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Duality-symmetric axion electrodynamics and haloscopes of various geometries

Within the dual symmetric point of view, the theory for seeking axion dark matter via haloscope experiments is derived by exactly solving the dual symmetric axion electrodynamics equation. Notwithstanding that the conventional theory of axion electrodynamics presented in [Phys. Rev. Lett. 51, 1415 (1983) and J. Phys. A: Math. Gen. 19, L33 (1986)] is more commonly used in haloscope theory, we show that the dual symmetric axion electrodynamics has more advantages to apply to haloscope theory. First, the dual symmetric and conventional perspectives of axion electrodynamics coincide under long-wavelength approximation. Moreover, dual symmetric theory can obtain an exact analytical expression of the axion-induced electromagnetic field for any state of axion. This solution has been used in conventional theory for long-wavelength approximation. The difference between two theories can occur in directional axion detection or electric sensing haloscopes. For illustrative purposes, we consider the various type of resonant cavities: cylindrical solenoid, spherical solenoid, two-parallel-sheet cavity, toroidal solenoid with a rectangular cross-section, and with a circular cross-section. The resonance of the axion-induced signal, as well as the ratio of the energy difference over the stored energy inside the cavity, are investigated in these types of cavity.