Axions would be produced in the Sun through the scattering of photons from electric charges - the Primakoff effect - and their numbers could equal those of solar neutrinos. The idea behind the Brookhaven experiment, first proposed by Pierre Sikivie, was to put the Primakoff effect to work in reverse, using a magnetic field to catalyse the conversion of solar axions back into X-rays photons of a few keVs.
CAST uses a prototype LHC dipole magnet.
The conversion efficiency for axions increases as the square of the product of the transverse magnetic field component and its length.
The Sun would be a source of axions, producing them via Primakoff effect. Detection would be by the inverse process.