  Axions are a popular dark matter candidate which are often searched for in
experiments known as ``haloscopes" which exploit a putative axion-photon
coupling. These experiments typically rely on Transverse Magnetic (TM) modes in
resonant cavities to capture and detect photons generated via axion conversion.
We present a study of a resonant cavity design for application in haloscope
searches, of particular use in the push to higher mass axion searches (above
$\sim$60$\,\mu$eV). In particular, we take advantage of azimuthally varying
TM$_{m10}$ modes which, whilst typically insensitive to axions due to field
non-uniformity, can be made axion-sensitive (and frequency tunable) through
strategic placement of dielectric wedges, becoming a type of resonator known as
a Dielectric Boosted Axion Sensitivity (DBAS) resonator. Results from
finite-element modelling are presented, and compared with a simple
proof-of-concept experiment. The results show a significant increase in axion
sensitivity for these DBAS resonators over their empty cavity counterparts, and
high potential for application in high mass axion searches when benchmarked
against simpler, more traditional designs relying on fundamental TM modes.
