MADMAX: A new way of probing QCD Axion Dark Matter with a Dielectric Haloscope -- Foundations

In contrast to WIMPs, light Dark Matter candidates have increasingly come under the focus of scientific interest. In particular the QCD axion is also able to solve other fundamental problems such as CP-conservation in strong interactions. Galactic axions, axion-like particles and hidden photons can be converted to photons at boundaries between materials of different dielectric constants under a strong magnetic field. Combining many such surfaces, one can enhance this conversion significantly using constructive interference and resonances. The proposed MADMAX setup containing 80 high dielectric disks in a SI{10}{tesla} magnetic field would probe the well-motivated mass range of $40$--SI{400}{microelectronvolt}, a range which is at present inaccessible by existing cavity searches. We present the foundations of this approach and its expected sensitivity.