Vortex dynamics in a thin superconducting film with a non-uniform magnetic field applied at its center with a small coil

Abstract

This paper models the dynamics of vortices that are generated in the middle of a thin, large-area, superconducting film by a low-frequency magnetic field from a small coil, motivated by a desire to better understand measurements of the superconducting coherence length made with a two-coil apparatus. When the applied field exceeds a critical value, vortices and antivortices originate near the middle of the film at the radius where the Lorentz force of the screening supercurrent is largest. The Lorentz force from the screening supercurrent pushes vortices toward the center of the film and antivortices outward. In an experiment, vortices are detected as an increase in mutual inductance between the drive coil and a coaxial “pickup” coil on the opposite side of the film. The model shows that the essential features of measurements are well described when vortex pinning and the attendant hysteresis are included.