Axion Dark Matter Coupling to Resonant Photons via Magnetic Field

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 couplings are equal, and this has implicitly been 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 dark matter axion searches over a wide range of masses.