Bifurcation of radial electric field in tokamak edge pedestal in response to resonant magnetic perturbations

The radial electric field E_r can significantly influence the transport and stability of plasma in tokamak edge pedestal, as well as the plasma response to resonant magnetic perturbations (RMPs). Through the radial force balance, the radial electric field E_r can be determined from toroidal and poloidal flows, along with the pressure profiles. In presence of RMPs, the non-resonant neoclassical toroidal viscosity torque is able to drive toroidal rotation in the edge pedestal due to large diamagnetic drifts, in addition to the resonant electromagnetic torque on a rational surface. Both torques depend on the radial electric field E_r, which may eventually settle into a steady state through the torque balance. In this work, we solve for the steady state E_r in presence of RMPs through numerical iterations, based on the plasma response computed from the modified Rutherford equation or the MHD simulations using the NIMROD code. Mostly due to the existence of multiple neoclassical offset rotation roots in certain parameter regimes, the steady state E_r in the edge pedestal region tends to be multiple-valued as well, demonstrating bifurcation behaviors and suggesting potential mechanisms underlying the edge pedestal processes that rely on the plasma response in E_r to RMPs.