Sensitivity of Low-Mass and Resonant Axion Haloscopes using Poynting Theorem

The most sensitive haloscopes that search for axion dark matter through the two-photon electromagnetic anomaly, convert axions into photons through the mixing of axions with a large background DC magnetic field. In this work we apply Poynting theorem to the resulting axion modified electrodynamics and identify two possible Poynting vectors, one which is like the Abraham Poynting vector in electrodynamics and the other to the Minkowski Poynting vector [1]. The former is consistent with a zero total derivative and assume all surface effects go to zero in the low-mass limit, while the latter identifies additional surfaces, which contribute non-conservative terms to the sensitivity. We apply both Poynting theorems to both DC and AC haloscopes. We find that both Poynting theorems calculating the same sensitivity for a resonant DC haloscope. In contrast, there is a large difference in sensitivity calculations in the low mass when the Compton wavelength of the axion is much larger than the experimental dimensions for both the AC and DC haloscopes. We show low-mass haloscopes based on the Minkowski Poynting theorem predict orders of magnitude better sensitivity than those based on the Abraham Poynting theorem. Based on this work, we calculate the sensitivity of new low-mass haloscope topologies under investigation at the University of Western Australia [2,3].