Effective approximation of electromagnetism for axion haloscope searches

Abstract

The incorporation of axion-photon interaction into the classical Maxwell’s equations has provided insights for axion searches with microwave photons. In addition to current leading axion haloscope searches with resonant cavities for axions in resonance regime (10−6eV < ma < 10−4eV), new proposed experiments also make the most of the Maxwell’s equations to detect an induced electromagnetic field from the axion-photon interaction in long wavelength regime (ma ≪ 10−6eV). In this paper, we apply an effective approximation to the Maxwell’s equations to get a correct form of Maxwell’s equations only for the induced fields. We rigorously solve the Maxwell’s equations for the induced fields to get a close form of electromagnetic fields under various experimental conditions in the axion resonance regime. We attempt to get the electromagnetic field in the long wavelength regime, directly from the solutions in the resonance regime, by taking the long wavelength limit. Axion to photon conversion power in the axion resonance regime was also examined not only for on-resonance frequency, but also for off-resonance frequency region. This would provide information to estimate the conversion power even in off-resonant region of the cavity modes that can be applied for the axion searches.