Eigenmode Computation for Cavities with Perturbed Geometry Based on a Series Expansion of Unperturbed Eigenmodes

The geometry of an accelerator cavity determines its eigenmodes and thereby its performance characteristics. Therefore, accelerating performance and wakefield characteristics may be improved by an intentional modification of the geometry. However, undesired geometry perturbations due to manufacturing tolerances and operational demands can likewise impair it. To analyze the effects of geometry variations on the eigenmodes, parameter studies are to be undertaken. Using common eigenmode solvers it usually is necessary to perform a full eigenmode computation for each variation step, even if the geometry is only slightly altered. Parameter studies for cavity perturbations thus tend to be computationally extensive and inefficient. In this paper, we present the fundamentals of an efficient eigenmode computation method for varying cavity geometries. Knowing a set of initial eigenmodes of an unperturbed geometry, the method allows expanding the eigenmodes of any geometry that is part of the unperturbed one as a series of the initial eigenmodes. Thereby the computation effort may be reduced significantly. The method is demonstrated by means of analytically evaluable cavity geometries. INTRODUCTION The shift of the resonant frequency of a specific eigenmode arising from a deformation of a cavity’s geometry can be calculated using Slater’s Theorem [1]