Islands in the stream: The effect of plasma flow on tearing stability

Reducing plasma flow clearly decreases the stability of tearing modes in multiple regimes (sawtooth, hybrid) in both high- and low-aspect-ratio tokamaks (DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], Joint European Torus [M. Keilhacker and the JET Team, Plasma Phys. Controlled Fusion 41, 301 (1999)], National Spherical Torus Experiment [M. Ono, S. M. Kaye, Y.-K. M. Peng, Nucl. Fusion 40, 557 (2000)], each with distinct means of lessening rotation). Further, reducing flow makes pre-existing "saturated" islands larger at the same beta (beta). Thus lower plasma flow impairs high-beta operation owing both to the destabilization and to the impact of tearing-mode islands. Experimental results suggest that flow shear (not flow) at the tearing rational surface is classically stabilizing, making the effective tearing stability index Delta(') of the total current density profile more negative (more stable). In this picture, with profiles and all else the same, the minimum metastable beta at which neoclassical tearing modes (NTMs) can destabilize is proportional to -Delta(') and hence lower flow and flow shear lead to possible destabilization (depending on seeding) at lower beta. Similarly, if destabilized, the saturated NTM island width is proportional to -beta/Delta(') and thus increases as flow and flow shear are reduced. A working model gives a significant level of stabilizing shear if the plasma toroidal angular flow shear -d Omega(phi)/dr at a given rational surface is of order of the inverse of the product of the local values of the parallel magnetic shear length L-s and the Alfveacuten time tau(A). Experimental data are fitted for the effect of this normalization of flow shear in a simple empirical model for both onset and saturation of tearing modes. Most theoretical literature is on the consequence of flow shear on tearing stability at zero beta; tokamaks at high beta have large magnetic Prandtl number (an issue for the sign of the flow effect) and very large Lundquist number. It is in this regime that theory will be compared with experimentally based empirical models. The consequence for future tokamaks with low rotation may be lower tearing stability than now expected. (C) 2010 American Institute of Physics. [doi:10.1063/1.3333538]