We present the results of numerical calculations of the channelling and undulator radiation generated by an ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due either to the propagation of a transverse acoustic wave through the crystal, or due to the static strain as it occurs in superlattices. The periodically bent crystal serves as an undulator. We investigate the dependence of the intensities of both the ordinary channelling and the undulator radiations on the parameters of the periodically bent channel with simultaneous account for the dechannelling effect of the positrons. We demonstrate that there is a range of parameters in which the undulator radiation dominates over the channelling one and the characteristic frequencies of both types of radiation are well separated. This result is important, because the undulator radiation can be used to create a tunable source of X-ray and gamma-radiation.
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.
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.
The parabolic approximation is developed for high energy charged particles scattering in a bent crystal with variable curvature. The general form of parabolic equation is received for atomic chains located along coordinate axis of orthogonal curvilinear coordinate system.
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.
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.
This paper is devoted to a detailed analysis of the new type of the undulator radiation generated by an ultra-relativistic charged particle channeling along a crystal plane, which is periodically bent by a transverse acoustic wave, as well as to the conditions limiting the observation of this phenomenon. This mechanism makes feasible the generation of electromagnetic radiation, both spontaneous and stimulated, emitted in a wide range of the photon energies, from X- up to gamma-rays.
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…
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.
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 …
We discuss radiation generated by positrons channeling in a crystalline undulator. The undulator is produced by periodically bending a single crystal with an amplitude much larger than the interplanar spacing. Different approaches for bending the crystal are described and the restrictions on the parameters of the bending are established. We present the results of numeric calculations of the spectral distributions of the spontaneous emitted radiation and estimate the conditions for stimulated emission. Our investigations show that the proposed mechanism provides an efficient source for high ene…
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
We investigate, both analytically and numerically, the influence of the dechanneling process on the parameters of undulator radiation generated by ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due either to the propagation of a transverse acoustic wave through the crystal, or due to the static strain as it occurs in superlattices. In either case the periodically bent crystal serves as an undulator which allows to generate X-ray and gamma-radiation. We propose the scheme for accurate quantitative treatment of the radiation in pre…
We discuss the radiation generated by positrons channeling in a crystalline undulator. The undulator is produced by periodically bending a single crystal with an amplitude much larger than the interplanar spacing. Different approaches for bending the crystal are described and the restrictions on the parameters of the bending are discussed. We also present numeric calculations of the spontaneous emitted radiation and estimate the conditions for stimulated emission. Our investigations show that the proposed mechanism could be an interesting source for high energy photons and is worth to be studi…
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…
The electromagnetic radiation generated by ultra-relativistic positrons channelling in a crystalline undulator is discussed. The crystalline undulator is a crystal whose planes are bent periodically with the amplitude much larger than the interplanar spacing. Various conditions and criteria to be fulfilled for the crystalline undulator operation are established. Different methods of the crystal bending are described. We present the results of numeric calculations of spectral distributions of the spontaneous radiation emitted in the crystalline undulator and discuss the possibility to create th…
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.
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…
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 …
We analyze numerically the radiation and channeling properties of ultrarelativistic electrons and positrons propagating through a periodically bent diamond crystal grown on a straight single-crystal diamond substrate. Such systems can be called hetero-crystals and they are one of the experimentally realized samples for the implementation of crystalline undulators. We state that in such systems the channeling and radiation properties of projectiles are sensitive to the projectile particles energy as well as on the beam propagation direction, i.e. on whether the beam of particles enters the crys…
Particles passing through a crystal under planar channeling experience transverse oscillations in their motion. As channeled particles approach the atomic planes of a crystal, they are likely to be dechanneled. This effect was used in ion-beam analysis with MeV energy. We studied this effect in a bent crystal for positive and negative particles within a wide range of energies in sight of application of such crystals at accelerators. We found the conditions for the appearance or not of channeling oscillations. Indeed a new kind of oscillations, strictly related to the motion of over-barrier par…
An investigation on the mechanism of relaxation of axially confined 400 GeV/c protons to planar channeling in a bent crystal was carried out at the extracted line H8 from CERN Super Proton Synchrotron. The experimental results were critically compared to computer simulations, showing a good agreement. We firmly individuated a necessary condition for the exploitation of axial confinement or its relaxation for particle beam manipulation in high-energy accelerators. We demonstrated that with a short bent crystal, aligned with one of its main axis to the beam direction, it is possible to realize e…
