On the Coupling Impedance of a Resonant Cavity

Longitudinal coupling impedance of a resonant cavity is studied by the normal mode analysis using the Coulomb gauge. The vector potential giving a solenoidal electric field leads to a resonant form described by a parallel LCR circuit. The coupling impedance at resonance is equal to the shunt impedance of the cavity. The scalar potential giving an irrotational electric field results in a non-resonant and purely imaginary coupling impedance. Since this latter impedance plays no role in power consumption, it has no relation to the shunt impedance of a cavity. Explicit expressions of the coupling impedance are given for a pill-box cavity considered by Keil et al. It is shown that their result on higher-order mode loss is derived from the real part of the coupling impedance considered here.