Modified axion electrodynamics as impressed electromagnetic sources through oscillating background polarization and magnetization

Abstract

A reformulation of axion modified electrodynamics is presented where the equations maintain a similar form to the unmodified Maxwell’s equations, 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 bound current along with the axion induced polarization and magnetization with the former satisfying the charge–current continuity equation. This representation is of similar form to odd-parity Lorentz invariance violating background fields in the photon sector of the Standard Model Extension. 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 a large DC E→-field is applied, an oscillating background magnetization is induced at a frequency equivalent to the axion mass. It is evident 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 due to the inverse Primakoff effect converting energy from axions into oscillating electromagnetic fields. It is shown that the impressed electrical DC current that drives a DC magnetic field of an electromagnet, induces an impressed effective magnetic current (or voltage source) parallel to the DC electrical current oscillating at the Compton frequency of the axion. The effective magnetic current drives a voltage source through an electric vector potential and also defines the boundary condition of the oscillating axion induced polarization (or impressed axion induced electric field) inside and outside the electromagnet. This impressed electric field, like in any voltage source, represents an extra force per unit charge supplied to the system, which also adds to the Lorentz force.