Critical error fields for locked mode instability in tokamaks

Abstract

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.

Effect of resonant helical magnetic fields on plasma rotation

“…(a) Helical field penetration: For the plasma being originally stable to tearing modes, an applied resonant helical field (or error fields of experimental devices) can penetrate through the resonant surface and generate a magnetic island there [1][2][3][4][5][6][7][8][9]. Recently it was shown on TEXTOR that the relative frequency between the mode and the helical field is important in determining the field penetration [5,6], being in agreement with theoretical results [7][8][9].…”

Importance of plasma response to nonaxisymmetric perturbations in tokamaks

“…However, the relation is more complicated in tokamak plasmas, because of shielding or amplification, and poloidal harmonic coupling. Experiments have found that the critical amplitudes of the external field or the external current are approximately linear with locking densities [1][2][3][4][5][6], and also some theories have expected the positive correlation between the critical field and the locking density [10][11][12][13]. However, the approximation of the external resonant field for the resonant field driving islands has been often unsuccessful to find the correlation.…”

“…However, a significant degradation of performance in tokamak plasmas are observed for nonaxisymmetric magnetic perturbations as small as δB/B 0 ∼ 10 −4 . [1][2][3][4][5][6]. Tokamaks are difficult to build without such small errors.…”

Shielding of external magnetic perturbations by torque in rotating tokamak plasmas

“…The energy δW = (1/2) δ j ·δ Ad 3 x and the toroidal torque 3 x are produced by external perturbations, where δ j is the perturbed current, δ A is the perturbed vector potential, δ B is the perturbed field, andẑ is the symmetry axis of the tokamak. By integrating by parts for δW and τ ϕ , the perturbed energy and torque can be related to the total normal field at the boundary and the external currents producing the total normal field.…”