the temporal evolution from low to high ..beta.. due to ''adiabatic'' and nonadiabatic (i.e., neutral beam injection) heating of a cylindrical tokamak plasma with circular cross section and peaked current profiles is calculated analytically. The influence of shaping the initial safety factor profile and the beam deposition profile and the effect of minor radius compression on the equilibrium is analyzed.

  • ; ; ; ...
    The Flux Conserving Tokamak (FCT) model suggested that rapid heating would yield equilibria with high relative energy density (..beta.. = 2p/B/sup 2/) while nonetheless allowing control over q, the so-called safety factor for instability within the ideal magnetohydrodynamic (MHD) plasma model. In this study, we show that this is adequate to provide stability to ..beta.. values of 10%, if there is a conducting metal shell in the vicinity of the plasma.

  • Scenarios are worked out in straight circular cylindrical geometry for the evolution of flux conserving sequences of equilibria as the plasma is heated or compressed. It is shown that force-free currents are induced when the low pressure region at the edge of the plasma is compressed against a flux conserving wall. A force-free surface current is induced if there is a vacuum region between the expanding plasma and the wall. These edge currents run opposite to the direction of the current in the main body of the plasma. The force-free currents can be avoided or reversed at the edge ofmore » a plasma with diffuse resistivity profile by programming the total longitudinal current as the plasma is heated or compressed.« less

  • ; - Phys. Fluids; (United States)
    Using Grad's theory of generalized differential equations, the temporal evolution from low to high ..beta.. due to ''adiabatic'' and nonadiabatic (i.e., neutral beam injection) heating of a cylindrical tokamak plasma with circular cross section and peaked current profiles is calculated analytically. The influence of shaping the initial safety factor profile and the beam deposition profile and the effect of minor radius compression on the equilibrium is analyzed.

  • ;
    An approximate analytic theory is developed to calculate the poloidal beta ..beta../sub I/ and the diamagnetic parameter ..mu../sub I/ for a sequence of axisymmetric toroidal MHD equilibria confining high pressure plasmas (..beta.. approximately theta(a/R)) under the constraint of flux conservation. To satisfy the equilibrium equations, the plasma current must be increased with pressure as p/sup 1/3/ and previously calculated equilibrium limits on poloidal beta are avoided.