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We applied an effective approximation into Maxwell's equations with an axioninteraction for haloscope searches. A set of Maxwell's equations acquired fromthis approximation describes just the reacted fields generated by the anomalousinteraction. Unlike other approaches, this set of Maxwell's equationsinherently satisfies the boundary conditions for haloscope searches. Theelectromagnetic field solutions from the Maxwell's equations were evaluated forboth cylindrical and toroidal cavity geometries including when the axion massbecomes ultra-light (sub-meV). A small but non-zero difference between theelectric and magnetic stored energies appeared in both cases. The differencemay come from an anomalous non-dissipating current induced by oscillatingaxions.

Effective Approximation of Electromagnetism for Axion Haloscope Searches