  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.
