Quantifying the Resonant Drive for Magnetic Islands in Perturbed Ideal, Resistive, and Kinetic MHD Equilibria

We introduce the jump in the flux-normal derivative of the resonant magnetic field at a rational surface as a metric for resonant drive from 3D magnetic perturbations in resistive and kinetic tokamak plasmas. Presently, many efforts, such as the ITPA error field penetration threshold scaling law, use this metric with an ideal MHD model. However, where ideal MHD ceases to be a good model, such as with resistive or highly non-maxwellian plasmas, the ideal shielding sheet current is split or spread out and the application of this metric is non-trivial. Another metric in use is the resonant penetrated flux, which applies in these regimes but is necessarily zero in ideal models. We present efforts to characterize the implications each of these metrics have for determining which components of 3D fields are dangerous. We show that both the penetrated resonant field and the resonant field derivative jump can be calculated consistently in resistive perturbed equilibria, and demonstrate convergence to ideal values. Gaining a better understanding of these metrics will allow for better comparability between models that use resonant field derivative jump, like the ideal GPEC code and much of established tearing theory, and results from extended MHD codes like MARS-F, NIMROD, and M3D-C1 that exclusively present penetrated resonant field.