Avoided mode crossings in cylindrical microwave cavities.

Conventional axion haloscope detectors require high-Q cavities with tunable TM modes, the resonant electric fields of which occupy as much of the full volume of the cavity as possible. An analytical study of the effects of longitudinal symmetry breaking within microwave cavities is conducted to understand the mode structure. The study reveals that longitudinal symmetry breaking of the cavities is the mechanism for avoiding mode crossings in cylindrical microwave cavities. The results show the size of the gaps in the search frequency spectrum due to an avoided mode crossing is roughly proportional to the magnitude of the selective size of gaps between tuning mechanisms and cavity endcaps, or other deviations from perfect longitudinal uniformity of the cavity. The form factors of the modes in avoided mode crossings are equal when the frequencies of the modes are at the point of closest approach.