Critical error fields for locked mode instability in tokamaks

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 COMPASS-C [Proceedings of the 18th European Conference on Controlled Fusion and Plasma Physics, Berlin (EPS, Petit-Lancy, Switzerland, 1991), Vol. 15C, Part II, p. 61]. Experiments in Ohmically heated deuterium discharges with q≊3.5, n̄ ≊ 2 × 1019 m−3 and BT ≊ 1.2 T show that a much larger relative error field (Br21/BT ≊ 1 × 10−3) is required to produce a locked mode in the small, rapidly rotating plasma of COMPASS-C (R0 = 0.56 m, f≊13 kHz) than in the medium-sized plasmas of DIII-D (R0 = 1.67 m, f≊1.6 kHz), where the critical relative error field is Br21/BT ≊ 2 × 10−4. 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 (fR0/BT)4/3n̄2/3. 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 (1990)] (f=0.17 kHz, R0 = 6.0 m, BT = 4.9 T, n̄ = 2 × 1019 m−3) is Br21/BT ≊ 2 × 10−5. 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.