Tearing mode analysis in tokamaks, revisited Page: 4 of 34
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Understanding resistive magnetohydrodynamic (MHD) stability is important for long pulse
tokamak operations, since tearing modes form magnetic islands, and if islands of incommen-
surate helicity overlap, they can induce plasma disruptions.1 Also, the existence of a single
helicity magnetic island can deteriorate plasma confinement due to the change in magnetic
field line topology.2', In resistive MHD, tearing mode stability is determined by a parameter
delta prime (A'), which was first defined by Furth et al.;4 a positive A' implies instability.
Recently, A' was measured in Tokamak Test Fusion Reactor (TFTR) supershot plasma ex-
periments through an analysis of electron temperature fluctuations.5 It has been shown that
when m/n = 2/1 modes are present, A' > 0. This can be explained by classical tearing
mode theory. On the other hand, A' is observed to be negative for cases with m/n = 3/2
and m/n = 4/3 modes, which indicates the presence of destabilizing neoclassical effects.'
The qualitative framework of tearing mode theory seems to be well established.
In toroidal tokamak plasmas, Fourier harmonics of tearing modes are correlated to each
other, both through the poloidal mode coupling and nonlinear effects. These couplings can
play an important role in destabilizing the modes on magnetic surfaces of incommensurate
helicity. The final goal of our research is to investigate such a multi-mode coupled system,
for example, as pursued in the PEST-3 code.7 However, quantitative determination of the
tearing mode stability parameter A' still remains an essential issue: a precise prediction
of stability becomes important, especially when the tearing modes are marginally stable
(IA'l < 0). The value of A' is sensitive to the local current gradient even in the single helic-
ity case. For the purpose of seeking optimized discharge current profiles for the experiments
and simultaneous feedback control,' it is important to understand and clarify the nature of
the numerical procedures that correctly relate A' to the current profile.
A shooting-type code9 for determining the perturbed helical flux profile and hence A' is
compact, intuitively straightforward, and has fast convergence. Obtaining a A' value for a
single helicity case takes less than a second of cpu-time on nominal workstation computers.
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Nishimura, Y.; Callen, J.D. & Hegna, C.C. Tearing mode analysis in tokamaks, revisited, report, December 1, 1997; United States. (digital.library.unt.edu/ark:/67531/metadc707744/m1/4/: accessed November 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.