Transient thermal stress wave and vibrational analyses of a thin diamond crystal for X-ray free-electron lasers under high-repetition-rate operation

High-brightness X-ray free-electron lasers (FELs) are perceived as fourth-generation light sources providing unprecedented capabilities for frontier scientific researches in many fields. Thin crystals are important to generate coherent seeds in the self-seeding configuration, provide precise spectral measurements, and split X-ray FEL pulses, etc. In all of these applications a high-intensity X-ray FEL pulse impinges on the thin crystal and deposits a certain amount of heat load, potentially impairing the performance. In the present paper, transient thermal stress wave and vibrational analyses as well as transient thermal analysis are carried out to address the thermomechanical issues for thin diamond crystals, especially under high-repetition-rate operation of an X-ray FEL. The material properties at elevated temperatures are considered. It is shown that, for a typical FEL pulse depositing tens of microjoules energy over a spot of tens of micrometers in radius, the stress wave emission is completed on the tens of nanoseconds scale. The amount of kinetic energy converted from a FEL pulse can reach up to ∼10 nJ depending on the layer thickness. Natural frequencies of a diamond plate are also computed. The potential vibrational amplitude is estimated as a function of frequency. Due to the decreasing heat conductivity with increasing temperature, a runaway temperature rise is predicted for high repetition rates where the temperature rises abruptly after ratcheting up to a point of trivial heat damping rate relative to heat deposition rate.