Toroidal rotation in tokamak plasmas

A comprehensive transport equation for the evolution of toroidal rotation in tokamak plasmas is developed self-consistently from the two-fluid momentum equations taking account of the constraints imposed by faster time scale processes. The resultant plasma toroidal rotation equation includes the effects of collision-induced perpendicular viscosities, anomalous transport due to microturbulence in the plasma, momentum sources and collision-based parallel viscous forces due to 3D non-axisymmetric (NA) magnetic field components produced by external fields and MHD-type instabilities in the plasma. Non-resonant NA fields produce a toroidal torque throughout the plasma that relaxes the toroidal flow to an 'intrinsic' or 'offset' ion-temperature-gradient diamagnetic-type flow in the direction counter to the plasma current. A NA resonant field error causes a toroidal torque localized near its rational surface. The combination of resonant and non-resonant NA field components is found to predict scalings for error field penetration and mode locking thresholds that are in closer agreement with empirical data from tokamak plasmas.