Computer simulation of heat transfer in zone plate optics exposed to X-ray FEL radiation

Zone plates are circular diffraction gratings that can provide diffraction-limited nano-focusing of x-ray radiation. When designing zone plates for X-ray Free Electron Laser (XFEL) sources special attention has to be made concerning the high intensity of the sources. Absorption of x-rays in the zone material can lead to significant temperature increases in a single pulse and potentially destroy the zone plate. The zone plate might also be damaged as a result of temperature build up and/or temperature fluctuations on longer time scales. In this work we simulate the heat transfer in a zone plate on a substrate as it is exposed to XFEL radiation. This is done in a Finite Element Method model where each new x-ray pulse is treated as an instantaneous heat source and the temperature evolution between pulses is calculated by solving the heat equation. We use this model to simulate different zone plate and substrate designs and source parameters. Results for both the 8 keV source at LCLS and the 12.4 keV source at the European XFEL are presented. We simulate zone plates made of high Z metals such as gold, tungsten and iridium as well as zone plates made of low Z materials such as diamond. In the case of metal zone plates we investigate the influence of substrate material by comparing silicon and diamond substrates. We also study the effect of different cooling temperatures and cooling schemes. The results give valuable indications on the temperature behavior to expect and can serve as a basis for future experimental investigations of zone plates exposed to XFEL radiation.