Effect of Resonant and Non-resonant Magnetic Braking on Error Field Tolerance in High Beta Plasmas

Tokamak plasmas become less tolerant to externally applied non-axisymmetric magnetic “error” fields as beta increases, due to a resonant interaction of the non-axisymmetric field with a stable € n =1 kink mode. Similar to observations in low beta plasmas, the limit to tolerable € n =1 magnetic field errors in neutral beam injection heated H-mode plasmas is seen as a bifurcation in the torque balance, which is followed by error field driven locked modes and severe confinement degradation or a disruption. The error field tolerance is, therefore, largely determined by the braking torque resulting from the non-axisymmetric magnetic field. DIII-D experiments distinguish between a resonant-like torque, which decreases with increasing rotation, and a nonresonant-like torque, which increases with increasing rotation. While only resonant braking leads to a rotation collapse, modeling shows that non-resonant components can lower the tolerance to resonant components. The strong reduction of the error field tolerance with increasing beta, which has already been observed in early high beta experiments in DIII-D [R.J. La Haye, et al., Nucl. Fusion 32, 2119 (1992)], is linked to an increasing resonant field amplification resulting from a stable kink mode [A.H. Boozer, Phys. Rev. Lett. 86, 5059 (2001)]. The amplification of externally applied € n =1 fields is measured with magnetic pick-up coils and seen to increase with beta, with the increase accelerating above the no wall ideal MHD stability limit, where the ideal MHD stable kink mode converts to a kinetically stabilized resistive wall mode. The beta dependence was not previously appreciated, and was not included in the empirical scaling of the error field tolerance reported in the 1999 IPB [ITER Physics Basis, Nucl. Fusion 39, 2137 (1999)] leading to overly optimistic predictions for low torque, high beta scenarios. However, the measurable increase of the plasma response with beta can be exploited for “dynamic” correction (i.e. with slow magnetic feedback) of the amplified error field.