Channeling of particle beam in straight and bent single-wall nanotubes has been studied in computer simulations. We have found that the nanotubes should be sufficiently narrow in order to steer efficiently the particle beams, with preferred diameter in the order of 0.5-2 nm. Wider nanotubes, e.g. 10-50 nm, appear rather useless for channeling purpose because of high sensitivity of channeling to nanotube curvature. We have compared bent nanotubes with bent crystals as elements of beam steering technique, and found that narrow nanotubes have an efficiency of beam bending similar to that of cryst…
Channeling of high-energy particles in straight and bent multi-wall nanotubes (MWNT) has been studied in computer simulations and compared to the channeling properties of single-wall nanotubes (SWNT) and bent crystal lattices. It is demonstrated that MWNT can efficiently channel positively-charged high-energy particles trapped between the walls of MWNT. Bending dechanneling in MWNT has been computed as a function of the particle momentum to nanotube curvature radius ratio, $pv/R$. It is found that a bent MWNT can steer a particle beam with bending capabilities similar to those of bent silicon …
The usage of a Crystalline Undulator (CU) has been identified as a promising solution for generating powerful and monochromatic $γ$-rays. A CU was fabricated at SSL through the grooving method, i.e., by the manufacturing of a series of periodical grooves on the major surfaces of a crystal. The CU was extensively characterized both morphologically via optical interferometry at SSL and structurally via X-ray diffraction at ESRF. Then, it was finally tested for channeling with a 400 GeV/c proton beam at CERN. The experimental results were compared to Monte Carlo simulations. Evidence of planar ch…
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…
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.
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 1.E12, basing on multi-pass mechanism of channeling proposed theoretically and realised experimentally …
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…
An idea of producing a focused parametric X-ray radiation (PXR) is presented. The PXR is emitted by relativistic charged particles channeling along a bent crystal. Then the PXR emitted from the whole length of the bent crystal is going to the focus. Some properties of focused PXR are estimated for typical experimental conditions and possible applications are discussed. The experiment for observation of focused PXR is proposed.
Influence of volume capture on a process of volume reflection of ultrarelativistic particles moving in bent single crystals was considered analytically. Relations describing various distributions of particles involving in the process, the probability of volume capture and behavior of channeling and dechanneling fractions of a beam were obtained. Results of study will be useful at creation of multicrystal devices for collimation and extraction of beams on modern and future accelerators.
The article presents an overview of the results obtained at U-70 accelerator of IHEP to use bent crystals for beam control of high energy protons. Considerable attention is paid to practical application of crystals to create new modes of beam extraction from the accelerator to ensure experiments on high energy physics. It was shown that with the crystal deflectors the efficiency reached ~ 90% with intensity up to 10^12 protons per cycle of U-70. The results of experiments on the use of crystals to enhance the effectiveness of the absorption of the unused beam, as well as the use of crystals fo…
We suggest a new type of radiation (acoustically induced radiation - AIR), which is generated by ultrarelativistic particles channeling in crystal along a crystal plane (or axis), which is bent by a transverse acoustic wave. The AIR mechanism allows to make an undulator with characteristics inaccessible in the undulators based on the motion of particles in the periodic magnetic fields and also in the field of the laser radiation. The intensity of AIR can easily be made larger than the intensity of the radiation in a linear crystal and can be varied in a wide range by varying the frequency and …
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.
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…
New type of radiation in crystals is predicted and investigated in computer simulation. It is shown that process of volume reflection of electrons and positrons in bent crystals is accomplished with high-power radiation of photons. Volume reflection radiation has intensity comparable with known channeling radiation, but it is less sensitive to entrance angle and sign of charge of a particle. Simulated spectra of radiation power are presented for 10 GeV and 200GeV particles.
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…
While particle beam steering (and in particular, "scraping") in accelerators by bent channeling crystals is an established technique extensively tested at IHEP Protvino and other major high-energy labs, an interesting question is how one could improve channeling capabilities by applying modern nanotechnology. Theoretical research of nanotube channeling was in progress over recent years. In this work, we assess potential benefits from nanotube channeling for real accelerator systems. We report simulation studies of channeling in nanostructured material (carbon SWNT and MWNT) tested for possible…
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…
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…
Particle channeling in a bent crystal lattice has led to an efficient instrument for beam steering at accelerators, demonstrated from MeV to TeV energies. In particular, crystal focusing of high energy protons to micron size has been demonstrated at IHEP with the results well in match with Lindhard (critical angle) prediction. Channeling in crystal microstructures has been proposed as a unique source of a microbeam of high-energy particles. Channeling in nanostructures (single-wall and multi-wall nanotubes) offers the opportunities to produce ion beams on nanoscale. Particles channeled in a na…
The trapping of electrons in the ponderomotive potential wells, which governs a free electron laser or inverse free electron laser at high gain, is analogous to the channeling of charged particles by atomic planes of a crystal. A bent crystal is analogous to a period-tapered free electron laser. This analogy is different from the well-known one between channeling and undulator radiations.
