Simulating MADMAX in 3D: Requirements for Dielectric Axion Haloscopes

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 $50\,{\rm MHz}$ at $22\,{\rm GHz}$, corresponding to an axion mass of $90\,\mu{\rm eV}$. We find that the maximum allowed disk tilt is $100\,\mu{\rm m}$ divided by the disk diameter, the required disk planarity is $20\,\mu{\rm m}$ (min-to-max) or better, and the maximum allowed surface roughness is $100\,\mu{\rm m}$ (min-to-max). We show how using tiled dielectric disks glued together from multiple smaller patches can affect the beam shape and antenna coupling.