Magnetic-field and current-density distributions in thin-film superconducting rings and disks

We show how to calculate the magnetic-field and sheet-current distributions for a thin-film superconducting annular ring (inner radius a, outer radius b, and thickness d<a) when either the penetration depth obeys lambda<d/2 or, if lambda>d/2, the two-dimensional screening length obeys Lambda=2lambda(2)/d<a for the following cases: (a) magnetic flux Phi(z)(a) trapped in the hole in the absence of an applied magnetic field, (b) zero magnetic flux in the hole when the ring is subjected to an applied magnetic field H-a, and (c) focusing of magnetic flux into the hole when a magnetic field H-a is applied but no net current flows around the ring. We use a similar method to calculate the magnetic-field and sheet-current distributions and magnetization loops for a thin, bulk-pinning-free superconducting disk (radius b) containing a dome of magnetic flux of radius a when flux entry is impeded by a geometrical barrier.