Abstract
A general axion-electrodynamic formalism is presented on the phenomenological level when the environment is dielectric (permittivity and permeability assumed to be constants). Thereafter, a strong and uniform magnetic field is considered in the z direction, the field region having the form of a long material cylinder (which corresponds to the haloscope setup). If the axion amplitude depends on time only, the axions give rise to an oscillating electric current in the z direction. We estimate the magnitudes of the azimuthal magnetic fields and the accompanying Joule heating in the cylinder, taking the cylinder to have ordinary dissipative properties. We evaluate and calculate the electric current and the heat production separately, without using the effective approximation, both when there is a strong magnetic field and when there is a strong electric one, showing that with the magnetic field there is a heat production, while with the electric field there is not. The heat generation that we consider, is a nontrivial effect as it is generated by the electrically neutral axions, and has obvious consequences for axion thermodynamics. The heat production can moreover have an additional advantage, since the effect is accumulative and so grows with time. The boundary conditions (in a classical sense) are explained and the use of them in a quantum mechanical context is discussed. This point is nontrivial, accentuated in particular in connection with the Casimir effect. For comparison purposes, we present finally some results for heat dissipation taken from the theory of viscous cosmology.
Highlights
A general axion-electrodynamic formalism is presented on the phenomenological level when the environment is dielectric
Thereafter, a strong and uniform magnetic field is considered in the z direction, the field region having the form of a long material cylinder
We evaluate and calculate the electric current and the heat production separately, without using the effective approximation, both when there is a strong magnetic field and when there is a strong electric one, showing that with the magnetic field there is a heat production, while with the electric field there is not
Summary
An important point is whether one is able to detect the axions experimentally, preferably under terrestrial conditions. An interesting idea is to search experimentally for resonances between the axions and the dielectric particles in a long plasma cylinder, in the presence of a strong magnetic field in the axial z direction. This is the so-called haloscope approach discussed at various places; cf., for instance, Refs. Typical values for resonance frequencies are expected to lie in the region around 100 GHz. Axion electrodynamics contains many facets, and in the present paper we will be concerned with the oscillating electric current set up in the longitudinal z direction in a haloscope setup, and the accompanying Joule heating in the cylinder. We will by means of simple arguments consider Joule heating problems, both under terrestrial conditions and under astrophysical ones
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