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The article proposes an analytical model to describe a recently discovered phenomenon of reduction of multiple scattering of positively charged particles during channeling in (1 1 1) crystallographic silicon planes. The phenomenon represents a strong suppression of the mean square angle of multiple scattering of such particles in a plane perpendicular to the channeling plane (in comparing with the non channeling particles). The proposed model is based on the development of our previously considered approximate description of the diffusion process in short crystals. Using successive reductions, we extended this description to fairly long crystals. Our analytical model explains the phenomenon observed in the experiments and allows us to calculate the behavior of the root-mean-square angle of channeling particles as a function of the crystal thickness.

A multistage collimation system for the absorption of the growing halo of circulating beams is used at the Large Hadron Collider (LHC) to protect superconducting magnets and to ensure their reliable operation. A similar system is also planned for the Future Circular Collider (FCC). Studies for the improvement of the collimation system are performed prior to the operation of the LHC with a high luminosity. Studies have shown that one of the solutions to improve the beam collimation is the use of channeling in a short bent crystal, which serves as a primary collimator throwing particles deep into the secondary collimator by means of channeling. This system is very sensitive to the angular position of the crystal and various possible vibrations. In this work, another approach to beam collimation based on the bulk reflection of particles from bent crystal-lographic planes in a sequence of crystals has been proposed. Advantages of this scheme have been justified and a multistrip crystal device has been proposed to implement this scheme.

A fast algorithm of calculating the passage of particles through a chain of bent single crystals is proposed based on the phenomenon of reflection of a relativistic-particle beam from crystal atomic planes. The results of calculating the passage of particles through a sequence of eight bent crystals are compared with the experimental data.

We present the results of an experimental study of multiple scattering of positively charged high energy particles in bent samples of monocrystalline silicon. This work confirms the recently discovered effect of a strong reduction in the rms multiple scattering angle of particles channeled in the silicon (111) plane. The effect is observed in the plane orthogonal to the bending plane. We show in detail the influence of angular constraints on the magnitude of the effect. Comparison of the multiple scattering process at different energies indicates a violation of the law of inverse proportionality of the rms angle of channeled particles with energy. By increasing the statistics, we have improved the results of multiple scattering measurements for particles moving, but not channeled, in silicon crystals., arXiv admin note: text overlap with arXiv:1910.00250 minor fixes

Studies on the steering of particle beams using channeling in aligned bent crystals have been performed at IHEP for many years. Different types of extraction schemes with bent crystals and technical equipment have been developed for experiments to test new crystal devices and to study beam collimation processes. A special apparatus has been designed to control the crystal extraction system. In this article, we describe the crystal devices and in-vacuum goniometers, the beam diagnostic tools (intensity and profile measurements), and the beam feedback system.

The generation of beams of secondary particles (π and K mesons) at proton accelerators is a difficult scientific and engineering problem. To obtain narrow directional particle beams for experiments, intense extracted proton beams are used, secondary particles (π and K mesons) are generated at an external target, and they are focused and transferred through long magneto-optical channels. In this work, a surprisingly simple method based on a crystal focusing device has been proposed to obtain secondary beams. An experiment on the production of a secondary beam using a crystal has been performed at the U-70 accelerator. Schemes for the formation of beams with energies E ~ 1 TeV have been proposed for large colliders such as the Large Hadron Collider.

The UA9 setup, installed in the Super Proton Synchrotron (SPS) at CERN, was exploited for a proof of principle of the double-crystal scenario, proposed to measure the electric and the magnetic moments of short-lived baryons in a high-energy hadron collider, such as the Large Hadron Collider (LHC). Linear and angular actuators were used to position the crystals and establish the required beam configuration. Timepix detectors and high-sensitivity Beam Loss Monitors were exploited to observe the deflected beams. Linear and angular scans allowed exploring the particle interactions with the two crystals and recording their efficiency. The measured values of the beam trajectories, profiles and of the channeling efficiency agree with the results of a Monte-Carlo simulation., 25 pages, 13 figures

International audience; Experiments to measure the electric and the magnetic moments of short-lived baryons using an internal target and two bent crystals in the vicinity of one of the existing LHC detectors were recently proposed, in the frame of the Physics Beyond Colliders Working Group at CERN. Investigating fixed-target physics in the LHC with in-vacuum solid targets is an unprecedented challenge. As a preparatory step, the layout of the UA9 experiment, installed in the CERN SPS to explore beam manipulations assisted by bent crystals, has been modified to study the feasibility of the double-crystal scenario in a circular accelerator. Ideally, the first crystal should capture halo protons in channeling states directing them onto the internal target to produce rare baryons, whilst the second crystal, located just downstream of the target, should channel the baryons, rotate their polarization vector and deflect them towards the detector area. The upgraded UA9 layout is presented. Preliminary measurements providing an insight of the beam behavior are reported.

