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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

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