Bent Silicon Crystal Research Articles

Focusing Elements and Design Considerations for a Scanning Helium Microscope (SHeM)

We describe recent developments in the fabrication of an atom-optical mirror for focusing thermal helium atoms. A bent silicon crystal is, in principle, capable of high intensity, low aberration helium reflection; manipulation of the mirror's macrostructure minimizes optical aberrations in the device whilst chemical control over the mirror's microstructure ensures high intensity reflection. Incorporation of the atom mirror into a novel Scanning Helium Microscope (SHeM) is outlined, in the context of surface-structural studies. In particular, we refer to the expected operation, contrast mechanisms and resolution of such an instrument.

On the reduced interaction probability for fully stripped 33 TeV/c Pb ions channeled in a bent Si crystal

We compare experimental results and computer simulations on the reduction of inelastic interactions for 33 TeV Pb 82+ ions channeled in a bent silicon crystal. The comparison shows that a very small fraction of the initially channeled ions suffer nuclear interactions while traversing the 60 mm long crystal under perfect alignment, even though its thickness would correspond to about 1.2 nuclear interaction lengths for an amorphous material. This result indicates that a bent crystal approach to extraction of high energy, fully stripped ions from e.g. RHIC or LHC might be feasible.

Model of sagittally bent silicon crystals diffracting in the Laue mode: Effects of elastic anisotropy on the rocking-curve widths (abstract)

Sagittal focusing of synchrotron x rays with asymmetric Laue crystals has been proposed and demonstrated [Z. Zhong, C. C. Kao, D. P. Siddons, and J. B. Hastings, J. Appl. Crystallogr., Pts I&II (submitted)]. At high x-ray energies, sagittal focusing by a Laue crystal is preferred because of the small extent of the beam’s footprint on such a crystal, and the ability to use the inverse-Cauchois geometry in the meridional plane to improve energy resolution. Reflectivity curves of sagittally bent Laue crystals were measured at x rays energies from 15 to 70 keV. A model for the diffraction properties of sagittally bent Laue crystals, which takes into account the anisotropy in the elastic property of the crystals, was developed. Analytical formulas were derived for the rocking-curve width of such crystals, including both the contribution from the lattice angle change and the d-spacing change due to sagittal bending, across the thickness of the crystal. The contribution of the orientation-dependent elastic compliance S23 is as important as S13 in the specific case of sagittally bent Laue crystals. The widths of the rocking curves, calculated using the analytical model, were compared with measurements on crystals of two different orientations (111) and (100). Good agreements were found. An interesting sign reversal in the slope of the lattice angle versus depth curve between the (111)- and (100)-oriented crystals is predicted by the model, as a result of the highly anisotropic properties of silicon crystal. Results of depth-resolved rocking-curve measurements and high-resolution diffraction, designed to confirm these theoretical findings, are discussed.

Studying a Mode of Intense Proton Beam Extraction by a Bent Crystal with Simultaneous Operation with Internal Targets on the U-70 IHEP Accelerator

A method for extracting a proton beam from the U-70 IHEP synchrotron using a bent silicon crystal at a simultaneous operation of several internal targets is described. The optimal range of the crystal bending angles is 0.5–2.5 mrad, and the crystal length along the beam is 2–5 mm. The extracted-beam intensity can be varied from 107 to 6.0 × 1011 protons per cycle of the U-70 operation, depending on the requirements of physical experimental installations. The method developed for the accelerated-beam extraction with the use of short crystals significantly extends the possibilities of conducting physical experiments on the accelerator.

Experimental characterization of bent focusing crystals

It has been established with the aid of a double-crystal X-ray diffractometer that the nonuniform curvature of cylindrically, spherically, or thoroidally bent silicon and quartz crystals is of a periodic character. It is shown that this periodicity influences the spectral (energy) resolution of a focusing crystal, which becomes noticeable at the Bragg angle θ obeying the condition tan2 ≫ 1.