Strong reduction of multiple scattering for channeled particles has been observed in an experiment on the deflection of a 180 GeV/c π+-meson beam by bent silicon crystals. The RMS deflections due to multiple scattering for the channeled particles were about six times smaller than for non-channeled ones. It was shown that the approach suggested recently for the description of multiple scattering for channeled particles using the experimental data for random crystal orientations gives fair agreement with the experiment. Keywords: Crystal, Channeling, Multiple scattering, Dechanneling, Beam deflection

Phenomenon of the deflection of charged particle beam due to channeling in a bent crystal is good investigated and successfully applied for extraction of the beam in high-energy accelerators, at the energies of about 10 GeV and higher. However, a significant practical interest presents the problem of deflection and extraction of charged particles with energies below 1 GeV, for example, production of ultrastable beams of low emittance for medical and biological applications. That’s why two novel crystal techniques, namely: thin sequential straight crystal targets, and array of short bent crystal strips were investigated in this report as elements for extraction of the beam from U-70 accelerator. Experimental results were obtained for extraction of 1.3 GeV protons.

Currently, bent silicon single crystals are used at large accelerators to extract and collimate proton beams. A device for multiple deflection of a proton beam based on several bent silicon strips operating in the volume reflection mode has recently been developed. In this device, the bending of silicon strips successively located on the surface of a thick plate is implemented due to the internal stress induced by grooves mechanically formed on the crystal surface (Twyman effect). Topography based on angular scanning and synchrotron radiation was applied to measure the bending of individual deflector strips and the crystal as a whole. The measurement results are compared with the data obtained with a proton beam.

The possibility of the measurement of proton ionization loss in the Silicon (Si) layer of smoothly tunable thickness was demonstrated in an experiment with a 50-GeV proton beam. The Si surface-barrier detector with the depleted layer thickness controlled by the value of high-voltage power supply was used in the experiment. The measured spectra of ionization loss are discussed and compared with the calculated spectra. The possibilities of research of the evolution of electromagnetic field of ultrarelativistic particles traversing the media interface and the study of dynamics of particles moving in the channeling regime or the volume reflection regime with the use of detectors with smoothly tunable thickness are indicated.

Recently studies are started on the application of volume reflection of particles in crystals for the steering beams (for extraction and collimation of a circulating beam in accelerators). Volume reflection is more efficient than channeling, but requires amplification of the deflection angle by applying multicrystals. The report discusses two new applications of multicrystals made like multistrip structures: (i) the property of effective deflection of particle beam was used to protect the septum magnets of the U-70 in the process of extraction of the proton beam with energy of 50 GeV; (ii) the possibility of generation of gamma radiation was studied in the secondary electron beam with energy of 7 GeV. In both cases, promising preliminary data were obtained.

International audience; At large accelerators, bent crystals are employed to deflect weakly divergent proton beams at the stages of extraction and collimation. We demonstrate that a divergent particle beam may be efficiently deflected using a crystal with a focusing entry face. A 180 GeV/c pion beam with divergence near 0.060 mrad, which exceeds the Lindhard angle by a factor of 4, has been experimentally deflected by 0.25 mrad with efficiency near 22%. The proposed focusing crystal may serve as an element of a novel particle optics for secondary-particle beams in the TeV energy region.

Experimental results on deflection of a 180 GeV/c π+-meson beam by a 23 mm long bent silicon crystal are analyzed to study the dechanneling process of particles due to multiple scattering. A new approach for the determination of contributions from atomic nuclei and electrons to the multiple scattering using the experimental data for random crystal orientations is suggested. The results of simulations performed using this approach, in which the contribution from atomic electrons is considered according to the prescription of Bethe, are in a good agreement with the experiment.

The deflection of a 1-GeV charged particle beam by a system formed by fan-oriented thin silicon wafers has been studied theoretically and experimentally. Software has been developed for numerical simulation of a particle beam transmission through a fan crystal system. In the U-70 experiment on a proton beam, the particles were deflected by such a system through an angle exceeding 1 mrad. Thus, a new method has been demonstrated for rotating a particle beam, which can be used for creating accelerator beams for medical purposes.