The results of numerical simulation of the channeling of ultra-relativistic 270 MeV electrons and positrons in a diamond crystal are presented. Using the MBN Explorer package, the trajectories of the have been determined of the particles incident on a 20 microns thick crystal along (110) crystallographic plane. The channeling parameters and radiation spectra of electrons and positrons have been computed for the cases of straight and periodically bent diamond crystals.
We suggest a new type of the undulator radiation which is generated by an ultra-relativistic particle channeled along a periodically bent crystallographic plane or axis. The electromagnetic radiation arises mainly due to the bending of the particle's trajectory, which follows the shape of the channel. The parameters of this undulator, which totally define the spectrum and the angular distribution of the radiation (both spontaneous and stimulated), depend on the type of the crystal and the crystallographic plane (axis), on the type of a projectile and its energy, and on the shape of the bent ch…
Beam Steering and Radiation Generation of Electrons in Bent Crystals in the Sub-GeV Domain
University of Ferrara（费拉拉大学）；INFN Ferrara（意大利国家核物理研究所费拉拉分部）；Department of Physics, University of Padua（帕多瓦大学物理系）；INFN Laboratori Nazionali di Legnaro（意大利国家核物理研究所莱尼亚罗国家实验室）；Institut für Kernphysik, Universität Mainz（美因茨大学核物理研究所）
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…
We present the experimental observation of the reduction of multiple scattering of high-energy positively charged particles during channeling in single crystals. According to our measurements the rms angle of multiple scattering in the plane orthogonal to the plane of the channeling is less than half that for non-channeled particles moving in the same crystal. In the experiment we use focusing bent single crystals. Such crystals have a variable thickness in the direction of beam propagation. This allows us to measure rms angles of scattering as a function of thickness for channeled and non-cha…
The feasibility to generate powerful monochromatic radiation of the undulator type in the gamma region of the spectrum by means of planar channeling of ultra-relativistic electrons in a periodically bent crystal is proven. It is shown that an electron-based crystalline undulator operates in the regime of higher beam energies than a positron-based one does. A numerical analysis is performed for a 50 GeV electron channeling in Si along the (111) crystallographic planes.
It is shown that a narrow plane cut near the crystal surface considerably increases the probability of capture into the stable channeling motion of positively charged particles entering a crystal at angles smaller than a quarter of the critical channeling angle with respect to the crystal planes. At smallest incidence angles the capture probability reaches 99 percent. A pair of crystals with cuts bent in orthogonal planes allows to reach a 99.9 percent efficiency of single-pass deflection of a proton beam with an ultra small divergence. Conditions necessary for efficient single-pass deflection…
This paper presents simulations of the trajectories of high-energy ions through several bent crystal layers. At certain layer alignments volume reflection occurs from each layer and the resultant multiple volume reflection angle is correspondingly increased, along with the range of entrance angles over which ions undergo volume reflection. Another feature is that the range of entrance angles for which bent crystal channeling occurs is also increased in passing through several bent layers. The use of several bent crystal layers to produce multiple volume reflection provides an alternative appro…
We suggest a way to capture by a focusing crystal the short-lived particles (tau leptons, charmed baryons) produced in the decays downstream of a target hit by primary protons. The beam of captured short-lived particles can be extracted from the debris produced in the target and bent onto experimental setup over a distance of centimetres. The debris is rejected by the crystal, i.e. it remains nonchannelled. The technique can handle the particles with decay length cτ down to 1 micron.
This paper is devoted to the investigation of the radiation energy losses of an ultra-relativistic charged particle channeling along a crystal plane which is periodically bent by a transverse acoustic wave. In such a system there are two essential mechanisms leading to the photon emission. The first one is the ordinary channeling radiation. This radiation is generated as a result of the transverse oscillatory motion of the particle in the channel. The second one is the acoustically induced radiation. This radiation is emitted because of the periodic bending of the particle's trajectory created…
We discuss the features of a crystalline undulator of the novel type based on the effect of a planar channeling of ultra-relativistic electrons in a periodically bent crystals. It is demonstrated that an electron-based undulator is feasible in the tens of GeV range of the beam energies, which is noticeably higher than the energy interval allowed in a positron-based undulator. Numerical analysis of the main parameters of the undulator as well as the characteristics of the emitted undulator radiation is carried out for 20 and 50 GeV electrons channeling in diamond and silicon crystals along the …
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.
