Characteristics of Neoclassical Toroidal Viscosity in NSTX and KSTAR for Rotation Control and the Evaluation of Plasma Response

Three-dimensional magnetic fields producing non-resonant magnetic braking allow control of the plasma rotation profile, $\omega_{\varphi}$, in tokamaks. Experimental angular momentum alteration created by 3D field configurations with dominant $n = $ 2 and $n$~$=$~3 components in NSTX is compared to theoretical neoclassical toroidal viscosity (NTV) torque density profiles, $T_{NTV}$. Large radial variations of $T_{NTV}$ are typically found when flux surface displacements are computed using ideal MHD assumptions. In contrast, experimentally measured $T_{NTV}$ does not show strong torque localization. This may be explained by ion banana width orbit-averaging effects. A favorable characteristic for $\omega_{\varphi}$ control clearly illustrated by KSTAR experiments is the lack of hysteresis of $\omega_{\varphi}$ when altered by non-resonant NTV. Results from a model-based rotation controller designed using NBI and NTV from the applied 3D field as actuators are shown. The dependence of $T_{NTV}$ on $\delta $\textbf{\textit{B}}$^{2}$ significantly constrains the allowable field amplification in plasma response models when compared to experiment. Initial analysis shows that the single fluid model in the M3D-C$^{1}$ resistive MHD code produces a flux surface-averaged $\delta $\textbf{\textit{B}} consistent with the experimentally measured $T_{NTV}$.