Resonant magnetic perturbations and divertor footprints in poloidally diverted tokamaks

General formula describing both the divertor strike point splitting and width of magnetic islands created by resonant magnetic perturbations (RMPs) in a poloidally diverted tokamak equilibrium is derived. Under the assumption that the RMP is produced by coils at the low-field side such as those used to control edge localized modes (ELMs) it is demonstrated that the width of islands on different magnetic surfaces at the edge and the amount of divertor splitting are related to each other. Explanation is provided of aligned maxima of the perturbation spectra with the safety factor profile - an effect empirically observed in models of many perturbation coil designs.