Plasma response and flow relaxation induced by resonant magnetic perturbation in the Rutherford regime

Externally applied non-axisymmetric magnetic fields such as error field and resonant magnetic perturbation (RMP) can influence the plasma momentum dynamics through plasma response in a tokamak, whereas the plasma response itself strongly depends on the plasma flow as well. Such a nonlinear interaction between the two has been modeled in an extended error field theory for a coupled system of toroidal and poloidal torque balance and magnetic island evolution equations in the Rutherford regime. For a more complete and self-consistent account, we solve for the nonlinear plasma response and the associated flow relaxation induced by a single-helicity RMP to a tokamak equilibrium with an initial uniform toroidal flow, using the full resistive MHD model in the NIMROD code. Simulations show that the time evolution of the parallel flow or ``slip frequency" and its asymptotic relaxation to steady state are different from the island rotation frequency on resonant surface, which invalidates the ``no-slip" condition often assumed for the Rutherford regime. The difference between theory and simulation also suggests nontrivial contributions from the non-resonant response.