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Abstract

The nature of dark matter is one of the enduring mysteries of modern physics. For more than eight decades there has been evidence for a mysterious in- visible substance that constitutes most of the matter in the universe, “dark matter”. While there are many possible particle physics candidates for this elusive substance, one of the most popular is the axion. Originally introduced to resolve the absence of charge-parity violation in the Strong force (the Strong CP Problem), the axion is a light pseudo-scalar arising from the breaking of a high energy global symmetry. Axions would be produced non-thermally in the early universe, providing the correct density of dark matter. Due to the lightness of axions, they have a unique phenomenology and so require dedi- cated experiments to detect. Much of the well motivated parameter space is yet to be explored, meaning that novel ideas are needed to push forward the search for axions. We study the underlying theory of dielectric haloscopes, a new way to detect dark matter axions. When an interface between different dielectric me- dia is inside a magnetic field, the oscillating axion field acts as a source of electromagnetic waves, which emerge in both directions perpendicular to the surface. The emission rate can be boosted by multiple layers judiciously placed to achieve constructive interference and by a large transverse area. Starting from the axion-modified Maxwell equations, we calculate the efficiency of this new dielectric haloscope approach. We do both a classical calculation and a quantum calculation of the produced power. The classical calculation is based on transfer matrices, solving for the electric field throughout the system. The quantum calculation uses conventional first-order perturbative calculation of the transition probability between a quantised axion state and the photon state, which is distorted in the presence of the dielectric media, resulting in an overlap integral. Both methods agree on the produced power in electro- magnetic radiation. With dielectric haloscopes one could potentially search the unexplored high-frequency range of 10–100 GHz (axion mass 40–400 μeV), where traditional cavity resonators have difficulties reaching the required vol- ume. We also describe non-zero velocity effects for axion-photon mixing in a magnetic field and for the phenomenon of photon emission from interfaces be- tween different dielectric media. As velocity effects are only important when the haloscope is larger than about 20% of the axion de Broglie wavelength, for the planned MADMAX experiment with 80 dielectric disks the velocity dependence can safely be neglected. However, an augmented MADMAX or a second generation experiment would be directionally sensitive to the axion velocity, and thus a sensitive measure of axion astrophysics.