Final Report Summary - CUTE (Crystalline Undulator: Theory and Experiment)
The main goal of the CUTE project is to facilitate the collaborative research towards theory, design, manufacture and experimental tests of high-quality periodically bent crystalline structures as well as theoretical and experimental studies of the radiation formed in crystalline undulators (CU). Strong electrostatic fields inside a crystal are able to steer the particles much more effectively than even the most advanced superconductive magnets. Hence, a crystal with periodically bent crystallographic planes forces particles to move along nearly sinusoidal trajectories and radiate electromagnetic waves in hard X ray and gamma ray frequency range.
The activities within the project constitute 4 work packages. Below, for each work package, as indicated, we present a summary description of the objectives as well as a description of the work performed since the beginning of the project (01.04.2011) accompanied by the description of the main results achieved.
WP1: Manufacture of periodically bent structures.
Objectives. (a) To produce graded composition strained layer superlattice crystals by Molecular Beam Epitaxy (MBE), by periodic doping of Chemical Vapour Deposition (CVD) grown diamond to be used in the experiments at the Mainz Microtron (MAMI).
(b) Production of CUs based on the methods of indentations and of film deposition. Characterization of the fabricated samples.
Descriptions of the work performed and of the main results achieved.
Various CUs were produced (by the UAAR team) using by means of femto-second laser ablation in both silicon and diamond crystals as well as by manufacturing of Si1-xGex graded composition strained layer superlatices using molecular beam epitaxy (MBE). Extensive characterization of samples via XRD and ion-beam analysis have been carried out in parallel to fabrication. The manufactured CUs were forwarded to the Institute for Nuclear Physics of the Mainz University and have been used in the experiments at the MAMI electron accelerator facility.
The achievement concerns the manufacture of a SiGe based crystalline undulators with small amplitude (0.2-0.6 Å) and short period (λu=400 nm). These undulators were further used in the experiments at MAMI with 855 MeV electron energies and at the SLAC facility at higher projectile energies.
The method of surface grooving, developed in last years by the SSL-FU team, has been refined and tested to manufacture periodically bent crystalline structures suitable to be used in electron channeling experiments at MAMI. Surface grooving produces permanent plastic deformation in the neighborhood of the grooves. Experiments based on x-ray diffraction showed that the crystalline structure of grooved samples is uniformly curved.
Characterization of a sample of a crystalline undulator with 400 GeV/c protons has been carried out. The experimental result on the profile of deflected beam after interaction with the sample is in good agreement with Monte-Carlo simulations performed for a perfect sinusoidal undulator.
An alternative method, based on deformations induced by tensile or compressive thin films has been under development. Preliminary results highlighted the possibility to deform, in a highly controllable and reproducible way, silicon substrates by deposition of thin films. The method allows one to keep intact both the crystalline quality of the crystal bulk and surface, increasing the volume of crystal available for channeling. White light interferometric charactherizations highlighted a perfect agreement between the crystal deformed shape and the shape predicted basing on the theory of elasticity.
The team from UJ performed a study of the bending of diamond by femto-second laser ablation method. A suite of diamonds for a systematic study was prepared which involved several similar synthetic diamonds with different crystallographic surfaces. The prepared samples were delivered to Aarhus (the location of the UAAR team) where the laser ablation was performed.
An innovative technique to produce thick self-standing bent crystals was developed by the SSL-FU team which utilizes depositing of a thick film composed of carbon fiber. Crystals up to 5 mm thick were bent with a radius of curvature up to 30 m. In order to demonstrate that the bending of crystals as thick as 5 mm is feasible, two self-standing bent silicon samples were produced. The two samples were shaped at the Sensor and Semi-conductor Laboratory (SSL) of Ferrara, Italy, through a high precision dicing saw. Then, the curvature of the samples was obtained by the deposition of a thick film of carbon fiber.
A graded Si1-xGex crystal has been manufactured by the SSL-FU team for operation with high-energy protons to excite coherent interactions of the particles with the crystal such as channeling and volume reflection. With current fabrication techniques, the curvature radius can be tailored up to some hundreds of meters and down to 15 m. Wafers 500 µm thick were cut from an ingot with the major surfaces of the wafer (111) oriented. Ge concentration was set to produce a cylindrical curvature on a small area. The crystal had the shape of a parallelepiped though its (111) atomic planes were curved at a radius of 25.6 m because of the graded Ge content.
