Feedforward and feedback control of locked mode phase and rotation in DIII-D with application to modulated ECCD experiments

The toroidal phase and rotation of otherwise locked magnetic islands of toroidal mode number n = 1 are controlled in the DIII-D tokamak by means of applied magnetic perturbations of n = 1. Pre-emptive perturbations were applied in feedforward to 'catch' the mode as it slowed down and entrain it to the rotating field before complete locking, thus avoiding the associated major confinement degradation. Additionally, for the first time, the phase of the perturbation was optimized in real-time, in feedback with magnetic measurements, in order for the mode's phase to closely match a prescribed phase, as a function of time. Experimental results confirm the capability to hold the mode in a given fixed-phase or to rotate it at up to 20 Hz with good uniformity. The control-coil currents utilized in the experiments agree with the requirements estimated by an electromechanical model. Moreover, controlled rotation at 20 Hz was combined with electron cyclotron current drive (ECCD) modulated at the same frequency. This is simpler than regulating the ECCD modulation in feedback with spontaneous mode rotation, and enables repetitive, reproducible ECCD deposition at or near the island O-point, X-point and locations in between, for careful studies of how this affects the island stability. Current drive was found to be radially misaligned relative to the island, and resulting growth and shrinkage of islands matched expectations of the modified Rutherford equation for some discharges presented here. Finally, simulations predict the as designed ITER 3D coils can entrain a small island at sub-10 Hz frequencies.