Characterization of the HAYSTAC axion dark matter search cavity using microwave measurement and simulation techniques.

Many searches for axion cold dark matter rely on the use of tunable electromagnetic resonators. Current detectors operate at or near microwave frequencies and use cylindrical cavities with cylindrical tuning rods. The cavity performance strongly impacts the signal power of the detector, which is expected to be very small even under optimal conditions. There is strong motivation to characterize these microwave cavities and improve their performance in order to maximize the achievable signal power. We present the results of a study characterizing the HAYSTAC (Haloscope At Yale Sensitive to Axion Cold dark matter) cavity using bead perturbation measurements and detailed 3D electromagnetic simulations. This is the first use of bead perturbation methods to characterize an axion haloscope cavity. In this study, we measured impacts of misalignments on the order of 0.001 in and demonstrated that the same impacts can be predicted using electromagnetic simulations. We also performed a detailed study of mode crossings and hybridization between the TM$_{010}$ mode used in operation and other cavity modes. This mixing limits the tuning range of the cavity that can be used during an axion search. By characterizing each mode crossing in detail, we show that some mode crossings are benign and are potentially still useful for data collection. The level of observed agreement between measurements and simulations demonstrates that finite element modeling can capture non-ideal cavity behavior and the impacts of very small imperfections. 3D electromagnetic simulations and bead perturbation measurements are standard tools in the microwave engineering community, but they have been underutilized in axion cavity design. This work demonstrates their potential to improve understanding of existing cavities and to optimize future designs.