A method for the fabrication of bent silicon crystals suited for steering electrons in the GeV energy range has been developed by the SSL-FU. Crystals are manufactured starting from a SOI wafer whose thickness is optimized for operations at the desired energy. Crystal bending in high-deformation regime exploits quasi-mosaic effect in order to obtain deformation of (111) planes, while strongly reducing unwanted anticlastic deformation. A full set of characterizations of the crystals was performed. Developed process allows manufacturing of crystals with thickness starting from a few tens of microns with no damaged surface layer, thus permitting to study coherent interactions with negatively charged particle beams in the GeV and sub-GeV energy range. In particular, two crystals were recently installed and tested at MAMI (MAinz MIcrotron) to steer a 855 MeV electrons beam (thickness 30.5 μm, bending angle 905 μrad), and at SLAC, to deflect an electron beam in the 1 to 10 GeV range (thickness 60 μm, bending angle 402 μrad), demonstrating for the first time efficient steering of negatively charged particle beams in the GeV-energy range.
WP2: Experiments on channeling and radiation production in crystalline undulators.
Objectives: Experimental investigation of the channeling phenomenon of electrons in straight and periodically bent crystals. Tools to be developed characterizing the crystals for their suitability as X-ray radiation sources. The focus to be made on the experiments with electrons at MAMI with the beam energy between 180 and 855 MeV.
Descriptions of the work performed and of the main results achieved within the reporting period.
The undulator crystals produced at UAAR (WP1) have been tested with 270, 375 and 855 MeV high quality electron beam of the MAMI. The experiments (with participation of the UAAR team) were performed with 4-period epitaxially grown strained layer Si1−xGex undulator with a period length λu = 9.9 micron in order (1) to characterize its bending features, and (2) to explore its radiation emission characteristics.
Basing on the analysis of the measured Ge-content profile of the undulator, model calculations yielded the value of 4.79 Å for the amplitude of the periodic bending, assuming a sinusoidal. This result is in accord with the analysis of the emitted high energy bremsstrahlung spectrum.
A broad excess yield around the theoretically expected photon energies of 0.069 0.132 and 0.62 MeV has been observed at (110) planar channeling for electron beam energies 270, 375 and 855 MeV, respectively. The analysis of the emission spectra for 270 MeV and 375 MeV beams indicates that a weak undulator effect originates from a small fraction of electrons which channel stably in the periodically bent channel. The observed peaks seem to be shifted to lower energies. The obtained experimental data need further detailed analysis by means of Monte Carlo simulations of the channeling process. Preliminary results of this analysis were reported by FIAS-GU group [48,53].
The experimental work at MAMI has led to a much improved understanding of the advantages and limitations related to crystalline undulator investigations at the facility, which has also resulted in new ideas to pursue the proposal of the gamma-ray klystron. The request for beam time at FACET (SLAC National accelerator laboratory, MS, USA) has been approved in 2012. The experiments (the designation E-212, the spokesman Urlik I. Uggerhøj (UAAR)) were carried out in 2013-2015. Many members of the current IRSES-CUTE consortium were the members of the experimental team at FACET.
The method of surface grooving has been applied to manufacture CUs with geometrical parameters optimized for studies at the MAMI accelerator facility. The dependence of the crystal plasticization on the size of the grain of the diamond blade and on the grooving parameters (blade rotating and feed speed, groove width and depth) has been analyzed by the SSL-FU team. The next step will be in investigation of the best parameters which lead to optimal crystal deformation and minimization of the plasticized region.
Regarding crystalline undulators obtained by means of silicon nitride deposition, an extensive characterization of thin films of silicon nitride and silicon oxide has been carried on. Such characterization highlighted the role of film deposition conditions on the stress imparted to the film.
A set of collaborative (UAAR, SSL-FU, Mainz-Uni) experiments were performed at MAMI. In particular an experiment where crystalline undulator radiation in the small amplitude, short period regime has been measured using a SiGe crystal with wavelength 400 nm. To investigate electron channeling in bent crystals, experiments were performed at the Mainz Microtron MAMI at a beam energy of 855 MeV. Various Si and Ge crystals were produced at the University of Ferrara using the quasimosaic effect for a bending of the (111) planes. Planar channeling and volume reflection were observed for the 30.5 µm Si crystal. Details of the results have been published. The tested crystal has also been used to investigate the radiation generated by 855 MeV electrons through the same coherent phenomena. The results obtained allow a better understanding of the dynamics and radiation generation of electrons subject to coherent interactions in a bent silicon crystal in the sub-GeV energy range, which is relevant for realization of a CU.
