  We consider subgap bands induced in a two-dimensional superconductor by a
densely packed chain of magnetic moments with ferromagnetic or spiral
alignments. We show that by contrast with sparsely packed chains a consistent
description requires that all wavelengths are taken into account for the
scattering at the magnetic moments. The resulting subgap states are a
composition of Yu-Shiba-Rusinov-type states and magnetic scattering states,
whose mixture becomes especially important to understand the nature and
dimensional renormalization of gap closures for spiral magnetic alignments
under increasing scattering strength, particularly as the spiral becomes
commensurate with the Fermi wavelength. The results are fully analytic in the
form of Green's functions and provide the tools for further analysis of the
properties of the subgap states.
