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Register a new userAbraham and Minkowski Poynting vector controversy in axion modified electrodynamics
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Michael Edmund Tobar
Publication date
2021
fields
Physics
and research's language is
English
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The most sensitive haloscopes that search for axion dark matter through the two photon electromagnetic anomaly, convert axions into photons through the mixing of axions with a large DC magnetic field. In this work we apply Poynting theorem to the resulting axion modified electrodynamics and identify two possible Poynting vectors, one similar to the Abraham Poynting vector and the other to the Minkowski Poynting vector in electrodynamics. The latter picks up the extra non-conservative terms while the former does not. To understand the source of energy conversion and power flow in the detection systems, we apply the two Poynting theorems to axion modified electrodynamics, for both the resonant cavity and broadband low-mass axion detectors. We show that both Poynting theorems give the same sensitivity for a resonant cavity axion haloscope, but predict markedly different sensitivity for a low-mass broadband capacitive haloscope. Hence we ask the question, can understanding which one is the correct one for axion dark matter detection, be considered under the framework of the Abraham-Minkowski controversy? In reality, this should be confirmed by experiment when the axion is detected. However, many electrodynamic experiments have ruled in favour of the Minkowski Poynting vector when considering the canonical momentum in dielectric media. In light of this, we show that the axion modified Minkowski Poynting vector should indeed be taken seriously for sensitivity calculation for low-mass axion haloscope detectors in the quasi static limit, and predict orders of magnitude better sensitivity than the Abraham Poynting vector equivalent.
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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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