We show that theory predictions for volume reflection in bent crystals agree with recent experimental data. This makes possible to predict volume reflection angle and efficiency in a broad range of energy for various crystals. A simple formula is proposed for volume reflection efficiency. We derive the physical limits for application of crystal reflection at high-energy accelerators where it may help beam collimation.
Recent theoretical results on charged particle interaction with planarly oriented thin bent crystals are reviewed, with the emphasis on dynamics in the continuous potential. Influence of boundary conditions on the volume-reflected beam profile is discussed. Basic properties of coherent bremsstrahlung in a bent crystal are highlighted.
Preliminary results of numerical simulations of electron and positron channeling and emission spectra are reported for straight, uniformly bent and periodically bent silicon crystal. The projectile trajectories are computed using the newly developed module [1] of the MBN Explorer package [2,3]. The electron and positron channeling along Si(110) and Si(111) crystallographic planes are studied for the projectile energies 195--855 MeV.
Channeling properties and radiation spectra are studied on the grounds of numerical simulations for the 855 MeV electrons in a periodically bent diamond crystal. The bent crystalline profiles are shown to enhance the re-channeling of the projectiles and to produce distinct lines in the radiation spectra. The results obtained are analyzed and contrasted to the properties of the planar channeling and of the channeling in uniformly bent crystals.
Ideas of use the particle channeling in bent crystals for steer the beams have been checked up and advanced in many experiments. However, until now, this method of beam formation has limitations in application, since the channeling process involves beam particles with low angular divergence, limited by the angle of Lindhard. Here we test at the U-70 accelerator two crystal devices, the focusing crystal and multistrip crystal, which expand the boundaries of application of bent crystals at accelerators.
The short period atomic plane modulation is suggested to be applied to modify the electron channeling potential in order to make it possible to considerably increase electron channeling efficiency by the crystal structure brake ensured by either a plane crystal cut or amorphous layer beneath the crystal entrance surface. The achieved channeling efficiency of 60-70 \% can considerably facilitate the process of high energy electron beam focusing by specially cut bent crystals. Possible parameters of one TeV electron beam focusing region are estimated using simulations
Monte Carlo simulations have been performed for 855 MeV and 6.3 GeV electrons channeling in silicon single crystals at circular bent (111) planes. The aim was to identify critical experimental parameters which effect the volume-deflection and volume-capture characteristics. To these belongs the angular alignment of the crystal with respect to the nominal beam direction. The continuum potential picture has been utilized. The simulation results were compared with experiments. It turns out that the assumption of an anticlastic bending of the crystal, bent on the principle of the quasi-mosaic effe…
The process of photoproduction of electron-positron pairs in bent single crystals is considered in this paper. In particular, it is shown that the probability of the process for gamma-quanta with energies from 100 GeV on is significantly higher than the one in an amorphous medium. A possible scenario for the experimental validation of the process is discussed and the positive features of the photoproduction in bent crystals compared to straight ones are underlined from the point of view of possible applications.
Results of numerical simulations of electron channeling and emission spectra are reported for straight and uniformly bent silicon crystal. The projectile trajectories are computed using the newly developed module [1] of the MBN Explorer package [2,3]. The electron channeling along Si(110) crystallographic planes is studied for the projectile energy 855 MeV.
We report on the results of theoretical simulations of the electron channeling in a bent silicon crystal. The dynamics of ultra-relativistic electrons in the crystal is computed using the newly developed part [1] of the MBN Explorer package [2,3], which simulates classical trajectories of in a crystalline medium by integrating the relativistic equations of motion with account for the interaction between the projectile and crystal atoms. A Monte Carlo approach is employed to sample the incoming electrons and to account for thermal vibrations of the crystal atoms. The electron channeling along S…
Basing on experiments at SLAC, MAMI, CERN, and on Monte Carlo simulations, we assess the physical limits on efficiency and reachable angles of electron deflection in bent crystals in the energy range from sub-GeV to sub-TeV. We find that applications of electron channeling for beam deflection are possible, limited by maximal deflection angle of 2-3 mrad at sub-GeV, 1-2 mrad at multi-GeV, and 0.5-1 mrad at sub-TeV energy. This opens opportunities for crystal-assisted electron beam extraction from accelerator rings.
Results obtained with a new Monte-Carlo code ChaS for channeling of 855 MeV electrons along the crystallographic plane (110) in a bent silicon crystal are presented. The dependence of the dechanneling length and the asymptotic acceptance of the channel on the crystal bending is studied.
Planar channeling of 855 MeV electrons and positrons in straight and bent tungsten (110) crystal is simulated by means of the \MBNExplorer software package. The results of simulations for a broad range of bending radii are analyzed in terms of the channel acceptance, dechanneling length, and spectral distribution of the emitted radiation. Comparison of the results with predictions of other theories as well as with the data for (110) oriented diamond, silicon and germanium crystals is carried out.
