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.

9 pages, 7 figures