  We show that the magnetic component of the photon field produced by dark
matter axions via the two-photon coupling mechanism in a Sikivie Haloscope is
an important parameter passed over in previous analysis and experiments. The
interaction of the produced photons will be resonantly enhanced as long as they
couple to the electric or magnetic mode structure of the Haloscope cavity. For
typical Haloscope experiments the electric and magnetic coupling is the same
and implicitly assumed in past sensitivity calculations. However, for future
planned searches such as those at high frequency, which synchronize multiple
cavities, the sensitivity will be altered due to different magnetic and
electric couplings. We define the complete electromagnetic form factor and
discuss its implications for current and future high and low mass axion
searches, including some effects which have been overlooked, due to the
assumption that the two couplings are the same.
