Plasma Rotation and Radial Electric Field Response to Resonant Magnetic Perturbations in DIII-D

Analysis of DIII-D experiments have revealed a complex picture of the evolution of the toroidal rotation $v_{tor}$ and radial electric field $E_r$ when applying edge resonant magnetic perturbations (RMPs) in H-mode plasmas. Measurements indicate that RMPs induce changes to the plasma rotation and $E_r$ across the plasma profile, well into the plasma core where islands or stochasticity are not expected. In the pedestal, the change in $E_r$ comes primarily from the $v\times B$ changes even though the ion diamagnetic contribution to $E_r$ is larger. This allows the RMP to change $E_r$ faster than the transport timescale for altering the pressure gradient. For $n=3$ RMPs, the pedestal $v_{tor}$ goes to zero as fast as the RMP current rises, suggesting increased toroidal viscosity with the RMP, followed by a slow rise in co-plasma current $v_{tor}$ (pedestal ``spin-up'') as the pedestal density pumps out. This spin-up could result from a reduction in ELM-induced momentum transport or a resonant $j\times B$ torque due to radial current. As $v_{tor}$ becomes more positive and the pressure pedestal narrows, the electron perpendicular rotation $\sim$0 point moves out toward the top of the pedestal; increasing the RMP current moves this crossing point closer to the top of the pedestal. These changes reduce the mean $E\times B$ shearing rate across the outer half of the discharge from several times the linear growth rate for intermediate-scale turbulence to less than the linear growth rate, consistent with increased turbulent transport. Full-f kinetic simulations with self-consistent plasma response and $E_r$ using the XGC0 code have qualitatively reproduced the observed profile and $E_r$ changes. These results suggest that similar to their role in regulating H-mode plasma transport and stability, plasma rotation and $E_r$ play a critical role in the effect of RMPs on plasma performance.