Eigenmode Calculations for the TESLA Cavity Considering Wave-Propagation Losses through Fundamental and Higher-Order Mode Couplers

The presented work focuses on the computation of three-dimensional eigenmodes for a single TESLA 1.3 GHz cavity considering a lossy behavior resulting from dedicated components like the fundamental and the higher-order mode couplers (HOM) but also from the attached beam tubes. Because the structural elements are manufactured using superconductive materials, the dissipative behavior of the model does not arise from the material itself but is instead attributed to the fact that appropriate matched waveguides are attached to the coupling elements. In contrast to previous examinations, the applied numerical method is immediately capable to set up and solve complex-valued eigenvalue problems derived from precisely modeled three-dimensional structures and suitable boundary conditions. In this context, the eigenvectors represent the distribution of the electric and magnetic fields while the eigenvalues describe the respective resonance frequency as well as the quality factor. The work intends to provide a detailed overview of the electromagnetic field distribution and related properties of the first 194 modes up to the fifth dipole passband where the influence of the main coupler, the two HOM couplers and the two beam pipes is precisely taken into account