Simulations of Critical Currents in Polycrystalline Superconductors Using Time-Dependent Ginzburg–Landau Theory

In this thesis, we investigate the in-field critical current density of polycrystalline superconducting systems with grain boundaries modelled as Josephson-type planar defects, both analytically and through computational time-dependent Ginzburg--Landau (TDGL) simulations in 2D and 3D. For very narrow SNS Josephson junctions (JJs), with widths smaller than the superconducting coherence length, we derive what to our knowledge are the first analytic expressions for across a JJ over the entire applied magnetic field range. We extend the validity of our analytic expressions to describe wider junctions and confirm them using TDGL simulations. We model superconducting systems containing grain boundaries as a network of JJs by using large-scale 3D TDGL simulations applying state-of-the-art solvers implemented on GPU architectures. These simulations of have similar magnitudes and dependencies on applied magnetic field to those observed experimentally in optimised commercial superconductors. They provide an explanation for the dependence found for in high temperature superconductors and are the first to correctly provide the inverse power-law grain size behaviour as well as the Kramer field dependence, widely found in many low temperature superconductors.