A new first-principles calculation of field-dependent RF surface impedance of BCS superconductor and application to SRF cavities

There is a need to better 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 (M-B) theory of the RF surface impedance of BCS superconductors based on the shifted Density of States (DoS) resulting from coherently moving Cooper pairs [1].The surprising reduction in resistance with increasing field is explained to be an intrinsic effect. Using this analysis coded in MathematicaTM, survey calculations have been completed which examine the sensitivities of this surface impedance to variation of the BCS material parameters and temperature.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 Jefferson Lab (JLab) and Fermi National Accelerator Lab (FNAL) with carefully, yet differently, prepared niobium material. The results present a refined description of the "best theoretical" performance available to potential applications with corresponding materials. [1]Xiao, B.P., C.E. Reece, and M.J. Kelley, Superconducting surface impedance under radiofrequency field. Physica C: Superconductivity, 2013. 490(0): p. 26-31.