A Time-Dependent Ginzburg-Landau Framework for Sample-Specific Simulation of Superconductors for SRF Applications

Abstract

Modern superconducting radio frequency (SRF) applications demand precise control over material properties across multiple length scales - from microscopic composition, to mesoscopic defect structures, to macroscopic cavity geometry. We present a time-dependent Ginzburg-Landau (TDGL) framework that incorporates spatially varying parameters derived from experimental measurements and ab initio calculations, enabling realistic, sample-specific simulations. As a demonstration, we model Sn-deficient islands in Nb$_3$Sn and calculate the field at which vortex nucleation first occurs for various defect configurations. These thresholds serve as a predictive tool for identifying defects likely to degrade SRF cavity performance. We then simulate the resulting dissipation and show how aggregate contributions from multiple small defects can reproduce trends consistent with high-field $Q$-slope behavior observed experimentally. Our results offer a pathway for connecting microscopic defect properties to macroscopic SRF performance using a computationally efficient mesoscopic model.