Axion haloscope detectors require high-$Q$ cavities with tunable TM$_{010}$ modes whose resonant electric field occupies as much of the full volume of the cavity as possible. An analytical study of the effects of longitudinal symmetry breaking within microwave cavities was conducted to better understand the mode structure. The study revealed longitudinal symmetry breaking of the cavities was the mechanism for avoided mode crossings (AMC) in cylindrical microwave cavities. The results showed the size of the gaps in the search frequency spectrum due to an AMC was roughly proportional to the magnitude of symmetry breaking for small perturbations.
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