An equivalent circuit model and power calculations for the APS SPX crab cavities.

An equivalent parallel resistor-inductor-capacitor (RLC) circuit with beam loading for a polarized TM110 dipole-mode cavity is developed and minimum radio-frequency (rf) generator requirements are calculated for the Advanced Photon Source (APS) short-pulse x-ray (SPX) superconducting rf (SRF) crab cavities. A beam-loaded circuit model for polarized TM110 mode crab cavities was derived. The single-cavity minimum steady-state required generator power has been determined for the APS SPX crab cavities for a storage ring current of 200mA DC current as a function of external Q for various vertical offsets including beam tilt and uncontrollable detuning. Calculations to aid machine protection considerations were given.