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 channel, and, thus, can be varied significantly by varying these characteristics.
As an example, we consider the acoustically induced radiation (AIR) which is generated by ultra-relativistic particles channeled in a crystal which is bent by a transverse acoustic wave. The AIR mechanism allows to make the undulator with the main parameters varying in wide ranges, which are 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 be easily 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 the amplitude of the acoustic wave in the crystal. A possibility to generate stimulated emission of high-energy photons (in keV - MeV region) is also discussed.
The focusing of high energy charged particles by a bent crystal is considered. The limits and constraints of focusing imposed by dynamics of particles are pointed out. The crystalline geometry provided the maximum magnification and minimum focusing size is proposed. The focusing parameters are compared with current experimental results.
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 proportionali…
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.
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 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 accoun…
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…
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 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…
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 …
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…
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…
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…
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.
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 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)…
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.
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 feasibility of gamma-ray light sources based on the channeling phenomenon of ultrarelativistic electrons and positrons in oriented crystals that are periodically bent with Small Amplitude and Short Period (SASP) is demonstrated by means of rigorous numerical modelling that accounts for the interaction of a projectile with all atoms of the crystalline environment. Numerical data on the spectral distribution, brilliance, number of photons and power of radiation emitted by 10 GeV electron and positron beams passing through diamond, silicon and germanium crystals are presented and analyzed. Th…
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…
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…
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 …
Ultrarelativistic charged particles are predicted to emit hard electromagnetic radiation of undulator type while being channeled in a crystal with periodically bent crystallographic planes. The recently proposed crystalline undulator with the bending amplitude smaller than the distance between the bent planes and the bending period shorter than the period of channeling oscillations is far superior to what was proposed previously. In the same time, it is more challenging from the technical point of view because its bending period has to be in the sub-micron range. It is shown that a mixed cryst…
Simulations of electron and positron channelling in a crystalline undulator with a small amplitude and a short period (A Kostyuk, Phys. Rev. Lett. 110 (2013) 115503) were repeated by V G Bezchastnov, A V Korol and A V Solov'yov (J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 195401)for the same parameter set but using another computer code, MBN Explorer, which implements a different model of projectile scattering by crystal atoms. The authors of the latter paper claim that their approach, in contrast to the one of the former paper, allows them to observe short-period undulator oscillations in plots…
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…
If an ultrarelativistic charged particle channels inside a single crystal with periodically bent crystallographic planes, it emits hard electromagnetic radiation of the undulator type. Due to similarity of its physical principles to the ordinary (magnetic) undulator, such a device is termed as the crystalline undulator. Recent development of a new Monte Carlo code ChaS made possible a detailed simulation of particle channeling and radiation emission in periodically bent crystals. According to recent findings, energy of the electron beam below 1 GeV is sufficient to observe the undulator effect…
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.
We report the results of theoretical and numerical analysis of the crystalline undulators planned to be used in the experiments which are the part of the ongoing PECU project [1]. The goal of such an analysis was to define the parameters (different from those pre-set by the experimental setup) of the undulators which ensure the highest yield of photons of specified energies. The calculations were performed for 0.6 and 10 GeV positrons channeling through periodically bent Si and Si$_{1-x}$Ge$_x$ crystals.
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 …
Tabrizi et al. [physics/0701342] discuss the feasibility of an electron-based crystal undulator (e-CU) by planar channeling of 50 GeV electrons through a periodically bent crystal. We show that their scheme is not feasible. First, their undulator parameter is K >> 1 always, which destroys photon interference. Second, they overestimate the electron dechanneling length in e-CU by an order of magnitude, which shortens the number N of e-CU periods from 5-15 (as they hope) to just 1-2. This kills their e-CU concept again. We made first simulation of electron channeling in undulated crystal and conc…
The UA9 Experiment at CERN-SPS investigates channeling processes in bent silicon crystals with the aim to manipulate hadron beams. Monitoring and characterization of channeled beams in the high energy accelerators environment ideally requires in-vacuum and radiation hard detectors. For this purpose the Cherenkov detector for proton Flux Measurement (CpFM) was designed and developed. It is based on thin fused silica bars in the beam pipe vacuum which intercept charged particles and generate Cherenkov light. The first version of the CpFM is installed since 2015 in the crystal-assisted collimatio…
Under coherent interactions, particles undergo correlated collisions with the crystal lattice and their motion result in confinement in the fields of atomic planes, i.e. particle channeling. Other than coherently interacting with the lattice, particles also suffer incoherent interactions with individual nuclei and may leave their bounded motion, i.e., they de-channel. This latter is the main limiting factor for applications of coherent interactions in crystal-assisted particle steering. We experimentally investigated the nature of dechanneling of 120 GeV/c $e^{-}$ and $e^{+}$ in a bent silicon…
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.
This paper discusses the undulator radiation emitted by high-energy positrons during planar channeling in periodically bent crystals. We demonstrate that the construction of the undulator for positrons with energies of 10 GeV and above is only possible if one takes into account the radiative energy losses. The frequency of the undulator radiation depends on the energy of the particle. Thus the decrease of the particle's energy during the passage of the crystal should result in the destruction of the undulator radiation regime. However, we demonstrate that it is possible to avoid the destructiv…
We discuss design and practical realization of novel gamma-ray Crystal-based Light Sources (CLS) that can be constructed through exposure of oriented crystals (linear, bent, periodically bent) to beams of ultrarelativistic charged particles. In an exemplary case study, we estimate brilliance of radiation emitted in a Crystalline Undulator (CU) LS by available positron beams. Intensity of CU radiation in the photon energy range $10^0-10^1$ MeV, which is inaccessible to conventional synchrotrons, undulators and XFELs, greatly exceeds that of laser-Compton scattering LSs and can be higher than pr…
The crystalline undulator is a single crystal with periodically bent crystallographic planes. If ultrarelativistic charged particles channel through such a crystal, they emit hard radiation of undulator type. A crystalline undulator with a bending amplitude smaller than the distance between the bent planes and a bending period shorter than the period of channeling oscillations is proposed. Heretofore, it was believed that such a range of bending parameters was unsuitable for a crystalline undulator. This point of view is refuted. In fact, the undulator with a small amplitude and a short period…
This paper discusses the undulator radiation emitted by high-energy positrons during planar channeling in periodically bent crystals. We demonstrate that the construction of the undulator for positrons with energies of 10 GeV and above is only possible if one takes into account the radiative energy losses. The frequency of the undulator radiation depends on the energy of the particle. Thus the decrease of the particle's energy during the passage of the crystal should result in the destruction of the undulator radiation regime. However, we demonstrate that it is possible to avoid the destructiv…
A crystalline undulator (CU) with periodically deformed crystallographic planes is capable of deflecting charged particles with the same strength as an equivalent magnetic field of 1000 T and could provide quite a short period L in the sub-millimeter range. We present an idea for creation of a CU and report its first realization. One face of a silicon crystal was given periodic micro-scratches (grooves), with a period of 1 mm, by means of a diamond blade. The X-ray tests of the crystal deformation have shown that a sinusoidal-like shape of crystalline planes goes through the bulk of the crysta…
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…
A new scheme for amplification of coherent gamma rays is proposed. The key elements are crystalline undulators - single crystals with periodically bent crystallographic planes exposed to a high energy beam of charged particles undergoing channeling inside the crystals. The scheme consists of two such crystals separated by a vacuum gap. The beam passes the crystals successively. The particles perform undulator motion inside the crystals following the periodic shape of the crystallographic planes. Gamma rays passing the crystals parallel to the beam get amplified due to interaction with the part…