Extraction of a 70-GeV/cProton Beam to the RAMPEX Setup by Using a Silicon Crystal

The experimental data on the formation of a stable proton beam with a 70-GeV/cmomentum extracted from the U-70 accelerator (Protvino) to the 14th channel with a bent silicon crystal (under conditions of operation of several setups) are presented. The beam is intended for the RAMPEX experimental facility with a polarized target. The beam intensity, angular divergence, and spot size on the target should be at least 5 × 106protons per cycle, below 2.5 mrad, and no larger than 10 (horizontal) and 14 (vertical) mm, respectively. The results obtained show that the beam is stable in the single extraction mode, but its dimensions are slightly larger than those required by the experiment. An instability of the beam is observed when the beam is extracted to several experimental setups in parallel. Further investigations are planned in order to optimize the position and parameters of the silicon single crystal.

Instrumentation of the ESRF medical imaging facility

At the European Synchrotron Radiation Facility (ESRF) a beamport has been instrumented for medical research programs. Two facilities have been constructed for alternative operation. The first one is devoted to medical imaging and is focused on intravenous coronary angiography and computed tomography (CT). The second facility is dedicated to pre-clinical microbeam radiotherapy (MRT). This paper describes the instrumentation for the imaging facility. Two monochromators have been designed, both are based on bent silicon crystals in the Laue geometry. A versatile scanning device has been built for pre-alignment and scanning of the patient through the X-ray beam in radiography or CT modes. An intrinsic germanium detector is used together with large dynamic range electronics (16 bits) to acquire the data. The beamline is now at the end of its commissioning phase; intravenous coronary angiography is intended to start in 1999 with patients and the CT pre-clinical program is underway on small animals. The first in vivo images obtained on animals in angiography and CT modes are presented to illustrate the performances of these devices.

On the energy dependence of proton beam extraction with a bent crystal

Proton beam extraction from the CERN SPS by means of a bent silicon crystal is reported at three different energies, 14 GeV, 120 GeV and 270 GeV. The experimental results are compared to computer simulations which contain a sound model of the SPS accelerator as well as the channeling phenomena in bent crystals. The overall energy dependence of crystal assisted proton beam extraction is understood and provides the basis to discuss such a scheme for future accelerators.

A novel application of bent crystal channeling to the production of simultaneous particle beams

Channeling of a 450 GeV/ c proton beam through a bent silicon crystal has found a novel application to the production of simultaneous particle beams. A pair of simultaneous, nearly-collinear beams of long- and short-lived neutral kaons has thereby been derived. These beams form an integral part of an experiment, NA48, at CERN, designed to measure the CP-violation parameter ϵ′ ϵ with high precision.

First results from bent crystal extraction at the Fermilab Tevatron

First results from Fermilab Experiment 853 are presented. E853 is an experiment to test the feasibility and efficiency of extracting a low-intensity beam from the halo of the Tevatron using channeling in a bent silicon crystal. The motivation of the experiment is to apply crystal extraction to trans-TeV accelerators like the LHC. Extensive simulation work has been carried out. Two accelerator operating modes have been developed for crystal studies, “kick” mode and diffusion mode. Results from the first successful extraction in kick mode are presented.

Deflection efficiency and energy loss distributions for high energy protons in a bent crystal

Energy loss distributions and the deflection efficiency of 450 GeV protons during their passage through a (111) bent silicon crystal have been calculated by computer simulation. The path dependent stopping power and local electron density averaged along the particle trajectories were used to construct the energy loss spectra for the considered crystal layers. It was shown that the most probable energy loss for deflected particles and their straggling increase during the passage through the crystal part with increasing curvature. The observed characteristics of the calculated energy loss distributions for deflected and undeflected particles are in good agreement with experiment.

