Quantifying resonant drive in resistive perturbed tokamak equilibria

Resonant drive in tokamaks is routinely quantified using a variety of different metrics that target different aspects of a resonant response to an external perturbation. Two of the most direct metrics, $\Delta_{mn}$ and $b_{pen}$, are widely used but their relative behavior was previously uncharacterized. This work examines how these metrics representing the shielding current and penetrated field relate in resistive perturbed tokamak equilibria using asymptotically matched solutions with a resistive MHD inner layer model in GPEC. $b_{pen}$ scales with Lundquist number as $S^{-2/3}$ until saturation at low $S$, and $\Delta_{mn}$ remains consistent with its ideal definition but is affected by global kink structure. Both metrics are shown to yield closely similar dominant coupling modes within the same resistive model. However, the resistive physics shifts this dominant mode spectrum to lower poloidal mode numbers $m$ in a low-rotation ITER equilibrium. This alteration is predicted to be observable in experiment in the form of optimal relative phasings of resonant magnetic perturbation coils.