A beam of six-charged carbon ions with an energy of 24.8 GeV/nucleon is extracted from the U-70 synchrotron by means of a silicon crystal bent through 85 mrad. A total of 200000 particles are observed in beamline 4a upon forcing 109 circulating ions to the crystal. The geometrical parameters, timing structure, and composition of the beam have been measured. It has been shown for the first time that, using a bent single crystal, an ion beam with required parameters can be extracted from the accelerator ring and formed for regular use in physics experiments.

Extraction and collimation of the 50-GeV proton beam with a bent silicon crystal at the U-70 accelerator of the Institute for High Energy Physics (Protvino, Russia) was investigated. Until recently, proton beam extraction (and collimation) from accelerators has been effected using crystals with the (111) or (110) plane orientation, when the beam propagates far from the crystal axes. In the described experiment, the silicon crystal was oriented so that the proton beam was incident on it near the 〈110〉 axis. Under these conditions, a part of the beam was deflected by the crystal owing to the dynamic chaos phenomenon. The maximum beam extraction efficiency was as high as ~80%.

It has recently been realized that the focusing of high-energy particle beams at a distance of about 1 cm is promising. A new idea is proposed in this work to focus the beam at a short distance by using a bent plane–parallel silicon plate whose side edges are rotated at a small angle with respect to crystallographic planes. At the U-70 accelerator (IHEP, Protvino), a 50-GeV proton beam has been focused to a narrow line with a width of no more than 30 μm at a distance of 17 cm.

The problem of creation of high energy neutrino beams on the basis of modern and future circular proton accelerators with the help of traditional technology seems to be expensive and difficult. In our previous article we proposed a new method for generation of neutrino beams for 6.5 TeV protons at the LHC based on the use of focusing bent single crystals. However, in last years there have been publications devoted to proton colliders with an energy of 50 TeV. This encouraged us to study the possibility of applying of the proposed method to generate neutrino beams at these colliders. In addition, we present some new information for proton energy 6.5 TeV.

Inelastic nuclear interaction probability of 400 GeV/c protons interacting with bent silicon crystals was investigated, in particular for both types of crystals installed at the CERN Large Hadron Collider for beam collimation purposes. In comparison to amorphous scattering interaction, in planar channeling this probability is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 36\%$$\end{document}∼36% for the quasi-mosaic type (planes (111)), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 27\%$$\end{document}∼27% for the strip type (planes (110)). Moreover, the absolute inelastic nuclear interaction probability in the axial channeling orientation, along the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 110\rangle $$\end{document}⟨110⟩ axis, was estimated for the first time, finding a value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.6\%$$\end{document}0.6% for a crystal 2 mm long along the beam direction, with a bending angle of 55 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu $$\end{document}μrad. This value is more than two times lower with respect to the planar channeling orientation of the same crystal, and increases with the vertical angular misalignment. Finally, the correlation between the inelastic nuclear interaction probability in the planar channeling and the silicon crystal curvature is reported.

The problem of creation of high energy neutrino beams on the basis of modern and future circular proton accelerators with the help of traditional technology seems to be expensive and difficult. Because of this, we propose the solution of this problem based on the usage of focusing bend single crystals. In the paper we demonstrate the possibilities of acceptance and focusing of a pion beam with the help of a crystal optical lens system. As an illustration of these features the calculated neutrino fluxes for energy of circulating proton beam equal to 6.5 TeV are presented., Comment: 16 pages, 6 figures, Latex

International audience; Recent discussions about accelerators in high energy physics identified several challenges for the future, where it is necessary to focus particle beams over a distance of a few cm. In this paper, we investigate the focusing of particles by a new crystal device having such a capability. The trajectories of 180 GeV/ c pions passing through a 500 µm thick focusing crystal were reconstructed using silicon microstrip detectors. It is shown that a parallel beam of particles can be focused in one plane at a distance of 15.5 cm from the crystal, in a narrow line with an rms width of 8 µm.

