  We propose a novel design of a laboratory search for axions based on photon
regeneration with superconducting RF cavities. Our particular setup uses a
toroid as a region of confined static magnetic field, while production and
detection cavities are positioned in regions of vanishing external field. This
permits cavity operation at quality factors of $Q \sim 10^{10} - 10^{12}$. The
limitations due to fundamental issues such as signal screening and
back-reaction are discussed, and the optimal sensitivity is calculated. This
experimental design can potentially probe axion-photon couplings beyond
astrophysical limits, comparable and complementary to next generation optical
experiments.
