N-doped surfaces of superconducting niobium cavities as a disordered composite

The <italic>Q</italic>-factor of superconducting accelerating cavities can be substantially improved by a special heat treatment under N₂ atmosphere (N-doping). Recent experiments at Fermi National Laboratory investigated the dependence of <italic>Q</italic> on the RF frequency and showed, unexpectedly, both an increase and a decrease with the RF field amplitude. This paper shall explain this finding by extending a previously proposed model founded on the two fluid model of RF losses, percolation, and the proximity effect in a disordered composite.