High heat flux x-ray monochromators: What are the limits?

First optical elements at third-generation, hard x-ray synchrotrons, such as the Advanced Photon Source (APS), are subjected to immense heat fluxes. The optical elements include crystal monochromators, multilayers and mirrors, This paper presents a mathematical model of the thermal strain of a three-layer (faceplate, heat exchanger, and baseplate), cylindrical optic subjected to a narrow beam of uniform heat flux. This model is used to calculate the strain gradient of a liquid-gallium-cooled x-ray monochromator previously tested on an undulator at the Cornell High Energy Synchrotron Source (CHESS). The resulting thermally broadened rocking curves are calculated and compared to experimental data. The calculated rocking curve widths agree to within a few percent of the measured values over the entire current range tested (0 to 60 mA). The thermal strain gradient under the beam footprint varies linearly with the heat flux and the ratio of the thermal expansion coefficient to the thermal conductivity. The strain gradient is insensitive to the heat exchanger properties and the optic geometry. This formulation provides direct insight into the governing parameters, greatly reduces the analysis time, and provides a measure of the ultimate performance of a given monochromator.