Calculations of the equilibrium configurations of flux lines in thin films of type II superconductors

The London theory is used to calculate the equilibrium configurations of flux lines in thin films of a type II superconductor as a function of the applied magnetic field. Three possible geometrical configurations, of increasing complexity, are considered in detail, and the Gibbs function is minimized with respect to the parameters which define the configuration. The range of applied magnetic field for which each configuration is stable is determined, and hence B–H curves are constructed. A transition from one configuration to another causes a discontinuity in the B–H curve at values of H which roughly correspond to those found experimentally by Sutton.