Extended drift MHD theory of resonant layer field penetration with higher order flow and viscous effects

Magnetic perturbations arising in a tokamak can induce complex responses near the resonant layer as observed with error fields and RMPs. One such response of great interest is field penetration which can result in arresting the plasma rotation creating locked modes. In the linear regime, the plasma response can be characterized by the inner layer Δ, which can be used to estimate the field penetration threshold through the electromagnetic torque. Accurately predicting the field penetration threshold and its scaling is crucial for error field correction and RMP application to control ELMs. We apply a two-fluid drift-MHD model to identify the scaling of Δ while including additional physical effects such as ion parallel flow and electron viscosity. Namely, we predict a downwards shift in the natural resonant rotation towards the ion diamagnetic rotation implying an enhanced resistance to field penetration via ion current shielding. The effect is most enhanced in high β plasmas, however it is still predicted to be significant for current and next step fusion plasmas. Along with the analytic scaling of this shift in various parameter regimes, we also present numerical results characterizing this effect.