New results from the CERN-SPS beam deflection experiments with bent crystals

Results from five distinct bending experiments performed recently in the H8 beam at CERN are presented. Firstly, deflection of a positive pion beam at 200 GeV/c is compared to the “standard” 450-GeV/c proton beam for a bending angle of 3.1 mrad along the (111) plane in a 50 mm silicon crystal. Second, deflection of negative pions at 200 GeV/c is investigated for the same crystal, for incidence along the (111) plane as well as the 〈110〉 axis. Small deflection effects are seen, but no negative particles are bent through the full bending angle of the crystal. Third, the first results from beam deflection at high energy using a germanium crystal are shown. Slightly higher deflection efficiencies than for silicon are seen for large bending angles, but significantly smaller than expected for such a crystal with higher atomic number. Fourth, deflection efficiencies using a strongly irradiated silicon crystal have been measured for the first time, and a small reduction in efficiency is seen in the irradiated region. Finally, deflection of positive particles using axial alignment of a bent silicon crystal has been investigated at 450 GeV/c. Qualitatively similar behaviour as in previous experiments at 12 GeV/c is seen; the beam splits into several beams corresponding to the different planes, and even weak planes are observed.

Muon cooling via ionization energy loss in a crystal channel

A possible method for high energy muon cooling via ionization energy loss in a focusing crystal channel is outlined here. We show that starting with an initially ‘cool’ muon beam, e.g. coming from a 25 GeV photo-production source, with the normalized emittance of ϵ N = 10 −5 mrad, one can decrease the transverse emittance to less than ϵ N = 10 −7 mrad by passing muons through total of 280 m of the crystal absorber. For a practical implementation, we suggest a storage ring configuration, where sections of crystal absorber are alternated with a conventional high gradient re-acceleration (20 MeV/m) inserts. The necessary circular confinement (bending) would be provided by additional sections of bent crystals — employing powerful steering features of bent silicon crystal demonstrated by recent experiments. Required cooling length of 280 m constitutes only about 2 × 10 −3 of the muon lifetime in the laboratory frame (about 120 turns in our model ‘cooling ring‘). Dominant heating process (due to multiple scattering on electron gas inside a crystal channel) limits the minimum achievable emittance to about ϵ N = 10 −9, while the characteristic ionization cooling damping length is about 62.5 m. Feasibility of effective ionization cooling rests on the ultra high fundamental crystal fields available in a solid state environment.

Simulation results of bent crystal extraction in the Tevatron

We present simulation results describing parasitic extraction of a high energy proton beam from the Tevatron via a bent Silicon crystal — demonstrated recently by E853 experiment at Fermilab. In a spirit of parasitic extraction the transverse phase-space of the beam is initially prepared, so that only high amplitude particles from the beam halo interact with the Silicon crystal (inserted into the beam), without affecting the ‘core’ of the beam. As a result of the beam halo-crystal interaction (multiple scattering and wide angle nuclear interaction), some fraction of the beam halo channels into the crystal — a multi-turn extraction occurs. The ultra strong focusing environment of a crystal channel combined with the externally imposed curvature (vertically bent crystal) provide excellent guiding features of an efficient extraction line. Here, we use a realistic model of the Tevatron lattice to describe the beam optics of the machine. Presented phase-space simulation describes a ‘kick’ mode of the E853 experiment. To enhance the beam halo interaction with the crystal, the proton beam is initially excited by firing a transverse kicker, which induces horizontal oscillations of the beam centroid on the subsequent turns. A realistic phase-space tracking yields turn-by-turn channeling efficiency, which sheds light on multi-turn extraction mechanisms. It also allows us to optimize experimental configuration parameters for maximum extraction efficiency.

High efficiency multi-pass proton beam extraction with a bent crystal at the SPS

Recent measurements of 120 GeV proton extraction by means of a bent silicon crystal at the CERN-SPS accelerator are summarized. The existence of multi-pass extraction has been proven by blocking first-pass extraction: using a crystal covered with an amorphous layer, extracted beam with high efficiency was observed, which provides a direct proof for the importance of the multi-pass mechanism. This opens new possibilities in the design and optimization of a bent crystal extraction scheme.

