We present a reformulation of axion modified electrodynamics with all modifications redefined within the constitutive relations between the D,H,B and E fields. This allows the interpretation of the axion induced background bound charge, polarization current and background polarization and magnetization satisfying the charge-current continuity equation. This representation is of similar form to photon sector odd-parity Lorentz invariance violating background fields. We show that when a DC B-field is applied an oscillating background polarization is induced at a frequency equivalent to the axion mass. In contrast, when DC E-field is applied, an oscillating background magnetization is induced at a frequency equivalent to the axion mass. We show that these terms are equivalent to impressed source terms, analogous to the way that voltage and current sources are impressed into Maxwells equations in circuit and antenna theory. The impressed source terms represent the conversion of external energy into electromagnetic energy, and in the case of axion modified electrodynamics this is due to the inverse Primakoff effect converting energy from axions into photons. The axion induced oscillating polarization under a DC magnetic field is analogous to a permanent polarised electret oscillating at the axion Compton frequency, which sources an electromotive force from an effective impressed magnetic current source. In particular, it is shown that the impressed electrical DC current that drives the solenoidal magnetic DC field of an electromagnet, induces an impressed magnetic current parallel to the DC electrical current, oscillating at the Compton frequency of the axion. We show that the magnetic current drives a voltage source through an electric vector potential and also defines the boundary condition of the oscillating axion induced polarization inside and outside the electromagnet.
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