Thermal loading on crystals in an x-ray free-electron laser oscillator

Abstract

X-ray free electron laser oscillators (XFELOs) are future light sources that produce fully coherent hard x-ray pulses. Based on the low-gain principle, the XFELO traps x-ray pulses in an optical cavity composed of multiple Bragg-reflecting mirrors that have high reflectivity in a bandwidth of about ten meV. The crystal mirrors exposed to intense x-ray beams in the optical cavity are subject to thermal deformations that would shift and distort the Bragg reflectivity curve. Therefore, the stability of the XFELO operation depends on the ability of the mirrors to maintain the Bragg reflection under such thermal load. A new approach was used to analyze the thermal load of the mirrors. The approach utilizes a dedicated Bragg reflection physical process in geant4 to obtain precise absorption information of the XFELO pulses in the crystal. Following transient thermal behavior, including single pulse and multiple pulse inputs, was analyzed by finite element analysis software based on the energy absorption information extracted from the geant4 simulation. It is shown that, for a typical XFELO pulse depositing about ten microjoules energy the over a spot of tens of micrometers in radius, the thermal relaxation time across the thickness is on tens of nanoseconds scale. In this situation, a simplified heat-load model is then developed to integrate the heat load in the XFELO. With the simplified model, the potential impact of the thermal load on the XFELO operation is estimated. When a large amount of heat remains in the crystal, the pulse energy drops significantly and has large oscillations due to negative feedback of the temperature change on the pulse energy.