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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.

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.

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.

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.

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

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.

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 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

The possibilities of the extraction and collimation of a circulating beam by a new method due to the reflection of particles in crystals with axial orientation were experimentally investigated in the Fall-2010 run at the U_70 synchrotron. Such crystals have positive features, because the axial potential is five times larger than the planar potential. It has been shown that the collimation efficiency can reach 90% due to axial effects in the crystal. Losses of the circulating beam on a collimator have been reduced by several times; this makes it possible to suppress the muon jet near the steel collimator of the circulating beam.

The efficiency of the deflection of 50-, 15-, and 1.3-GeV proton beams by means of planar channeling in a bent silicon crystal has been compared to that by means of the stochastic mechanism of the deflection of charged particles by the bent crystal. The deflection of protons at single passage through the crystal has been simulated. The results of the experiment on the deflection of a circulating beam at the U-70 accelerator (Institute for High Energy Physics, Protvino, Moscow region) are presented. It has been shown that the efficiency of the stochastic deflection mechanism increases with a decrease in the energy, whereas the efficiency of the planar channeling for deflection decreases.

The phenomenon of the deflection of a charged particle beam due to channeling in a bent crystal is thoroughly investigated and successfully applied for the extraction of the beam in high-energy accelerators, at the energies of about 10 GeV and higher. However, a big practical interest lies in the task of bending and extracting charged particles with energies below 1 GeV, for example, for the production of ultrastable beams of low emittance for medical and biological applications. That is why a novel crystal technique, namely thin straight crystal targets, is investigated in this article, using crystals as elements for extraction and collimation of the circulating beam in a ring accelerator. The advantages of reflection in straight crystals in comparison with bent crystal channeling consist in the small length of straight crystals along the beam that reduces the amount of nuclear interactions and improves the background. Experimental results were obtained for the bending of a 100 MeV positron beam with using five sequential straight crystals.

The momentum dispersion of the proton beam extracted from the vacuum chamber of the U-70 accelerator by channeling was measured for the first time. At an 80-mrad bending angle of the Si single crystal, the following beam parameters were attained: an intensity of 107 protons/s for 1012 protons/s hitting the crystal, momentum dispersion of the beam Δp/p = 0.13%, and a background particle admixture of 0.03% or less.

Works on the steering of particle beams using channeling in aligned bent crystals have been carried out at IHEP over a number of years. Comprehensive theoretical and experimental studies have led to the creation of actually operating systems on the U-70 accelerator. In particular, a slow proton beam extraction with unprecedentedly high parameters, an extraction efficiency of about 85% at a beam intensity of 10[Formula: see text] particles per cycle, has been realized on U-70 using particle channeling in short bent crystals. In recent years, successful experiments on the extraction of carbon ions were performed. At present, crystal elements are used in regular U-70 runs and provide half of the particle beams for physical experiments. Here, we summarize the results of this unique experience in the world practice of accelerators and outline its prospects.

New crystalline equipment—an array of bent strips and fan reflector based on thin flat plates—has been used to investigate the extraction and collimation of a circulating beam in an accelerator with an energy of 50 and 1.3 GeV. It has been shown that new equipment can efficiently control the beam in a wide energy range. An extraction and collimation efficiency of 90%, which is a record for this method, has been achieved for 50-GeV protons.

Channeling in a short bent silicon crystal was investigated at the CERN SPS using 400-GeV/c protons with an angular spread much narrower than the critical channeling angle. Particle dechanneling due to multiple scattering on the atomic nuclei of the crystal was observed and its dechanneling length was measured to be about 1.5 mm. For a crystal with length comparable to such dechanneling length, an efficiency of 83.4% was recorded, which is close to the maximum value expected for a parallel beam and exceeds the previously known limitation of deflection efficiency for long crystals.

The staff of the Institute of High-Energy Physics together with researchers from Russian and foreign scientific centers have discovered a new physical phenomenon – reflection of fast charge particles in curved crystals. This article presents the first experimental results using multiple reflections of protons in silicon crystals to increase the beam collimation efficiency in the U-70 accelerator. The experimental data are compared with theoretical models. The technology developed using reflecting crystals can be used to form oppositely propagating beams in accelerators and has prospects for extracting low-emittance beams on ~1 GeV accelerators for electronuclear facilities and in medicine and industry.

The emission of photons in the motion of a 10-GeV positron beam in bent silicon crystals has been experimentally investigated. The experimental data are compared with the theoretical calculations.

The paper is devoted to the study of volume reflection and volume capture of high energy particles moving in planar fields of bent single crystals. The influence of volume capture on the process of volume reflection was considered analytically. Relations describing various distributions of particles involved in the process, the probability of volume capture and the behavior of channeling and dechanneling fractions of a beam were obtained. Results of the study will be useful in the realization of multicrystal devices for collimation and extraction of beams on modern and future accelerators.

The calculations of the intensity of radiation in the crystal undulator for the conditions close to ones, which take place for IHEP undulator experiment, were carried out. Motion of positrons in the crystal undulator represents a superposition of the two types of motion: quasiperiodic motion between groves of the undulator and the similar motion in the channeling regime. Our calculations take into account the influence of the channeling motion on the intensity of the undulator radiation. The both parameters, characterizing the each type of motion, are larger then 1. The obtained results will be used for the comparison with the experimental data.

