  The scan rate of an axion haloscope is proportional to the square of the
cavity volume. In this paper, a new class of thin-shell cavities are proposed
to search for axionic dark matter. These cavities feature active volume much
larger (>20X) than that of a conventional cylindrical haloscope, comparable
quality factor Q, and a similar frequency tuning range. Full 3D numerical
finite-element analyses have been used to show that the TM_010 eigenmodes are
singly polarized throughout the volume of the cavity and can facilitate
axion-photon conversion in uniform magnetic field produced by a superconducting
solenoid. To mitigate spurious mode crowding and volume loss due to
localization, a pre-amplification binary summing network will be used for
coupling. Because of the favorable frequency-scaling, the new cavities are most
suitable for centimeter-wavelength (~ 10-100 GHz), corresponding to the
promising post-inflation axion production window. In this frequency range, the
tight machining tolerances required for high-Q thin-shell cavities are
achievable with standard machining techniques for near-infrared mirrors.
