New experiments on COMPASS-D, DIII-D and JET have identified the critical scalings of error field sensitivity and harmonic content effects, enabling predictions of the requirements for larger devices such as ITER. Thresholds are lowest at low density, a regime proposed for H mode access on ITER. Results suggest a moderate error field sensitivity (δB/B~10-4) for ITER, comparable with the size of its intrinsic error, although there are uncertainties in scaling behaviour. Other studies on COMPASS-D and DIII-D show that sideband harmonics to the (2,1) component play an important role. Thus a correction system for ITER will be important, with flexibility to correct sidebands desirable, possibly assisted by beam rotation. Such a system has been designed and is capable of reducing multiple harmonic error levels to ~2×10-5 .

A set of external coils (A-coils) capable of producing nonaxisymmetric, predominantly n=1, fields with different toroidal phase and a range of poloidal mode m spectra has been used to determine the threshold amplitude for mode locking over a range of plasma parameters in Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda, P. Bonoli, S. Fairfax, C. Fiore, J. Goetz, S. Golovato, R. Granetz, M. Greenwald et al., Phys. Plasmas 1, 1511 (1994)]. The threshold perturbations and parametric scalings, expressed in terms of (B21∕BT), are similar to those observed on larger, lower field devices. The threshold is roughly linear in density, with typical magnitudes of order 10−4. This result implies that locked modes should not be significantly more problematic for the International Thermonuclear Experimental Reactor [I. P. B. Editors, Nucl. Fusion 39, 2286 (1999)] than for existing devices. Coordinated nondimensional identity experiments on the Joint European Torus [Fusion Technol. 11, 13 (1987)], DIII-D [Fusion Technol. 8, 441 (1985)], and C-Mod, with matching applied mode spectra, have been carried out to determine more definitively the field and size scalings. Locked modes on C-Mod are observed to result in braking of core toroidal rotation, modification of sawtooth activity, and significant reduction in energy and particle confinement, frequently leading to disruptions. Intrinsic error fields inferred from the threshold studies are found to be consistent in amplitude and phase with a comprehensive model of the sources of field errors based on “as-built” coil and bus-work details and coil imperfections inferred from measurements using in situ magnetic diagnostics on dedicated test pulses. Use of the A-coils to largely cancel the 2∕1 component of the intrinsic nonaxisymmetric field has led to expansion of the accessible operating space in C-Mod, including operation up to 2 MA plasma current at 8 T.

Abstract. Using resonant magnetic perturbations with toroidal mode number n = 3, we have produced H-mode discharges without edge localized modes (ELMs) which run with constant density and radiated power for periods up to about 2550 ms (17 energy confinement times). These ELM suppression results are achieved at pedestal collisionalities close to those desired for next step burning plasma experiments such as ITER and provide a means of eliminating the rapid erosion of divertor components in such machines which could be caused by giant ELMs. The ELM suppression is due to an enhancement in the edge particle transport which reduces the edge pressure gradient and pedestal current density below the threshold for peeling-ballooning modes. These n = 3 magnetic perturbations provide a means of active control of edge plasma transport.2

Otherwise stable discharges can become nonlinearly unstable to disruptive locked modes when subjected to a resonant m =2, n= 1 error field from irregular poloidal field coils, as in DIII-D [Nucl. Fusion 31, 875 (1991)], or from resonant magnetic perturbation coils as in Experiments in Ohmically heated deuterium discharges with q-3.5, n z 2 x 1019 me3 and BT z 1.2 T show that a much larger relative error field (Br21/BT =: 1 X 10e3) is required to produce a locked mode in the small, rapidly rotating plasma of COMPASS-C (Re = 0.56 m, f z 13 kHz) than in the medium-sized plasmas of DIII-D (Re = 1.67 m, f z 1.6 kHz), where the critical relative error field is Brzl/BT =: 2 X 10m4. This dependence of the threshold for instability is explained by a nonlinear tearing theory of the interaction of resonant magnetic perturbations with rotating plasmas that predicts the critical error field scales as (fRo/BT)4'3i?'3. Extrapolating from existing devices, the predicted critical field for locked modes in Ohmic discharges on the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 30, 1183] (f=O.17 kHz, Rc = 6.0 m, BT = 4.9 T, ii = 2 X 1019 mm3) is &I/BT = 2 X lo-'. Such error fields could be produced by shifts and/or tilts of only one of the larger poloidal field coils of as little as 0.6 cm with respect to the toroidal field. A means to increase the rotation frequency would obviate the sensitivity to error fields and increase allowable tolerances on coil construction.

͑2000͔͒ reveal the commonalities of resistive wall mode ͑RWM͒ stabilization by sufficiently fast toroidal plasma rotation in devices of different size and aspect ratio. In each device the weakly damped n = 1 RWM manifests itself by resonant field amplification ͑RFA͒ of externally applied n = 1 magnetic fields, which increases with the plasma pressure. Probing DIII-D and JET plasmas with similar ideal magnetohydrodynamic ͑MHD͒ stability properties with externally applied magnetic n = 1 fields, shows that the resulting RFA is independent of the machine size. In each device the drag resulting from RFA slows the toroidal plasma rotation and can lead to the onset of an unstable RWM. The critical plasma rotation required for stable operation in the plasma center decreases with increasing q 95 , which is explained by the inward shift of q surfaces where the critical rotation remains constant. The quantitative agreement of the critical rotation normalized to the inverse Alfvén time at the q = 2 surface in similar DIII-D and JET plasmas supports the independence of the RWM stabilization mechanism of machine size and indicates the importance of the q = 2 surface. At low aspect ratio the required fraction of the Alfvén velocity increases significantly. The ratio of the critical rotation in similar NSTX and DIII-D plasmas can be explained by trapped particles not contributing to the RWM stabilization, which is consistent with stabilization mechanisms that are based on ion Landau damping. Alternatively, the ratio of the required rotation to the sound wave velocity remains independent of aspect ratio.