Modeling Inhomogeneous Superconductors in a Finite Element Formulation of Time-Dependent Ginzburg-Landau Theory

Modern superconducting radio frequency (SRF) applications require precise control of a wide range of material properties, from microscopic material parameters to mesoscopic/macroscopic surface structures. Mesoscopic simulation of superconductors has proven itself to be a powerful tool in SRF development, connecting microscopic properties to the mesoscopic structures of the material. We outline a finite element formulation of the Time-Dependent Ginzburg-Landau equations which allows for inhomogeneous material parameters, and discuss how these parameters connect to microscopic properties. We demonstrate a few applications of this formulation. First, we model vortex nucleation in Nb3Sn grain boundaries using microscopic parameters from DFT and inhomogeneities similar to real world cavities. We also study dissipation due to nano-hydrides in bulk Nb.