Thermo-mechanical analysis and design optimization of front-end compound refractive lens

Abstract

The X-ray power absorption by the Beryllium compound refractive lenses (CRL) installed in the ESRF ID10 front-end reaches 139 W. This non-negligible power leads to an excessive temperature in the lens such that the induced thermal stress is much larger than the yield stress of Beryllium. The thermal fatigue damage of the lens occurred after certain number of operation cycles. Sudden loss of focusing ability was observed recently after 6 ~ 7 years frequent operation. SEM and phase contrast images confirmed the damage of the CRL. Following these observations, optimization of some design parameters (width, and thickness of the thin part between two holes) of the CRL has been carried out as well as some operational parameters (cooling of the lens, vertical aperture of the X-ray beam on the lens). An optimized Beryllium CRL for the ID10 front-end should have a width of 10 mm instead of 2 mm and the thickness of the thin part between two holes should be increased to 0.2 mm. The temperature of the CRL can be reduced by a better cooling of the lens, for instance by improving the thermal contact between the Beryllium and the copper cooling block, or by reducing the vertical aperture of the X-ray beam from 4 mm to 2 mm (eventually to 1 mm).