  RADES (Relic Axion Detector Exploratory Setup) is a project with the goal of
directly searching for axion dark matter above the $30 \mu$eV scale employing
custom-made microwave filters in magnetic dipole fields. Currently RADES is
taking data at the LHC dipole of the CAST experiment. In the long term, the
RADES cavities are envisioned to take data in the (baby)-IAXO magnet. In this
article we report on the modelling, building and characterisation of an
optimised microwave-filter design with alternating irises that exploits maximal
coupling to axions while being scalable in length without suffering from
mode-mixing. We develop the mathematical formalism and theoretical study which
justifies the performance of the chosen design. We also point towards the
applicability of this formalism to optimise the MADMAX dielectric haloscopes.

High Energy Physics - Experiment;High Energy Physics - Phenomenology