Non-Linear Eigenmode Computations for Conducting and Superconducting Cavities With a Surface Impedance Boundary Condition

In this paper, the eigenmodes and quality factors of cavity resonators are computed by a non-linear finite element eigenvalue solver, exploiting surface impedance boundary conditions (SIBCs). In the last few years, the accurate calculation of losses and resonance frequencies of (super)conducting cavities has become a central part in the design of high-performance particle accelerators. However, solving the governing equations in the material is computationally unfeasible, since its penetration depth is many orders of magnitude smaller than the cavity dimensions. Therefore, the material behavior is modeled by an SIBC. However, the SIBC introduces a square-root operator in the corresponding eigenvalue formulation. This necessitates the use of a non-linear eigenvalue solver, for which a contour integral approach is proposed. This paper recommends a generic approach for coupling an SIBC formulation with a non-linear eigenvalue solver.