How moats protect superconductor films from flux trapping

Trapping of residual magnetic field degrades the performance and, in extreme cases, destroys operability of superconductor digital circuits. It is known that moats or narrow cuts made in superconductor thin films are able to 'immunize' them from flux trapping. So far, an intuition rather than science has played a more significant role in the selection of geometry and density of these moats. We formalized an estimation of the moat efficiency. This procedure involves the calculation of Gibbs potentials of arbitrary shaped films in a magnetic field and comparison of the potentials with and without vortices in the film and magnetic flux frozen in the moats. We numerically simulate evolutions of the Gibbs potentials of films slowly cooled in a constant residual magnetic field. The simulations allow forecasting equilibrium distributions of vortices and fluxes trapped in the moats corresponding to the lowest potentials. The superconductor film becomes immune to the trapping Pearl vortices if the lowest Gibbs potential can be achieved without such Pearl vortices.