An investigation on stochastic deflection of high-energy charged particles in a bent crystal was carried out. In particular, we investigated the deflection efficiency under axial confinement of both positively and negatively charged particles as a function of the crystal orientation, the choice of the bending plane, and of the charge sign. Analytic estimations and numerical simulations were compared with dedicated experiments at the H4 secondary beam line of SPS North Area, with 120 GeV/$c$ electrons and positrons. In the work presented in this article, the optimal orientations of the plane of…
We report the observation of the steering of 855 MeV electrons by bent silicon and germanium crystals at the MAinzer MIkrotron. 15 $μ$m long crystals, bent along (111) planes, were exploited to investigate orientational coherent effects. By using a piezo-actuated mechanical holder, which allowed to remotely change the crystal curvature, it was possible to study the steering capability of planar channeling and volume reflection vs. the curvature radius and the atomic number, Z. For silicon, the channeling efficiency exceeds 35 %, a record for negatively charged particles. This was possible due …
The propagation of a modulated positron beam in a planar crystal channel is investigated. It is demonstrated that the beam preserves its modulation at sufficiently large penetration depths which opens the prospect of using a crystalline undulator as a coherent source of hard x-rays. This finding is a crucial milestone in developing a new type of lasers radiating in the hard x-ray and gamma-ray range.
The Large Hadron Collider (LHC) uses a multi-stage collimator system to absorb the growing halo of circulating beams to protect and ensure reliable operation of superconducting magnets. A similar system is planned for the Future Circular Collider (FCC). In anticipation of the LHC operation with high luminosity, research is being conducted to improve the collimation system. Studies have shown that one of the solutions to improve beam collimation is to use channeling in a short curved crystal, which acts as a primary collimator, throwing particles deep into the secondary collimator by channeling…
Channeling and radiation are studied for the relativistic electrons and positrons passing through a Si crystal periodically bent with a small amplitude and a short period. Comprehensive analysis of the channeling process for various bending amplitudes is presented on the grounds of numerical simulations. The features of the channeling are highlighted and elucidated within an analytically developed continuous potential approximation. The radiation spectra are computed and discussed.
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 μm 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 show that using volume re…
This report overviews studies accomplished in the U70 proton synchrotron of IHEP-Protvino during the recent two decades. Major attention is paid to a routine application of bent crystals for beam extraction from the machine. It has been confirmed experimentally that efficiency of beam extraction with a crystal deflector of around 85% is well feasible for a proton beam with intensity up to 1012 protons per cycle. Another trend is to use bent crystals for halo collimation in a high energy collider. New promising options emerge for, say, LHC and ILC based on the "volume reflection" effect, which …
Recently it was proposed to apply a bent single crystal with decreasing curvature instead of uniform bending for improvement of extraction and collimation of a circulating beam in particle accelerators. In the given paper created crystal devices with a variable curvature, realizing this idea are described. Results of measurement of curvature along a crystal plate are informed. It is shown, that with the help of the developed devices it is possible to carry out also high energy beam focusing. The mathematical description of this process is proposed.
The LHC crystal-based collimation system is mainly addressed. A CRYSTAL simulation code for particle tracking in crystals is introduced. Its essence consists in both adequate and fast sampling of proton trajectories in crystals which is crucial for both correct description of experiments and quantitative prediction of new effects. The H8 single-pass experiment at the CERN SPS as well as 7 TeV proton deflection by a bent crystal at the LHC are simulated. We predict the existence of dechanneling peaks corresponding to the planar channeling oscillations as well as describe the possibility of thei…
A periodically bent Si crystal is shown to efficiently serve for producing highly monochromatic radiation in a gamma-ray energy spectral range. A short-period small-amplitude bending yields narrow undulator-type spectral peaks in radiation from multi-GeV electrons and positrons channeling through the crystal. Benchmark theoretical results on the undulator are obtained by simulations of the channeling with a full atomistic approach to the projectile-crystal interactions over the macroscopic propagation distances. The simulations are facilitated by employing the MBN Explorer package for molecula…
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 eff…
Proof-of-principle experiment of a novel beam extraction over millions of turns using stable resonance islands and bent crystal
CERN（欧洲核子研究中心）；Goethe University（歌德大学）；John Adams Institute at Royal Holloway, University of London（伦敦大学皇家霍洛威学院约翰亚当斯研究所）；Université Libre de Bruxelles（布鲁塞尔自由大学）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（德国重离子研究中心）
The T-980 bent crystal collimation experiment at the Tevatron has recently acquired substantial enhancements. First, two new crystals - a 16-strip one manufactured and characterized by the INFN Ferrara group and a quasi-mosaic crystal manufactured and characterized by the PNPI group. Second, a two plane telescope with 3 high-resolution pixel detectors per plane along with corresponding mechanics, electronics, control and software has been manufactured, tested and installed in the E0 crystal region. The purpose of the pixel telescope is to measure and image channeled (CH), volume-reflected (VR)…
For volume reflection process in a bent crystal, exact analytic expressions for positively- and negatively-charged particle trajectories are obtained within a model of parabolic continuous potential in each interplanar interval, with the neglect of incoherent multiple scattering. In the limit of the crystal bending radius greatly exceeding the critical value, asymptotic formulas are obtained for the particle mean deflection angle in units of Lindhard's critical angle, and for the final beam profile. Volume reflection of negatively charged particles is shown to contain effects of rainbow scatte…
It has been shown that the use of a bent crystal with a variable curvature radius makes it possible to reduce the fraction of dechanneled particles by an order of magnitude. This effect enables the strong reduction of the particle density at the edge of a collimator or the partition of a septum upon the multiturn extraction of a beam from a ring accelerator. In particular, the beam extraction efficiency at the U-70 synchrotron and Large Hadron Collider can be increased to 95 and 99.65%, respectively.
