It was shown in the first part to this paper how a simple magnetohydrodynamic model can be used to determine the stability of a tokamak plasma’s edge to peeling (external kink) modes. It was found that stability is determined by the value of , a normalized measure of the discontinuity in the radial derivative of the radial perturbation to the magnetic field at the plasma-vacuum interface. To avoid the possibility that numerical divergences near the -point might lead to misleading conclusions about plasma stability, this paper calculates the value of analytically. This is accomplished by showing that the method of conformal transformations can be applied to systems with a continuously varying nonzero boundary condition and using the technique to obtain analytical expressions for both the vacuum energy and . A conformal transformation is also used to obtain an equilibrium vacuum field surrounding a plasma with a separatrix and -point. This allows the analytical expressions for the vacuum energy and to be evaluated. The results here, combined with those in the first part of this paper, subsequently provide a quantitative description of the peeling mode’s growth rate as the plasma-vacuum boundary more closely approximates a separatrix with an -point.
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August 2009
Research Article|
August 17 2009
Magnetohydrodynamic stability at a separatrix. II. Determination by new conformal map technique
A. J. Webster
A. J. Webster
a)
Euratom/UKAEA Fusion Association,
Culham Science Centre
, Abingdon, Oxfordshire OX14 3DB, United Kingdom
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a)
Electronic mail: anthony.webster@ukaea.org.uk.
Phys. Plasmas 16, 082503 (2009)
Article history
Received:
January 26 2009
Accepted:
July 10 2009
Connected Content
A companion article has been published:
Magnetohydrodynamic stability at a separatrix. I. Toroidal peeling modes and the energy principle
Citation
A. J. Webster; Magnetohydrodynamic stability at a separatrix. II. Determination by new conformal map technique. Phys. Plasmas 1 August 2009; 16 (8): 082503. https://doi.org/10.1063/1.3194271
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