Resolution of a bent-crystal spectrometer for X-ray free-electron laser pulses: diamond versus silicon.

Vladimir M Kaganer,Ilia Petrov,Liubov Samoylova

doi:10.1107/s2053273321003697

Vladimir M Kaganer, Ilia Petrov + Show 1 more

Open Access

https://doi.org/10.1107/s2053273321003697

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Abstract

The resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters: (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, distance to a detector, and anisotropic elastic constants of the chosen crystal. The results allow the optimization of the parameters of bent-crystal spectrometers for the hard X-ray free-electron laser sources.

Highlights

The self-amplified spontaneous emission (SASE) radiation pulses of an X-ray free-electron laser (XFEL) originate from random current fluctuations in the electron bunch (Saldin et al, 2000)
It is shown that the resolution is controlled by two parameters: (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, distance to a detector, and anisotropic elastic constants of the chosen crystal
We would like to keep the resolution given by the Rayleigh criterion for the cases of the best available resolution, when the resolution function is given by sinc2g, as in Figs. 2(b) and 5(a)

Summary

Introduction

The self-amplified spontaneous emission (SASE) radiation pulses of an X-ray free-electron laser (XFEL) originate from random current fluctuations in the electron bunch (Saldin et al, 2000). To resolve the entire spectrum of a pulse, the bending radius needs to be chosen such that each wavelength in the spectrum finds a position at the bent crystal where its Bragg condition is satisfied. A practical limit on the thickness of the bent crystal comes from the need to reach such small bending radii. Zhu et al (2012) combined two bent-crystal spectrometers, with different bending radii and employing different reflections, one to cover the whole energy range and the other to reach a high resolution in a limited energy range. Because of the strong bending, the orientation of the crystal with respect to the incident X-ray wave deviates from the Bragg condition within the Darwin width ÁB in an interval of distances that is small compared with the extinction length Ã.

Time-integrated diffraction intensity

Resolution of a bent-crystal spectrometer

Discussion

Conclusions