An experiment performing channeling and volume reflection of a high-energy electron beam using a quasimosaic, bent silicon (111) crystal was carried out at the End Station A Test Beam at SLAC with. 3.35 and 6.3 GeV electron beams. These are the first quantitative measurements of channeling and volume reflection using a primary beam of multi-GeV electrons. The crystal was manufactured by SSL-FU, the UAAR team participated on the data taking on the beam.
A graded Si1-xGex crystal was exposed to a 400 GeV/c proton beam at the external lines of CERN Super Proton Synchrotron to probe its capability to steer high-energy particles in the experiment carried out with the participation of the SSL-FU team. Measured deflection efficiency was 62% under planar channeling and 96% under volume reflection. Such values were critically compared to their counterparts for a standard bent Si crystal under peer conditions. A Monte Carlo simulation of the dynamics of channeled and volume reflected particles in a graded crystal including the effect of Ge impurities and of lattice dislocations has been carried out.
WP3: Theoretical study of physical processes involved in crystal bending.
Objectives. To develop theoretical models of a quantitative description of physical phenomena accompanying the process of crystal bending. It is aimed to achieve a better control over the parameters of periodically bent crystals obtained in various technological processes. The ultimate goal of the WP is in attaining the ability to calculate technological conditions for obtaining bent crystals with pre-assigned shape of channels.
Descriptions of the work performed and of the main results achieved.
A model based on the theory of anisotropic bent plates has been developed (the SSL-FU team) to foresee and adjust the curvature of grooved samples. The model relies on the assumption that plasticized layer behaves as a compressive film on the substrate. Hence, the Stoney approach is used to determine the curvature of grooved crystals. The same approach has been applied to the design and calculation of stress and strain parameters in periodically bent crystals.
A numerical code capable to predict stress and strain fields in crystals uniformly bent by means of patterned thin films has been developed and experimentally validated. The same code is being applied to the calculation of stress and strain fields arising in periodically bent crystals.
The code has been developed and tested which allows one to carry out large-scale molecular dynamic simulations of the structure deformation in the bulk of a crystalline material under the surface stress. A theoretical study on quasimosaic effect in anomalous directions such has been performed. The results were in agreement with experiments performed at ESRF for diffraction of hard X rays.
A theoretical model for qualitative and quantitative analysis of the influence of imperfect structure of a crystalline undulator (in particular, the influence of the variation of the bending amplitude over the crystal thickness due to the stress applied to its surface) on the spectral distribution of the radiation has been developed by the FIAS-GU team. Based on the developed formalism the Fortran code has been constructed and tested which allows one to compute (a) the variation of the bending amplitude over the crystal thickness as well as of the presence of the subharmonics with smaller bending period, (b) the spectral and spectral-angular distribution of the emitted the radiation emitted in imperfect undulator.
A code has been developed for the molecular-dynamics simulation of the crystalline structure of a crystal doped with atoms of another element. The first numerical results, obtained with the code, were reported in 2014 [79]. They concern modelling of the binary SixGe1-x crystal as well as simulation of the trajectories of ultra-relativistic electrons and positrons channeling through the crystal. The structure modelling was carried out by applying the methods and algorithms of the molecular dynamics. The molecular dynamic approach was applied to study the deformation of an ideal Si crystal due to its doping with germanium atoms. To simulate the crystalline structure the bond-ordered potential due to Stillinger and Weber (Phys. Rev. B 31 (1984) 5262) was used. This potential accounts not only for pairwise interaction forces between the atoms but also for the angles of bonds between neighbouring particles. Numerical calculations were performed for the whole range of the dopant concentration, x: 0≤x≤1, where x=0 corresponds to a pure Silicon monocrystal, and x=1 to the Germanium monocrystal. Special attention was paid to the range x≈0.05 which corresponds to the dopant concentration used in the manufacturing process of Si1-xGex graded composition strained layer superlattices using molecular beam epitaxy (see WP1).
WP4: Development of the theory, codes, computer simulations of particle channeling through periodically bent structures and of the radiation emission.
