Frequency Dependence of the Superheating Field of Type II Superconductors Under Generalized Time-Dependent Ginzburg-Landau Theory

Modern superconducting radio frequency (SRF) applications require precise control of a wide range of material properties, from microscopic material properties to mesoscopic/macroscopic surface structures. Historically, Nb has been the primary superconducting material in SRF cavities. The past decade has seen increasing amounts of research into the development of cavities using next generation materials, such as Nb₃Sn. These materials have great promise for improving SRF performance, but their small coherence lengths require even greater control of surface and material defects. Mesoscopic simulation of superconductors with time-dependent Ginzburg-Landau (TDGL) theory have proven to be a powerful tool in SRF development, connecting the results of ab initio/quantum calculations to the mesoscopic structures of the material, allowing for investigation of many phenomena which are difficult to probe experimentally. Despite these sucesses, TDGL has many theoretical limitations which restrict the quantitative power of the theory. One such limitation is the assumption of gapless superconductivity, which can be remedied by the use of generalized TDGL (GTDGL). We introduce computational simulations of GTDGL and discuss their differences from typical TDGL. We demonstrate the usage of GTDGL by determining the frequency dependence of the superheating field, and discuss the implication of this for future SRF fabrication and simulation efforts.