Frequency Dependence of Superconducting Cavity Q and Magnetic Breakdown Field

A theoretical explanation is given to account for the unexpected observation that L- and S-band Nb superconducting cavities were found to have lower Q and lower magnetic breakdown field than those of the higher X-band frequencies. Both effects can be related to the trapping of magnetic flux in the cavity walls. The frequency dependence arises from the frequency dependence of the resistivity of oscillating fluxoids. Calculations based on this model are in agreement with experimental observations.