Calculating the Superconducting Superheating Field within Eilenberger Theory

For Type II superconductors in an applied magnetic field, the superconducting Meissner state can persist metastably up to a theoretical maximum, "superheating field", Hsh. Superconducting Resonance Frequency (SRF) cavities are a critical component of particle accelerators for which Hsh represents a fundamental limit to performance. As the accelerator community explores materials for next-generation cavities, such as Nb3Sn, better estimates of Hsh are needed for candidate materials. Previous calculations have used Ginzburg-Landau theory (valid near Tc), however SRF cavities often operate well below the critical temperature. Extensions to Eilenberger theory (valid at all temperatures) in the high-kappa and dirty limits have also been done. Here, we discuss the calculation of Hsh in Eilenberger theory in the clean limit. In addition to an accurate temperature dependence, the clean limit of the Eilenberger theory includes material-specific parameters for the density of states at the Fermi surface. I discuss implications for SRF cavity development.