Time-dependent Ginzburg-Landau treatment of rf magnetic vortices in superconductors: Vortex semiloops in a spatially nonuniform magnetic field

We apply time-dependent Ginzburg Landau (TDGL) numerical simulations to study the finite frequency electrodynamics of superconductors subjected to intense rf magnetic field. Much recent TDGL work has focused on spatially uniform external magnetic field and largely ignores the Meissner state screening response of the superconductor. In this work, we solve the TGDL equations for a spatially non-uniform magnetic field created by a point magnetic dipole in the vicinity of a semi-infinite superconductor. A novel two-domain simulation is performed to accurately capture the effect of the inhomogeneous applied fields and the resulting screening currents. The creation and dynamics of vortex semiloops penetrating deep into the superconductor domain is observed and studied, and the resulting third-harmonic nonlinear response of the sample is calculated. The effect of point-like defects on vortex semi-loop behaviour is also studied. This simulation method will assist our understanding of the limits of superconducting response to intense rf magnetic fields.