Q of a coaxial cavity with a superconducting inner conductor

A coaxial TEM resonant cavity, with normally conducting outer tube and end walls and a superconducting inner rod, is analysed. Assuming R_sn varies as omega ¹2/ and R_ss varies as omega ², the surface-resistance cross-over frequency f_c for the two conductors is used as a figure of merit and an expression for the unloaded Q-factor is derived. Graphs are presented that enable the Q-factors of mixed-conductor, all-superconductor and all-normal conductor cavities to be compared easily as a function of resonance frequency over the range 10⁶12 Hz with 10⁸c<10¹¹ Hz as a parameter. The graphs can be used for cavity design either to maximise the Q-factor or to maximise the sensitivity of the Q-factor to variation in crossover frequency.