Simulation of heat transfer in zone plate optics irradiated by X-ray free electron laser radiation

Zone plates are high quality optics that have the potential to provide diffraction-limited nano-focusing of hard X-ray free electron laser radiation. The present publication investigates theoretically the temperature behavior of metal zone plates on a diamond substrate irradiated by 0.1 nm X-rays from the European X-ray Free Electron Laser. The heat transfer in the optic is simulated by solving the transient heat equation with the finite element method. Two different zone plate designs are considered, one small zone plate placed in the direct beam and one larger zone plate after the monochromator. The main result is that for all investigated cases the maximum temperature in the metal zone plate layer is at least a factor 2 below the melting point of the respective material, proving the efficiency of the proposed cooling scheme. However, zone plates in the direct beam experience large and rapid temperature fluctuations of several hundred Kelvin that might prove fatal to the optic. The situation is different for optics behind the monochromator with fluctuations in the 20 K range and maximum temperatures well below room temperature. The simulation results give valuable indications on the temperature behavior to be expected and are a basis for future experimental heat transfer and mechanical stability investigations of fabricated nanostructures.