International audience; This paper is devoted to an experimental study of focusing and defocusing positively charged particle beams with the help of specially bent single crystals. Four crystals have been fabricated for this purpose. The studies have been performed at the CERN SPS in 400 GeV/c proton and 180 GeV/c pion beams. The results of measurements of beam envelopes are presented. The rms size of the horizontal profile at the focus was 5–8 times smaller than at the exit of the crystals. The measured focal lengths were 4–21 m. The results of measurements are in good agreement with calculations. Possible applications of focusing crystals in present and future high energy accelerators are discussed.

The results of the experimental observation of characteristic X-ray radiation (CXR) excited in solid targets by the extracted and circulated 450 MeV/u C+6 ions beams and circulating 1.3 GeV protons beam are presented. The spectra of X-ray radiation measured from different targets are presented and discussed. It was found that the background radiation near the beams is low enough that allows the observation of the CXR spectral peaks with energies from a few to tens keV by semiconductor X-ray detectors. Applications of the CXR for monitoring of the number of accelerated particles in experimental applied and basic research, including radiobiology and radiation medicine as well as the relativistic nuclear physics and steering of beams by bent crystalline deflectors are proposed.

In this report, the continuation of studies (Afonin et al., 2003, 2012; Scandale et al., 2014) of focusing properties of bent single crystals is presented. Recently, the possibility of transforming a parallel beam into the point-like one has been demonstrated theoretically and experimentally (Scandale et al., 2014). Here we study an inverse problem of conversion of a point-like beam into the parallel one. It is shown that, by exploiting such a capability, the significantly more intensive secondary particle beams could be generated compared to usage of other conventional method.

At large accelerators, bent crystals are employed to deflect weakly divergent proton beams at the stages of extraction and collimation. We demonstrate that a divergent particle beam may be efficiently deflected using a crystal with a focusing edge. A proton beam with divergence near 1 mrad, which exceeds the Lindhard angle by a factor of 30, has been experimentally deflected by 1.8 mrad with efficiency near 15%. The proposed focusing crystal may serve as an element of a novel optical system for secondary-particle beams in the TeV energy region.

International audience; The ordered positions of atoms in crystals give a reason to study multiple Coulomb scattering of high energy charged particles within them. In addition, the accurate representation of multiple scattering of high energy protons in a bent crystal is important for studies of crystal assisted collimation at the SPS and the LHC. Multiple scattering of 400 GeV/c protons in bent silicon crystals was measured for orientations far from the directions of main crystallographic planes and axes in conditions excluding channeling of protons. The observed RMS widths of the angular distributions are a little larger than those obtained from the Moliere theory. Simulation of multiple scattering in a model of binary collisions with the crystal atoms shows about 3.5% decrease of the RMS deflection with respect to the model of a sequence of random collisions. We consider this as a possible indication of a reduction of multiple scattering of protons in a crystal in comparison with its amorphous state.

The effect of multiple volume reflections in one crystal was observed in each of several bent silicon strips for 400 GeV/c protons. This considerably increased the particle deflections. Some particles were also deflected due to channeling in one of the subsequent strips. As a result, the incident beam was strongly spread because of opposite directions of the deflections. A modified multi-strip deflector produced by periodic grooves on the surface of a thick silicon plate was used for these measurements. This technique provides perfect mutual alignment between crystal strips. Such multi-strip deflector may be effective for collider beam halo collimation and a study is planned at the CERN SPS circulating beam.

Channeling is the confinement of the trajectory of a charged particle in a crystalline solid. Positively charged particles channeled between crystal planes oscillate with a certain oscillation length , which depends on particle energy. A crystal whose thickness is half the oscillation length for planar channeling may act as a mirror for charged particles. If the incident angle of the particle trajectory with the crystal plane is less than the critical angle for channeling, under-barrier particles undergo half an oscillation and exit the crystal with the reversal of their transverse momentum, i.e., the particles are “mirrored” by the crystal planes. Unlike the traditional scheme relying on millimeter-long curved crystals, particle mirroring enables beam steering in high-energy accelerators via interactions with micrometer-thin straight crystal. The main advantage of mirroring is the interaction with a minimal amount of material along the beam, thereby decreasing unwanted incoherent nuclear interactions. The effectiveness of the mirror effect for ultrarelativistic positive particles has been experimentally proven at external lines of CERN-SPS. The mirroring effect in a 26.5-μm-thick Si crystal has been studied in the experiment with a narrow beam of 400 GeV/ c protons at the CERN-SPS. The reflection efficiency for a quasi-parallel beam is larger than 80%.

