Temperature distribution, deformations, and x-ray diffraction in the inclined high heat load monochromator: Analytical solutions

Analytical solutions for the temperature distribution and displacement field gradients in the high heat load monochromator are presented. The footprint of the incident x-ray beam on the crystal surface is approximated by an infinitely long narrow strip, which is applicable in the case of the inclined diffraction geometry. The two-dimensional problem in the cross section of the crystal normal to the footprint is considered. The solutions for the temperature distribution and displacement field gradients are found in terms of Fourier integrals. These expressions are also valid for x-ray mirrors. The deviation of the incident beam from exact Bragg position produced by this deformation is calculated. All numerical examples are calculated for the special undulator which is to be installed in the sector III of the Advanced Photon Source