Estimating the effect of grain boundaries on the superconducting superheating field in 2D Ginzburg-Landau Theory

The Meissner effect is the expulsion of an applied magnetic field by a superconducting material. For large applied fields, a surface effect creates barrier to vortex nucleation so that the Meissner state may persist in a meta-stable state up to a critical, superheating field. We study the role of grain boundaries, including surface morphology and material inhomogeneity, on vortex nucleation within two-dimensional Ginzburg-Landau theory. Our simulations mimic conditions observed in Nb₃Sn SRF cavities using in particle accelerators. We show how defects lower the superheating field and discuss implications for SRF cavity performance and development.