Abstract
We present 3D calculations for dielectric haloscopes such as the currently envisioned MADMAX experiment. For ideal systems with perfectly flat, parallel and isotropic dielectric disks of finite diameter, we find that a geometrical form factor reduces the emitted power by up to 30 % compared to earlier 1D calculations. We derive the emitted beam shape, which is important for antenna design. We show that realistic dark matter axion velocities of 10-3 c and inhomogeneities of the external magnetic field at the scale of 10 % have negligible impact on the sensitivity of MADMAX. We investigate design requirements for which the emitted power changes by less than 20 % for a benchmark boost factor with a bandwidth of 50 MHz at 22 GHz, corresponding to an axion mass of 90 μ eV. We find that the maximum allowed disk tilt is 100 μ m divided by the disk diameter, the required disk planarity is 20 μ m (min-to-max) or better, and the maximum allowed surface roughness is 100 μ m (min-to-max). We show how using tiled dielectric disks glued together from multiple smaller patches can affect the beam shape and antenna coupling.
Highlights
To the radiation emitted by a perfect mirror of the same area and under the same B-field
For ideal systems with perfectly flat, parallel and isotropic dielectric disks of finite diameter, we find that a geometrical form factor reduces the emitted power by up to 30 % compared to earlier 1D calculations
We present simulations taking some of the most important realistic boundary conditions for an open booster into account, i.e., first of all the fact that the disks are of finite size, and implications from a finite axion velocity, magnetic field inhomogeneities, mechanical tolerances, imprecise disk geometries, tilts and tiled disks
Summary
Where√em are the coefficients for the mode expansion, kz,m is the propagation constant and k0 = ω In free space these eigenmodes of the dielectric disks in general do not propagate independently anymore, because they are no longer solutions of the scalar wave equation under the free space boundary conditions. Since they are orthogonal and complete, we still can expand fields at r < R into these modes, but during propagation they mix with each other, i.e., E(r, φ, z) =. On the other hand, the system is tuned to be very resonant for a specific mode, the difference in kz,m for the other modes will make them rapidly dephase, i.e., make all other modes irrelevant
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