X-ray focusing optics. II. Properties of doubly bent crystals with an extended x-ray source

Calculations and analysis of an extended x-ray source image with a 2D focusing geometry are presented. Based upon the calculations for an x-ray point source image (Paper Ia), theoretical expressions are derived which reveal the contributions from both the Bragg and the optical (Fresnel) diffractions to the intensity distribution of the image at the focal plane. That is, for a given focusing geometry, the intensity distribution of the image of an extended source consists not only of the crystal rocking curves for a bent crystal, due to the Bragg diffraction; but also of the optical diffraction, the Fresnel integral, due to the phase correlations of the thickness and the spatial extent of a doubly bent crystal. The contribution from the optical diffraction depends solely upon the bent crystal focusing geometry. The relationship between the source and the image at the focal plane is obtained, and the intensity distribution of an extended x-ray source image with a 2D bent silicon crystal is given.

X-ray focusing optics. I. Applications of wave optics to doubly curved crystals with a point x-ray source

A wave optics approach to the calculations of the intensity distribution of an x-ray point source image with a two-dimensional (2D) focusing geometry is presented. Analytical formulas are derived to calculate the intensity distribution at the focal plane. This approach has taken into account the effects of x-ray scattering within a 2D bent crystal, which includes the x-ray refraction and absorption inside the crystal, and the effects of elastically deformed crystals described by the anisotropic elasticity theory. Based upon the elastic bending model, the modified Bragg law and 2D lens equations are discussed. In addition, the x-ray extinction distance for curved crystals is found to be dependent on the size and the bending radius of bent crystals. For a monochromatic x-ray point source, calculation of the intensity distribution with a 2D bent silicon crystal is given for both perfect and misaligned sources. The spatial resolution and the size of the image are determined.

High-resolution x-ray spectrometer based on a cylindrically bent crystal in nondispersive geometry

The results from a new crystal spectrometer for high-resolution inelastic scattering and resonant Raman scattering spectroscopy are presented. It is based on a cylindrically bent silicon crystal in standard Rowland circle geometry where the energy dispersion is obtained nonconventionally by placing a position sensitive detector perpendicular to the scattering plane. The advantage of this geometry is that the energy dispersion is only about one order of magnitude larger than the intrinsic energy resolution of the instrument, allowing the optimization of the collection efficiency within a narrower energy range of interest while preserving the practical realization of a cylindrically bent crystal. A total energy resolution of 0.7 eV at 8 keV with an energy dispersion of only a few eV was reached. Potential applications of this new geometry as well as comparison with other focusing geometries are also discussed.

Two-dimensional focusing X-ray optics: application of anisotropic elasticity theory for characterization of bent crystals

Anisotropic elasticity theory is applied to calculations of the one- and two-dimensional curved crystals widely employed in X-ray optics. The expression for the displacement vector involved in the process of X-ray Bragg diffraction by a curved crystal is derived. The derivation takes into account the anisotropic elasticity effects for a crystal plate subjected to pure bending. Expressions for the angular deviation from the Bragg angle along the crystal surface are obtained for cylindrically, spherically and toroidally bent crystal geometries. The relationship between the radii of curvature of the crystal and the crystal's compliance tensor is discussed. It is shown that, for a given crystal, the occurrence of the anticlastic curvature effect directly depends on the crystal orientation. Bent silicon crystal plates with (200), (111) and (220) orientations are used to illustrate the influence of the anisotropic elasticity effects on the shape of the diffracting region on the crystal's surface.

Extraction from TeV-range accelerators using bent crystal channeling

Plans and first results from Fermilab Experiment 853 are presented. E853 is an experiment to test the feasibility and efficiency of extracting a low-intensity beam from the halo of the Tevatron using channeling in a bent silicon crystal. The motivation of the experiment is to apply crystal extraction to trans-TeV accelerators like the LHC. Channeling developments related to crystal extraction and some early results from accelerator studies at the Tevatron are presented.