Title: Magnetic feedback control of 2/1 locked modes in tokamaks
Description: This thesis presents simulation and experimental work on feedback control of the \emph{phase} of non-rotating magnetic islands (locked modes) in the DIII-D tokamak, as well as its application to synchronized modulated current drive, for stability studies and control of the locked mode \emph{amplitude}. A numerical model has been developed to predict mode dynamics under the effect of various electromagnetic torques, due to the interaction with induced currents in the wall, error fields, and applied resonant magnetic perturbations (RMPs). This model was adapted to predict entrainment capabilities on ITER, suggesting that small (5~cm) islands can be entrained in the sub-10~Hz frequency range. Simulations and subsequent experiments on DIII-D demonstrated a novel technique to prevent locked modes. Preemptive entrainment applies a rotating RMP before a neoclassical tearing mode fully decelerates such that it will be entrained by the RMP and mode rotation can be sustained. A feedback control algorithm was designed and implemented on DIII-D to offer the ability to prescribe any toroidal phase to the mode and to allow for smoother entrainment.

Experimental results confirmed simulation predictions of successful entrainment, and demonstrated one possible application to electron cyclotron current drive (ECCD). Feedback-controlled mode rotation and pre-programmed ECCD modulation were synchronized at DIII-D. This allowed a fine control of the ECCD deposition relative to the island O-point. Experiments exhibited a modulation of the saturated island width, in agreement with time-dependent modeling of the modified Rutherford equation. This work contributes to control and suppression of locked modes in future devices, including ITER.