Computation of high frequency fields in resonant cavities based on perturbation theory

The eigenmodes of an accelerator cavity are essential for the determination of its performance characteristics, comprising resonant frequencies and field distributions inside the cavity. Apart from the material properties the eigenmodes depend on the cavity geometry. Due to manufacturing tolerances and operational demands deviations of the actual cavity shape from the desired one are inevitable. Any geometry perturbation results in a shift of the resonant frequencies and modified field distributions. Slater's theorem offers an efficient way to compute the changed resonant frequencies, however, not the changed fields. In this work, we will analyse a generalisation of Slater's theorem proposed in literature. The method enables the computation of the resonant frequencies and the field distributions of a slightly perturbed cavity by using a set of eigenmodes of the unperturbed cavity. We evaluate the practicability of the method by applying it to cavity geometries for which the eigenmodes are analytically known, ascertain the effort of reasonable computation results and describe the limitations of the method.