Analytical characterization of fundamental mode in pillbox cavities with beam pipe

Pillbox cavities were treated analytically using matching technique and `port approximation’ approach based on expansion of the fields in terms of evanescent modes for transient and drift regions. For most cases of practical interest the simple model gives high accuracy for resonant frequency, shunt impedance, quality factor and transit-time factor. The model demonstrates agreement with computations done with the well-known 2D and 3D codes Superfish and GdfidL for cylindrical and rectangular cavities. A detailed comparison of the results is given for these two different configurations in a wide range of geometry dimensions. The model can be used for fast analysis of cavities for klystron amplifiers or accelerating structures and extended to calculate loss-factors in a frequency domain.