A New First-Principles Calculation of Field-Dependent RF Surface Impedance of BCS Superconductor

There is a need to understand the intrinsic limit of radiofrequency (RF) surface impedance that determines the performance of superconducting RF cavities in particle accelerators. Here we present a field-dependent derivation of Mattis-Bardeen theory of the RF surface impedance of BCS superconductors based on the shifted density of states resulting from coherently moving Cooper pairs. Our theoretical prediction of the effective BCS RF surface resistance (Rs) of niobium as a function of peak surface magnetic field amplitude agrees well with recently reported record low loss resonant cavity measurements from JLab and FNAL with carefully, yet differently, prepared niobium material. The surprising reduction in resistance with increasing field is explained to be an intrinsic effect