X-ray prism spectrometry schemes for experimental investigations of fast processes are considered. Diamond and beryllium prism dispersion parameters and special features of transmission spectra for crystal prisms are analyzed. It is shown that relative energy resolution E/AE at photon energies E ～ 10 keV may reach 10~3-10~4 and the total working spectral band is ～100 keV. This opens unique possibilities for measuring fine structures of single-shot absorption spectra for quasi-parallel beams and continuous monitoring of the fundamental and high-frequency harmonics of an X-ray free electron laser.
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