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

Abstract

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.

Diffraction properties of a strongly bent diamond crystal used as a dispersive spectrometer for XFEL pulses

“…In the case of intense pulses with high repetition rates, one should also consider the emerging transient thermal strain waves. It has been shown that the impact of these waves can become critical for ultra-thin diamond crystals with thickness of $10 mm and repetition rates of 100 kHz and above (Yang et al, 2018).…”

Stability of Bragg reflectors under megahertz heat load at XFELs

“…The quasi-static three-dimensional effect of pulsed heat load in a Bragg reflector has been investigated in detail for low temperatures (Qu et al, 2021). Dynamic three-dimensional wave propagation has been investigated theoretically by Yang et al (2018) and Qu (2020) using numerical approaches. Three-dimensional wave propagation at low temperatures has been investigated experimentally and theoretically in the context of a PhD project (Bahns, 2021), which is related to the topic of this paper.…”

X-ray diffraction performance of thermally distorted crystals

“…Bushuev applied his model to estimate the performance of the self-seeding crystal monochromator of the European XFEL. Yang et al [ 17 ] investigated the transient thermal stress wave and vibration to describe the thermomechanical issues for thin diamond crystals under high-repetition-rate operation of an XFEL, but no further analysis was carried out about the distortion of the rocking curve induced by the non-uniform thermal load. Based on Bushuev’s work, Qu et al [ 18 ] further formulated the factors (such as the maximum strain and non-uniform thermal load) that affect the central wavelength shift and the distortion of the rocking curve, and they discussed these effects separately and quantitatively by an analytical method.…”