Calculation of High Frequency Fields in Resonant Cavities Based on Perturbation Theory*

The knowledge of the eigenmodes of resonant accelerator cavities is essential for the determination of their performance characteristics, comprising resonant frequencies and field distributions inside the cavities. Apart from the material properties the eigenmodes of a cavity depend on its geometry. In spite of the high elaborateness during the complex fabrication process, minor deviations of the actual cavity shape from the desired one are inevitable. Moreover, especially superconducting cavities are subject to extreme operating conditions that may cause deformations of their shape. Any geometry perturbation results in a shift of the resonant frequencies and modified field distributions. In this paper, we will analyse a generalisation of Slater’s theorem [1] proposed in literature [2], [3]. The method allows for the calculation of resonant frequencies and field distributions of a slightly perturbed cavity by using a set of precomputed eigenmodes of the unperturbed cavity. We will evaluate the practicability of the method by applying it to cavity geometries for which the eigenmodes are analytically known, ascertain the effort to achieve reasonable calculation results and describe its limitations.