Abstract
Recently there has been a surge of new experimental proposals to search for ultra-light axion dark matter with axion mass, $m_a\lesssim1\,\mu$eV. Many of these proposals search for small oscillating magnetic fields induced in or around a large static magnetic field. Lately, there has been interest in alternate detection schemes which search for oscillating electric fields in a similar setup. In this paper, we explicitly solve Maxwell's equations in a simplified geometry and demonstrate that in this mass range, the axion induced electric fields are heavily suppressed by boundary conditions. Unfortunately, experimentally measuring axion induced electric fields is not feasible in this mass regime using the currently proposed setups with static primary fields. We show that at larger axion masses, induced electric fields are not suppressed, but boundary effects may still be relevant for an experiment's sensitivity. We then make a general argument about a generic detector configuration with a static magnetic field to show that the electric fields are always suppressed in the limit of large wavelength.
Highlights
Starting about 104 years after the big bang and lasting 1010 years after, the gravitational evolution of the Universe was driven mostly by dark matter (DM)
Unlike the more thoroughly constrained DM candidate, the weakly interacting massive particle (WIMP), the axion is expected to be extremely light with mass 10−14 ≲ ma ≲ 1 eV
We showed that the solution E 1⁄4 −gaγγaB is part of the full solution of the modified Maxwell’s equations; by itself it does not satisfy the required boundary conditions
Summary
Starting about 104 years after the big bang and lasting 1010 years after, the gravitational evolution of the Universe was driven mostly by dark matter (DM). In the limit of large λa, the typical approach is to build a detector with a strong DC magnetic field and search for an induced AC B field IV, we generalize this conclusion and show that for a broad class of detectors, the MQS approximation is always valid in the large-λa limit and that the suppression of the electric field is a generic quality From this we conclude that in this mass regime, an experiment with a static B field will always be more sensitive to axion-induced magnetic fields over electric fields. This is because the de Broglie wavelength is about 3 orders of magnitude larger than the oscillation wavelength (λD ≈ 103λa), and spatial gradient terms are suppressed
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