Toroidal torque across layers due to resonant magnetic fields and complex rotational dependencies

Toroidal torque balance across resonant layers with non-axisymmetric magnetic fields is the key to understanding of perturbed equilibria with rotating or externally forced magnetic islands. Here two-fluid drift-MHD layer formulations have been revisited with numerical integrations in particular using the Riccati transformation. This allows the reliable and efficient finding of the matching condition to the outer layers called the delta-prime in wide multi-variable space, improving the predictions to well-known asymptotic regimes as well as revealing transitions from one to another. The investigations over practical tokamak conditions show the complex rotational dependencies of the torque towards electron and ion diamagnetic frequencies, with characteristic nearby minimums before rising gradually at higher rotation where inertia effects become dominant. This formulation can also be readily coupled with ideal plasma response, giving the reconnected flux and the torque as a function of screening currents and conventional tearing mode indexes at each resonant layer. The predictions of parametric scaling for the field penetration will also be compared with other reduced MHD simulations or empirical regression, to establish the validity as well as the limitations of linear approaches.