Characterization of transmission-type curved-crystal X-ray optics for fast ion-beam spectroscopy

The behavior of curved-crystal X-ray spectrometers in combination with fast moving sources is studied. A three-dimensional Monte-Carlo ray-tracing calculation is presented for cylindrically bent crystals used in transmission. The method allows an accurate calculation of two-dimensional line shapes and of geometrical aberrations. The geometrical formulae derived can be used for the design of spectrometers and for the analysis of experiments. For some limiting cases analytical expressions for the X-ray images are given and compared with the numerical calculations.