  Axions are a compelling dark matter candidate, and one of the primary
techniques employed to search for them is the axion haloscope, in which a
resonant cavity is deployed inside a strong magnetic field so that some of the
surrounding axions may convert into photons via the inverse Primakoff effect
and become trapped inside the resonator. Resonant cavity design is critical to
the sensitivity of a haloscope, and several geometries have been utilised and
proposed. Here we consider a relatively simple concept - a rectangular resonant
cavity with a tunable wall - and compare it to the standard tuning rod-type
resonators employed in the field. We find that the rectangular cavities support
similar modes to cylindrical tuning rod cavities, and have some advantages in
terms of axion sensitivity and practicality, particularly when moving to higher
frequencies which are of great and growing interest in the international axion
dark matter community.