The generation of neutrino beams at proton accelerators is a difficult scientific and engineering problem. To obtain narrow directional neutrino beams for experiments, intense extracted proton beams are used, secondary particles ([Formula: see text] and [Formula: see text] mesons) are generated at an external target. Further, to obtain parallel beams of these neutrino parent particles, high-current electromagnetic lenses are used. In this work, a surprisingly simple method based on a crystal focusing device has been proposed to obtain neutrino beams. Neutrino fluxes are calculated in comparison with the traditional scheme.

It has been recently proposed using a bent crystal with a declining curvature instead of a uniformly bent crystal in order to improve extraction and collimation of the circulating beam in the accelerator. Variable curvature crystal devices developed to implement this idea are described. Curvature values measured along the crystal plate are presented. It is shown that focusing of high energy beams can also be focused using the developed devices.

We studied the dechanneling length of 150 GeV / c π − interacting with a short bent silicon crystal. Dechanneling length measures the rate and the strength of incoherent interactions of channeled particles in a crystal. The mechanism of dechanneling of negatively charged particles has been elucidated through simulation and experiment. It was found that the dechanneling length for negative particles is comparable to the nuclear dechanneling length for positive charges. Indeed, dechanneling of negative particles occurs as a result of incoherent interactions with the nuclei because the trajectories of such particles always intersect atomic planes, explaining the lower channeling efficiency for such particles. Obtained results can be useful for the design of crystals for manipulating high-energy negative particle beams through channeling.

A deflection efficiency of about 61 % was observed for 400 GeV/c protons due to channeling, most strongly along the 〈110〉 axis of a bent silicon crystal. It is comparable with the deflection efficiency in planar channeling and considerably larger than in the case of the 〈111〉 axis. The measured probability of inelastic nuclear interactions of protons in channeling along the 〈110〉 axis is only about 10 % of its amorphous level whereas in channeling along the (110) planes it is about 25 % . High efficiency deflection and small beam losses make this axial orientation of a silicon crystal a useful tool for the beam steering of high energy charged particles.

The process of radiation of 120 GeV positrons moving in a channeling regime in (011) plane of a single crystal was considered. At the beginning on the basis of the theory of nonlinear oscillations, the trajectory of moving positrons at different initial conditions was derived. Then taking into account the nonlinearity of motion, the distribution function over oscillation amplitudes of channeling particles was found. After this, the intensity of radiation at different initial conditions was calculated with the help of two various methods. These results may be useful for comparison with experimental data at positron energies from 100 and more GeV.

Two high-accuracy goniometers equipped with two bent silicon crystals were installed in the betatron cleaning insertion of the CERN Large Hadron Collider (LHC) during its long shutdown. First beam tests were recently performed at the LHC with 450 GeV/c and 6500 GeV/c stored proton beams to investigate the feasibility of beam halo collimation assisted by bent crystals. For the first time channeling of 6500 GeV/c protons was observed in a particle accelerator. A strong reduction of beam losses due to nuclear inelastic interactions in the aligned crystal in comparison with its amorphous orientation was detected. The loss reduction value was about 24. Thus, the results show that deflection of particles by a bent crystal due to channeling is effective for this record particle energy., peer-reviewed

The paper devoted to investigation of volume reflection and channeling processes of ultrarela- tivistic positive charged particles moving in germanium single crystals. We demonstrate that the choice of atomic potential on the basis of Hartree-Fock method and correct choice of Debye tem- perature allow us to describe the above mentioned processes in a good agreement with the recent experiments. Moreover, the presented in the paper universal form of equations for volume reflection gives true description of the process at a wide range of particle energies. Standing on this study we make predictions for mean angle reflection (as a function of bending radius) of positive and negative particles for germanium (110) and (111) crystallographic planes., Comment: 5 pages, 2 figures, PACS number: 41.60.-m

The efficiency of the beam extraction and collimation systems in circular accelerators with the use of the channeling effect in a bent crystal is determined. The dependences of the extraction efficiency on the geometrical parameters of the crystal (its length, thickness, and bending angle), the azimuthal location of the system components, and the offset of the septum or scraper are presented. The influence of crystal imperfections (amorphous layers, misorientation, and torsion) on the efficiency of the systems is considered, and their tolerances are proposed. It is shown that an extraction efficiency of >95% can be attained over a wide energy range from 2 GeV to 7 TeV by optimizing the crystal parameters and the positions of the system components., 8 pages, 9 figures