The axion is a hypothetical low-mass boson predicted by the Peccei-Quinn mechanism solving the strong CP problem. It is naturally also a cold dark matter candidate if its mass is below $sim$,1,meV, thus simultaneously solving two major problems of nature. All existing experimental efforts to detect QCD axions focus on a range of axion masses below $sim$,25$,mu$eV. The mass range above $sim$,40$,mu$eV, predicted by modern models in which the Peccei-Quinn symmetry was restored after inflation, could not be explored so far. The MADMAX project is designed to be sensitive for axions with masses (40--400$),mu$eV. The experimental design is based on the idea of enhanced axion-photon conversion in a system with several layers with alternating dielectric constants. The concept and the proposed design of the MADMAX experiment are discussed. Measurements taken with a prototype test setup are discussed. The prospects for reaching sensitivity enough to cover the parameter space predicted for QCD dark matter axions with mass in the range around 100,$mu$eV is presented.
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