  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 Maxwell's 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.
