Simulating MADMAX in 3D: Requirements for Dielectric Axion Haloscopes

TL;DR

This paper provides detailed 3D simulations for dielectric haloscopes like MADMAX, analyzing geometrical effects, beam shape, and design tolerances to optimize axion detection sensitivity.

Contribution

It introduces comprehensive 3D modeling of dielectric haloscopes, including geometrical form factors, beam shape, and realistic tolerances, advancing the design and understanding of MADMAX.

Findings

Geometrical form factor reduces emitted power by up to 30% compared to 1D models.

Realistic axion velocities and magnetic field inhomogeneities have negligible impact on sensitivity.

Design tolerances include maximum disk tilt of 100 μm per diameter, planarity of 20 μm, and surface roughness of 100 μm.

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.