Simulating MADMAX in 3D: Requirements for Dielectric Axion Haloscopes
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 μeV. We find that the maximum allowed disk tilt is 100 μm divided by the disk diameter, the required disk planarity is 20 μm (min-to-max) or better, and the maximum allowed surface roughness is 100 μm (min-to-max). We show how using tiled dielectric disks glued together from multiple smaller patches can affect the beam shape and antenna coupling.