Formulae to Calculate the Power Consumption of the SPL SC Cavities

This collection of formulae was assembled as a "toolbox" for power calculations concerning the operation of superconducting cavities. Treated are cavity voltage, reflected voltage, generator power, reflected power, and cooling power needed from the cryogenic system. Detailed derivations for some of the used equations can be found in [1] and [2]. Further information was gathered in [3], [4], and [5]. The formulae are then applied for the specific case of the SPL to calculate the power needs for the 2nd conceptual design report [6]. In accordance with most linac papers, the linac definition of the shunt impedance is used.