Theory of angular dispersive imaging hard x-ray spectrographs

A spectrograph is an optical instrument that disperses photons of different energies into distinct directions and space locations, and images photon spectra on a position-sensitive detector. Spectrographs consist of collimating, angular dispersive, and focusing optical elements. Bragg reflecting crystals arranged in an asymmetric scattering geometry are used as the dispersing elements. A ray-transfer matrix technique is applied to propagate x-rays through the optical elements. Several optical designs of hard x-ray spectrographs are proposed and their performance is analyzed. Spectrographs with an energy resolution of 0.1 meV and a spectral window of imaging up to a few tens of meVs are shown to be feasible for inelastic x-ray scattering (IXS) spectroscopy applications. In another example, a spectrograph with a 1-meV spectral resolution and 85-meV spectral window of imaging is considered for Cu K-edge resonant IXS (RIXS).Comment: 15 pages, 8 figures, 3 tables (one table with 9 figures

Maximizing Spectral Flux from Self-Seeding Hard X-ray FELs

Fully coherent x-rays can be generated by self-seeding x-ray free-electron lasers (XFELs). Self-seeding by a forward Bragg diffraction (FBD) monochromator has been recently proposed [1] and demonstrated [2]. Characteristic time To of FBD determines the power, spectral, and time characteristics of the FBD seed [3]. Here we show that for a given electron bunch with duration sigma_e the spectral flux of the self-seeding XFEL can be maximized, and the spectral bandwidth can be respectively minimized by choosing To ~ sigma_e/pi and by optimizing the electron bunch delay tau_e. The choices of To and tau_e are not unique. In all cases, the maximum value of the spectral flux and the minimum bandwidth are primarily determined by sigma_e. Two-color seeding takes place To >> sigma_e/\pi. The studies are performed, for a Gaussian electron bunch distribution with the parameters, close to those used in the short-bunch (sigma_e ~ 5 fs) and long-bunch (sigma_e ~ 20 fs) operation modes of the LCLS XFEL

Time-delayed beam splitting with energy separation of x-ray channels

We introduce a time-delayed beam splitting method based on the energy separation of x-ray photon beams. It is implemented and theoretically substantiated on an example of an x-ray optical scheme similar to that of the classical Michelson interferometer. The splitter/mixer uses Bragg-case diffraction from a thin diamond crystal. Another two diamond crystals are used as back-reflectors. For energy separation the back-reflectors are set at slightly different temperatures and angular deviations from exact backscattering. Because of energy separation and a minimal number (three) of optical elements, the split-delay line has high efficiency and is simple to operate. Due to the high transparency of diamond crystal, the split-delay line can be used in a beam sharing mode at x-ray free-electron laser facilities. The delay line can be made more compact by adding a fourth crystal

Aberration-free imaging of inelastic scattering spectra with x-ray echo spectrometers

We study conditions for aberration-free imaging of inelastic x-ray scattering (IXS) spectra with x-ray echo spectrometers. Aberration-free imaging is essential for achieving instrumental functions with high resolution and high contrast. Computational ray tracing is applied to a thorough analysis of a 0.1-meV/0.07-nm$^{-1}$-resolution echo-type IXS spectrometer operating with 9-keV x-rays. We show that IXS spectra imaged by the x-ray echo spectrometer that uses lenses for the collimating and focusing optics are free of aberrations. When grazing-incidence mirrors (paraboloidal, parabolic Kirkpatrick-Baez, or parabolic Montel) are used instead of the lenses, the imaging system reveals some defocus aberration that depends on the inelastic energy transfer. However, the aberration-free images can be still recorded in a plane that is tilted with respect to the optical axis. This distortion can be thus fully compensated by inclining appropriately the x-ray imaging detector, which simultaneously improves its spatial resolution. A full simulation of imaging IXS spectra from a realistic sample demonstrates the excellent performance of the proposed designs.Comment: 20 pages, 15 fgures, 6 table

An X-Ray Regenerative Amplifier Free-Electron Laser Using Diamond Pinhole MIrrors

Free-electron lasers (FELs) have been built ranging in wavelength from long-wavelength oscillators using partial wave guiding through ultraviolet through hard x-ray FELs that are either seeded or start from noise (SASE). Operation in the x-ray spectrum has relied on single-pass SASE due either to the lack of seed lasers or difficulties in the design of x-ray mirrors. However, recent developments in the production of diamond crystal Bragg reflectors point the way to the design of regenerative amplifiers (RAFELs) which are, essentially, low-Q x-ray free-electron laser oscillators (XFELOs) that out-couple a large fraction of the optical power on each pass. A RAFEL using a six-mirror resonator providing out-coupling of 90% or more through a pinhole in the first downstream mirror is proposed and analyzed using the MINERVA simulation code for the undulator interaction and the Optics Propagation Code (OPC) for the resonator. MINERVA/OPC has been used in the past to simulate infrared FEL oscillators. For the present purpose, OPC has been modified to treat Bragg reflection from diamond crystal mirrors. The six-mirror resonator design has been analyzed within the context of the LCLS-II beamline under construction at the Stanford Linear Accelerator Center and using the HXR undulator which is also to be installed on the LCLS-II beamline. Simulations have been run to optimize and characterize the properties of the RAFEL, and indicate that substantial powers are possible at the fundamental (3.05 keV) and third harmonic (9.15 keV).Comment: 9 pages, 14 figure

Nanoradian angular stabilization of x-ray optical components

An x-ray free electron laser oscillator (XFELO) has been recently proposed [K. Kim, Y. Shvyd'ko, and S. Reiche, Phys. Rev. Lett. 100, 244802 (2008)]. Angular orientation and position in space of Bragg mirrors of the XFELO optical cavity must be continuously adjusted to compensate instabilities and maximize the output intensity. An angular stability of about 10 nrad (rms) is required [K. Kim and Y. Shvyd'ko Phys. Rev. STAB 12, 030703 (2009)]. To approach this goal, a feedback loop based on a null-detection principle was designed and used for stabilization of a high energy resolution x-ray monochromator ($\Delta E/E \simeq 4 \times 10^{-8}$, $E$ = 23.7 keV) and a high heat load monochromator. Angular stability of about 13 nrad (rms) has been demonstrated for x-ray optical elements of the monochromators.Comment: 8 figure