Nanometer-thin multilayer coatings can enable high performance of focusing X-ray telescopes to energies up to 200 keV and beyond. In this paper we discuss the multilayer parameters and their limitations necessary for the reflection of hard X-ray photons. We present several multilayer coating designs that are optimized with a Differential Evolution algorithm to perform a stochastic global search of the multi-parametric model space. The coating designs are based on the new specifications of the HEX-P mission geometry, optimizing within the energy range 60 keV - 200 keV. We compare the simulated reflectivity spectra of Si/Ni, Si/Pt and Si/W, at different incident angles. We find the effective upper limit of bilayers in the multilayer stack, beyond which reflectivity will not be increased. We discuss a hybrid multilayer coating design, consisting of either a Si/Pt or Si/W multilayer with a top Si/Ni multilayer.
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