A phenomenological model of the fundamental power coupler for a superconducting resonator

In this study, a phenomenological model of the radio frequency (RF) behavior of a superconducting cavity fundamental power coupler is proposed by analyzing the simulation results of a transient beam-loading process in an extremely over-coupled superconducting cavity. Using this phenomenological model, the calculation of the transient reflected power from a superconducting cavity under beam loading can be mathematically simplified to algebraic operations without solving the differential equation governing the transient beam-loading process, while maintaining the calculation accuracy. Moreover, this phenomenological model can facilitate an intuitive understanding of the significant surge in the time evolution of reflected power from a superconducting cavity in certain beam-loading processes. The validity of this phenomenological model was carefully examined in various beam-loading processes and cavity conditions, and the method based on this phenomenological model was utilized in the transient RF analysis of the superconducting cavity system of the CAFe Linac, achieving satisfactory results.