The method of relativistic molecular dynamics is applied for accurate computational modelling and numerical analysis of the channelling phenomena for 855 MeV electrons in bent oriented silicon (111) crystal. Special attention is devoted to the transition from the axial channelling regime to the planar one in the course of the crystal rotation with respect to the incident beam. Distribution in the deflection angle of electrons and spectral distribution of the radiation emitted are analysed in detail. The results of calculations are compared with the experimental data collected at the MAinzer MI…
The evolution of a modulated positron beam in a planar crystal channel is investigated within the diffusion approach. A detailed description of the formalism is given. A new parameter, the demodulation length, is introduced, representing the quantitative measure of the depth at which the channelling beam preserves its modulation in the crystal. It is demonstrated that there exist crystal channels with the demodulation length sufficiently large for using the crystalline undulator as a coherent source of hard X rays. This finding is a crucial milestone in developing a new type of lasers radiatin…
In this paper we present the results of a systematic numerical analysis of the channeling properties of electrons and positrons in oriented straight and periodically bent diamond(110) crystals. We analyse dependence of the intensity of the radiation emitted on the projectile energy as well as on the bending amplitude. The analysis presented is based on the grounds of accurate numerical simulations of the channeling process. The simulation parameters, such as the crystal orientation, thickness and bending parameters of the crystals as well as the energy of the projectiles, were chosen to match …
An investigation on stochastic deflection of high-energy negatively charged particles in a bent crystal was carried out. On the basis of analytical calculation and numerical simulation it was shown that it exists a maximum angle at which most of the beam is deflected. The existence of a maximum, which is taken in the correspondence of the optimal radius of curvature, is a novelty with respect to the case of positively charged particles, for which the deflection angle can be freely increased by increasing the crystal length. This difference has to be ascribed to the stronger contribution of inc…
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 predictio…
A surprising small dechanneling length was observed at (111) channeling of ultrarelativistic electrons in a 60 $μ$m thick silicon single crystal with a bending radius of 0.15 m. The experiments were conducted at beam energies between 3.35 and 14 GeV at the Facility for Advanced Accelerator Experimental Tests (FACET at SLAC, USA). It is shown in this paper that the small dechanneling lengths can well be reproduced with a modified Fokker-Planck equation for plane crystals in which a crystal bending has been heuristically introduced. Encouraged by this result experiments have been reconsidered wh…
Radiation spectrum from high energy $e^\pm$ in a bent crystal with arbitrary curvature distribution along the longitudinal coordinate is evaluated, based on the stationary phase approximation. For a uniformly bent crystal a closed-form expression for the spectrum is derived. Features such as sharp end of spectrum and volume reflection turnover at beginning of the spectrum are discussed. The coherence length in a bent crystal appears to depend only on the crystal geometry and not on the electron or photon energies, which is essential for interpretation of the results. Estimates of non-dipole ra…
We suggest a way to compare the experiments and simulations of electron dechanneling length in bent crystals performed at different energies and different radii. As an example, we compare the SLAC experiment at 3-14 GeV with earlier published predictions of two different Monte Carlo codes for 855 MeV and 50 GeV, and with MAMI experiment at 855 MeV.
We predict peculiar changes in spectral distributions of radiation emitted by ultra-relativistic positrons and electrons in periodically bent crystals with variation of the bending amplitude. It is shown that the changes, being sensitive to the projectile energy, manifest themselves differently for negatively and positively charged projectiles. We demonstrate that the features observed are due to the interplay of different radiation mechanisms occurring in periodically bent crystals. The observations are important for design, practical realization and channeling experiments with periodically b…
The possibility of extracting highly energetic particles from the Super Proton Synchrotron (SPS) by means of silicon bent crystals has been explored since the 1990's. The channelling effect of a bent crystal can be used to strongly deflect primary protons and eject them from the synchrotron. Many studies and experiments have been carried out to investigate crystal channelling effects. The extraction of 120 and 270 GeV proton beams has already been demonstrated in the SPS with dedicated experiments located in the ring. Presently in the SPS, the UA9 experiment is performing studies to evaluate t…
A model for the simulation of orientational effects in straight and bent periodic atomic structures is presented. The continuum potential approximation has been adopted.The model allows the manipulation of particle trajectories by means of straight and bent crystals and the scaling of the cross sections of hadronic and electromagnetic processes for channeled particles. Based on such a model, an extension of the Geant4 toolkit has been developed. The code has been validated against data from channeling experiments carried out at CERN.