We analyze the scattering of 480 MeV positrons in bent crystal lattices carried out at the Beam Test Facility of the INFN – Laboratori Nazionali di Frascati. We observe experimentally that some particles follow the bending of the crystal lattice, presumably being guided by channeling phenomenon, and are deflected through the angles of about 10 mrad over length of 1 mm of silicon. This technique may lead to the use of channeling effect for steering of particle beams at the energies under 1 GeV, aimed at the production of ultrastable beams of low emittance for medical and biological applications.

In the present experiment, the radiation from positrons moving in a periodically deformed crystal was observed for the first time. The spectra of radiation are measured in a wide range of energy. The experimental indication showing the existence of an undulator peak in radiation was obtained at a qualitative level and was confirmed by calculations. Crystal undulators provide an equivalent magnetic field of 1000 T and periods in the submillimeter range and consequently can be applied to the generation of X-rays and gamma-rays, of energies a hundreds times higher than the radiation in usual undulators.

The application of bent crystals for extracting accelerated beams from high-energy accelerators is reviewed. The results of realizing highly efficient extraction of protons from the IHEP accelerator are presented. Proposals on using oriented crystals for designing efficient positron sources at linear colliders and on developing new undulators are discussed.

Accelerator-based sources of hard-photon radiation are a rapidly developing field. Coherent radiation of a particle beam in an undulator is a popular choice. The crystalline undulators with periodically deformed crystallographic planes offer electromagnetic fields of the order of 1000 T and could provide a period L in the sub-millimeter range. In this way, a hundred-fold gain in the energy of emitted photons would be reached, as compared to a usual undulator. The first real construction of a crystal channeling undulator was recently proposed and realised by the present collaboration. After the sine-like deformation of crystal was proven in X-ray tests, four undulators were tested for channeling in a beam of 70-GeV protons. It was observed in the experiment that the crystal cross-section is efficiently channeling high energy particles, similarly to usual crystal deflectors. The experimentally established transparence for channeling of high energy particles allows one to start a direct experiment on photon production from a positron beam in the crystalline undulator. Details of commissioning of the experimental setup in the first run with 3 GeV positron beam are presented.

IHEP Protvino has pioneered the wide practical use of bent crystals as optical elements in high energy beams for beam extraction and deflection on permanent basis since 1989. In the course of IHEP experiments, crystal channeling has been developed into efficient instrument for particle steering at accelerators, working in predictable, reliable manner with beams of very high intensity over years. Crystal systems extract 70 GeV protons from IHEP main ring with efficiency of 85% at intensity of 10 12 , basing on multi-pass mechanism of channeling proposed theoretically and realized experimentally at IHEP. Today, six locations on the IHEP 70 GeV main ring of the accelerator facility are equipped by crystal extraction systems, serving mostly for routine applications rather than for research and allowing a simultaneous run of several particle physics experiments, thus significantly enriching the IHEP physics program. The long successful history of large-scale crystal exploitation at IHEP should help to incorporate channeling crystals into accelerator systems worldwide in order to create unique systems for beam delivery. We report recent results from the research and exploitation of crystal extraction systems at IHEP.

Bent silicon monocrystals are used today in the planar channeling mode for beam extraction and collimation at large accelerators. Volume reflection is more efficient than channeling, though it has a small deflection angle. A device for repeated deflection of a proton beam using a few bent silicon strips in the reflection mode is described in this paper. Sequential silicon strips on the surface of a thick plate are bent by internal stresses in the crystal material resulting from the Twyman effect. As shown by the Monte Carlo calculations, this method for deflecting the beam is optimal for the teraelectronvolt energy range.

Bent crystals are used at large accelerators to deflect particle beams for extraction and collimation. Not only the deflection but also the focusing of beams by bent crystals can be required for recently formulated proposals for investigations at the Large Hadron Collider (LHC) with a fixed target. The experimental results on the focusing of a 50-GeV proton beam with a new crystal device, which can be used in a circulating beam of a large accelerator such as the LHC, have been reported.

A beam line for electrons with energies in the range of 1 to 45 GeV, low contamination of hadrons and muons and high intensity up to 10^6 per accelerator spill at 27 GeV was setup at U70 accelerator in Protvino, Russia. A beam tagging system based on drift chambers with 160 micron resolution was able to measure relative electron beam momentum precisely. The resolution sigma_p p was 0.13% at 45 GeV where multiple scattering is negligible. This test beam setup provided the possibility to study properties of lead tungstate crystals (PbWO_4) for the BTeV experiment at Fermilab.

The electromagnetic calorimeter for a new Fermilab collider program named BTeV is based on lead tungstate scintillating crystals (PbWO4). Various properties of crystals manufactured by Russian and Chinese companies were measured at the U70 accelerator in Protvino. A dedicated beam momentum tagging system was used to measure the energy and spatial resolution.

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.

The results of observation and studies of focusing of 400 GeV/ c proton beam with the help of bent single crystals are presented. Two silicon crystals have been used in the measurements. The focal length of the first and second crystals is found to be 1.48 m and 0.68 m, respectively. The mean square size of the horizontal profile in the focus was 3.1 and 4.3 times as small as at the exit of the crystals.