  A resonantly-enhanced photon-regeneration experiment to search for the axion
or axion-like particles is described. This experiment is a shining light
through walls study, where photons travelling through a strong magnetic field
are (in part) converted to axions; the axions can pass through an opaque wall
and convert (in part) back to photons in a second region of strong magnetic
field. The photon regeneration is enhanced by employing matched Fabry-Perot
optical cavities, with one cavity within the axion generation magnet and the
second within the photon regeneration magnet. Compared to simple single-pass
photon regeneration, this technique would result in a gain of (F/pi)^2, where F
is the finesse of each cavity. This gain could feasibly be as high as 10^(10),
corresponding to an improvement in the sensitivity to the axion-photon
coupling, g_(agg), of order (F/pi)^(1/2) ~ 300. This improvement would enable,
for the first time, a purely laboratory experiment to probe axion-photon
couplings at a level competitive with, or superior to, limits from stellar
evolution or solar axion searches. This report gives a detailed discussion of
the scheme for actively controlling the two Fabry-Perot cavities and the laser
frequencies, and describes the heterodyne signal detection system, with limits
ultimately imposed by shot noise.
