X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed.

Investigation on radiation generated by sub-GeV electrons in ultrashort silicon and germanium bent crystals

We report on the measurements of the spectra of gamma radiation generated by 855 MeV electrons in bent silicon and germanium crystals at MAMI (MAinzer MIkrotron). The crystals were 15 $$\upmu \text {m}$$ μ m thick along the beam direction to ensure high deflection efficiency. Their (111) crystalline planes were bent by means of a piezo-actuated mechanical holder, which allowed to remotely change the crystal curvature. In such a way it was possible to investigate the radiation emitted under planar channeling and volume reflection as a function of the curvature of the crystalline planes. We showed that, using volume reflection, intense gamma radiation can be produced – with intensity comparable to that obtained in channeling but with higher angular acceptance. We studied the trade-off between radiation intensity and angular acceptance at different values of the crystal curvature. The measurements of radiation spectra have been carried out for the first time in bent germanium crystals. In particular, the intensity of radiation in the germanium crystal is higher than in the silicon one due to the higher atomic number, which is important for the development of the X-ray and gamma radiation sources based on higher-Z deformed crystals, such as crystalline undulators.

First observation of ion beam channeling in bent crystals at multi-TeV energies

Planar channeling in bent crystals has been observed in LHC with multi-TeV proton beam in 2015. Two crystals, mounted on novel high-accuracy goniometers (one in the horizontal and one in the vertical plane), are integrated in the LHC collimation system, for studying the feasibility of the crystal-based collimation scheme. Using this experimental setup, tests with fully-stripped lead ion beams at both 450 Z and 6500 Z GeV were carried during dedicated LHC beam time. Planar channeling was observed for the first time with lead ions at these unprecedented energies surpassing by more than 1 order of magnitude the previous state-of-the-art for lead heavy ions and providing an important experimental basis for future applications of bent crystals in beam manipulations. The set of measurements performed to confirm this observation, as the local loss reduction in presence of channeling and the evidence of a deflected beam downstream of the crystal, are presented.

Redetermination of the strong-interaction width in pionic hydrogen

The hadronic width of the ground state of pionic hydrogen has been redetermined by X-ray spectroscopy to be $$\varGamma ^{\pi \mathrm {H}}_{1s}=(856\,\pm \,16_\mathrm{stat}\,\pm \,22_\mathrm{sys})$$ Γ 1 s π H = ( 856 ± 16 stat ± 22 sys ) meV. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institute by using the cyclotron trap and a high-resolution Bragg spectrometer with spherically bent crystals. Coulomb de-excitation was studied in detail by comparing its influence on the line shape by measuring the three different transitions K$$\alpha $$ α , K$$\beta $$ β , and K$$\gamma $$ γ at various hydrogen densities. The pion-nucleon scattering lengths and other physical quantities extracted from pionic-atom data are in good agreement with the results obtained from pion-nucleon and nucleon-nucleon scattering experiments and confirm that a consistent picture is achieved for the low-energy pion-nucleon sector with respect to the expectations of chiral perturbation theory.

General method to calculate the elastic deformation and X-ray diffraction properties of bent crystal wafers

Toroidally and spherically bent single crystals are widely employed as optical elements in hard X-ray spectrometry at synchrotron and free-electron laser light sources, and in laboratory-scale instruments. To achieve optimal spectrometer performance, a solid theoretical understanding of the diffraction properties of such crystals is essential. In this work, a general method to calculate the internal stress and strain fields of toroidally bent crystals and how to apply it to predict their diffraction properties is presented. Solutions are derived and discussed for circular and rectangular spherically bent wafers due to their prevalence in contemporary instrumentation.

Layouts for fixed-target experiments and dipole moment measurements of short-lived baryons using bent crystals at the LHC

Several studies are on-going at CERN in the framework of the Physics Beyond Collider study group, with main aim of broadening the physics research spectrum using the available accelerator complex and infrastructure. The possibility to design a layout that allows fixed-target experiments in the primary vacuum of the CERN Large Hadron Collider (LHC), without the need of a dedicated extraction line, is part of these studies. The principle of the layouts presented in this paper is to deflect beam halo protons on a fixed-target placed in the LHC primary vacuum, by means of the channeling process in bent crystals. Moreover, the presence of a second bent crystal adjacent to the target opens a unique opportunity for the first direct measurement of electric and magnetic dipole moments of short-lived baryons. Two possible layouts are reported, together with a thorough evaluation on their expected performance and impact on LHC operations.

X-ray diffraction reveals the amount of strain and homogeneity of extremely bent single nanowires

Core–shell nanowires (NWs) with asymmetric shells allow for strain engineering of NW properties because of the bending resulting from the lattice mismatch between core and shell material. The bending of NWs can be readily observed by electron microscopy. Using X-ray diffraction analysis with a micro- and nano-focused beam, the bending radii found by the microscopic investigations are confirmed and the strain in the NW core is analyzed. For that purpose, a kinematical diffraction theory for highly bent crystals is developed. The homogeneity of the bending and strain is studied along the growth axis of the NWs, and it is found that the lower parts, i.e. close to the substrate/wire interface, are bent less than the parts further up. Extreme bending radii down to ∼3 µm resulting in strain variation of ∼2.5% in the NW core are found.