Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

Abstract

In this work, a quasi-linear model for the plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been self-consistently developed in the resistive-inertial and viscous-resistive regimes purely from the two-field reduced MHD model. Models for the plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e., the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work, we derive both the magnetic island response and the torque balance equations in a quasi-linear model for the plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the theoretical origins and physical meanings of quasi-linear forces and moments in the flow response equation are also clarified.