Theory of RF superconductivity for resonant cavities

An overview of a theory of electromagnetic response of superconductors in strong radio-frequency (RF) electromagnetic fields is given with the emphasis on applications to superconducting resonant cavities for particle accelerators. The paper addresses fundamentals of the BCS surface resistance, the effect of subgap states and trapped vortices on the residual surface resistance at low RF fields, and a nonlinear surface resistance at strong fields, particularly the effect of the RF field suppression of the surface resistance. These issues are essential for the understanding of the field dependence of high quality factors Q ( B a ) ∼ 10 10 – 10 11 achieved on the Nb cavities at 1.3–2 K in strong RF fields B a close to the depairing limit, and the extended Q ( B a ) rise which has been observed on Ti and N-treated Nb cavities. Possible ways of further increase of Q ( B a ) and the breakdown field by optimizing impurity concentration at the surface and by multilayer nanostructuring with materials other than Nb are discussed.