High intensity for diffraction experiments with high-energy resolution on an intense x-ray beam, like the bending magnet beam lines at the ESRF, requires a strict control of the curvature of the optical elements placed in the beam for geometrical focusing and for wavelength monochromatization. Unwanted curvatures can come from nonuniform and variable heating of the optical elements produced by the absorption of x rays. To design the CRG/D2AM beam line described in the accompanying paper, some new techniques were developed to control these effects based on geometrical, i.e., topological, considerations. (1) Cooling of the entrance mirror: longitudinal curvature can be strongly reduced by cooling the mirror from the sides (and not from the rear) and only near the reflecting surface (i.e., not over the whole lateral surface). The cooling can be achieved for instance with an isothermal liquid Ga eutectic bath. (2) Cooling of the first single-crystal Si monochromator: because of the size of the crystal, only cooling from the rear is conceivable in this case. It can be shown by calculation that the curvature due to the front-to-rear gradient can be exactly compensated by the thermal expansion of a metallic layer at the rear of the crystal, having a larger expansion coefficient than Si.
