Tearing mode analysis in tokamaks, revisited Page: 5 of 34
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This fast convergence is tractable for developing a feedback stabilization scheme for control-
ling tearing modes in tokamak discharges.8
Finite pressure effects were ignored in the previous analyses by Furth et al.9 and Wesson.'0
This is due to the fractional power-like singularity that arises at the mode rational surface
when pressure gradient effects are present. Furthermore, difficulties arise in separating the
large and the small solutions near the rational surface." In this work, a different type of
numerical algorithm was employed (integrate out from the singular surface rather than into
it). The algorithm converges correctly in a high 3 (0 > 7%) regime for cylindrical geometry
(P represents the ratio between the plasma and magnetic pressure). To check the validity
of our computational results, we start (see Section III) by comparing our results with the
Furth et al.9 results for zero-pressure cases.
The effects of toroidal geometry are considered in this work. The effects can be sepa-
rated into (1) distortion of the flux surfaces due to the Shafranov shift; (2) the existence
of an averaged magnetic well; and (3) mode coupling effects due to the 1/R dependence of
the magnetic field which is neglected here. We have included (1) and (2), and obtained 0'
as a function of 0.12 The Shafranov shift appear as a global effect contribution that enters
through changes in the geometry metric elements. The second effect appears as a localized
property near the mode rational surface; we have included toroidal curvature (the Mercier
index'3) in the analysis, but have not included resistive layer effects." The mode coupling
effect can be neglected in the case of a rotating tokamak plasma where shear flows are large
and modes at different surfaces decouple.'
As an example of multi-helicity mode analysis by the shooting method, we present initial
results for double tearing modes that are considered as a cause of an off axis sawtooth in
the recent experiments of reversed shear discharge in TFTR.'6 The growth rate predicted
by A' is compared with that obtained from the toroidal magnetohydrodynamic initial value
code FAR.'7
This paper is organized as follows. In Sec. II the original definition and the physical
significance of A' is discussed. In Sec. III the basic model of Furth et al.9 for the exterior3
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Nishimura, Y.; Callen, J. D. & Hegna, C. C. Tearing mode analysis in tokamaks, revisited, report, December 1, 1997; United States. (https://digital.library.unt.edu/ark:/67531/metadc707744/m1/5/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.