This paper describes the design and analysis of a contact-cooled channel-cut germanium monochromator for use on a high-heat-load x-ray beamline. This channel-cut monochromator is designed in the shape of a "Z" so that polishing the diffraction surfaces is easier. The incident x-ray beam, which is reflected from a mirror at a 0.15° angle, diffracts from one surface of the Z-monochromator, passes through an opening, and diffracts from the second surface. The monochromator is located 60 meters from the undulator x-ray source. The normal heat flux of the incident beam can be up to 7 W/mm2. Thermal and structural analyses are presented, and the deformation caused by gravity is considered.
The temperature gradients in a side-cooled mirror would create a thermal bending moment along the mirror length. For a slender side-cooled mirror with longitudinally uniform incident beam, the tangential slope error is primarily due to the bowing deformation caused by this thermal bending moment. The thermal bending moment depends on the temperature distribution, which is a function of the mirror geometry, heat load, and cooling design. Optimal design of a side-cooled mirror can achieve a “favorable” temperature profile to make the thermal bending moment, with respect to the substrate neutral plane, approach zero, so that the bowing deformation of the mirror is minimized. To understand the deformation of a side-cooled mirror and achieve an optimal design, a theoretical formulation is developed.
Single-crystal silicon is one of the substrate materials often used for x-ray optical components, such as mirrors and monochromators. Silicon crystal is elastically anisotropic, mechanical properties are direction dependent. Because anisotropic analysis is complicated, isotropic approximation is commonly used in the design of optical substrates. This approximation is satisfactory in most cases. However, a full anisotropic analysis is required to precisely characterize the performance of optical substrates or determine the effect of anisotropy. In this paper, single-crystal-silicon anisotropy and its effects on deformation of bendable optics are discussed. The resulting anticlastic bending is described, and a complete numerical solution as well as approximate analytical formulations, is provided. Anisotropy can be used advantageously to accentuate anticlastic bending.
The design of a contact-cooled horizontally reflecting high-heat-load mirror for use as the first optical element on an Advanced Photon Source (APS) beamline is described. The radiation source consists of a set of two collinear undulators producing an x-ray beam with up to 340 W/mm2 peak normal heat flux at the mirror located 30 m from the source. The beam incident angle is 2.6 mrad (0.15°). The mirror is 500 mm long and 75 mm wide. Specifications for this mirror are an rms tangential slope error ≤ 2 μrad and an rms roughness ≤ 2 Å. The mirror substrate is single crystal silicon. To selectively reflect photons with cut-off energies in the 7 to 33
keV range, the central part of the mirror may be coated with strips of Rh, Pt, and Be. Thermal and structural analyses of the mirror (steady state and transient) are reported. Two contact-cooling options considered are back and side cooling. The slope error of side cooling is smaller than that for back cooling. The influence of
the mirror thickness and the cooling zone are analyzed. Other options to reduce the slope error are discussed.