Calculations of integrated reflectivity for selected bent crystals used in x-ray spectrometers at the National Ignition Facility

Several x-ray spectrometers at the National Ignition Facility employ organic and semi-organic crystals with large lattice constants. Use of low-order Bragg reflections of these crystals enables x-ray spectroscopy in the soft and tender x-ray regimes. The crystals are curved to define spectrometer's key performance characteristics such as energy range and source focus. The curvature leads to elastic deformation of the crystal lattice which affects x-ray reflectivity in Bragg diffraction and thus the spectrometer's response. We performed calculations of x-ray reflectivity curves for several crystals of elliptical shape using pyTTE code. The code solves Takagi-Taupin's equations using models of elastic deformations of anisotropic crystal membranes bent to fixed radii of curvature. The deformation field for the elliptical crystals was approximated locally with that of a cylinder of a radius matching the local radius of curvature for the ellipse. The new results in the form of integrated reflectivity as a function photon energy were compared with earlier calculations using a similar strategy on assignment of the curvature and the multilamellar model of XOP program. In addition, the results were compared to those inferred from experimental measurements of crystal sensitivities.