Superconducting surface impedance under radiofrequency field

• SRF accelerator cavity performance (quality factor Qo) is controlled by surface impedance.
• A field-dependent derivation of the Mattis–Bardeen theory of SRF surface impedance is presented.
• The complete range of gradients is treated for the first time.
• Agreement with experiment is excellent.

Based on BCS theory with moving Cooper pairs, the electron states distribution at 0 K and the probability of electron occupation with finite temperature have been derived and applied to anomalous skin effect theory to obtain the surface impedance of a superconductor under radiofrequency (RF) field. We present the numerical results for Nb and compare these with representative RF field-dependent effective surface resistance measurements from a 1.5 GHz resonant structure.