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The construction and results of the Monte-Carlo ray-tracing simulations for a low energy x-ray crystal spectrometer designed for future experiments at the ESR storage ring with fast highly charged ions are presented. The spectrometer has a radius of the Rowland circle R = 0.5 m and operates in the Johann geometry. The x-rays emitted from a source are diffracted by spherically bent silicon Si(111) crystal and registered by two-dimensional deep depleted back-illuminated CCD camera. The estimated spectrometer efficiency, calculated according to a dynamical theory of x-ray diffraction is about 10−6. The energy resolution of the spectrometer obtained from the simulations is about 0.5 eV. Influence of the source size and Doppler broadening on the spectrometer resolution is discussed.