Distribution of pinning forces on trapped flux in a type I superconductor

The distribution density of the strength of pinning sites is investigated in superconducting lead films by counting the number of trapped flux tubes as a function of a monotonically increasing applied transport current. The flux tubes contain 100–200 flux quanta and are detected by high-resolution magnetooptics. Experiments were performed with Pb films containing only natural pinning sites and in samples containing artificial pinning centers in the form of small circular pits etched into the film surface. A detailed theoretical discussion is given of the various forces acting upon a pinned array of flux tubes. If edge pinning is dominant, the critical Lorentz force inducing steady-state flux flow is much larger than the force required for removing trapped flux tubes from the sample. This can be understood from the spatial dependence of the Gibbs free energy of the flux tubes near the sample edges.Supported by a grant from the Deutsche Forschungsgemeinschaft.Operated for the U.S. Department of Energy by Iowa State University under contract No. W-7405-Eng-82. This research was supported by the Director for Energy Research, Office of Basic Energy Sciences, WPAS-KC-02-02-03, and by the NATO Research Grants Program.