Objectives: To develop a microscopic theory of projectiles channeling in periodically bent crystals and of the accompanying photon emission. On its basis to construct computer codes for numerical analysis of the phenomena, and to carry out systematic computations of dechanneling lengths and the emission spectra. On the basis of this study, to produce suggestions for the experimentalists on the range of parameters of crystals, beams, bending shapes which are to be considered in the experiments.
Descriptions of the work performed and of the main results achieved.
A novel code has been developed to simulate trajectories of ultra-relativistic projectiles in a crystalline medium. For this purpose the approaches and algorithms used in modern molecular dynamics codes were applied. The motion of a projectile is treated classically by integrating the relativistic equations of motion with account for the interaction between the projectile and crystal atoms. The probabilistic element is introduced by a random choice of transverse coordinates and velocities of the projectile at the crystal entrance as well as by accounting for the random positions of the atoms due to thermal vibrations.
The calculated dependencies of the coordinates and velocities of the projectile on time were used as the input data to generate spectral and spectral-angular distributions of the emitted radiation.
Initial approbation and verification of the codes has been carried out by simulating the trajectories and calculating the radiation emitted by 6.7 GeV electrons and positrons in straight oriented Si(110) crystal and in amorphous silicon. The calculated spectra were compared with the experimental data and with predictions of the Bethe-Heitler theory for the amorphous environment.
By means of the developed code the electron channeling along Si(110) crystallographic planes was studied for the beam energies 195-855 MeV and for different curvatures of the bent crystal. Quantitative analysis was performed of the channel acceptance, dechanneling and rechanneling length and their dependence on the curvature, the evolution of the fraction of the channeling particles with penetration distance. This work was performed with active participation of the PTU team.
Another set of numerical simulations of electron and positron channeling and of calculation of the emission spectra were performed for straight, uniformly bent and periodically bent silicon crystal. The electron and positron channeling along Si(110) and Si(111) crystallographic planes was studied for the projectile energies 270-855 MeV. The emission spectra were computed for two distinct apertures. The first one, equal to 0.21 mrad (which is much smaller than the natural cone of the emission), corresponds to the experimental setup at MAMI. This aperture collects the radiation emitted primarily in the forward direction. The second aperture, equal to 2 mrad, exceeds greatly the natural cone, thus, it collects nearly all radiation.
The quantitative analysis of the channeling motion and of the emitted radiation was carried out for electron- and positron-based Crystalline Undulators (CU) with the parameters used in the experiments at the Mainz Microtron MAMI. A comparison theory-vs-experiment was carried out.
Numerical simulations of the channeling and the radiative processes have been carried out and reported for straight and uniformly bent silicon and diamond crystals. The electron channeling along Si(110) and Si(111) crystallographic planes was studied for the projectile energy 855 MeV. In the case of the planar channeling in diamond along the (110) plane the calculations were performed for electrons and positrons of the same energy. The calculations were performed for several values of the crystal thickness and in a wide range of the bending radius R, starting from the mm range up to the straight crystal limit (R=∞). The influence of the crystal bending on the dechanneling and rechanneling processes as well as on the spectral distribution of the radiation emitted within different apertures was analyzed quantitatively. This work was carried out with an active participation of the PTU team. Similar calculations and analysis were performed for 855 MeV electrons and positrons channeling in straight and bent Germanium (for (100), (110) and (111) planes) and Tungsten (for (100) and (110) ) monocrystals. The calculations were made in late 2014 in collaboration with the CNST-BNU and WIPM teams, and the results are currently being prepared for publication.
Simulation of axial channeling of sub-GeV electrons and positrons in straight and periodically bent Si crystals were carried out for different crystallographic axes. The numerical analysis of the channeling fraction (with and without rechanneling effect taken into account) was carried out providing one with the estimated values of the dechanneling lengths for both types of the projectile.
Theoretical simulations of the channeling and emergent radiation for the sub-GeV electrons and positrons in a periodically bent silicon crystal were carried out in collaboration with the FIAS-GU and PTU teams. A short-period small-amplitude bending has been addressed and shown to be promising for producing highly monochromatic undulator radiation in the spectral range well above the energies of the channeling radiation from the straight crystal. The incident beam energy of 855 MeV is relevant for the MAMI experimental facilities. The emergent radiation displays the undulator lines at the energies exceeding the energies of the spectral maxima in the channeling radiation from the straight crystals. The interference between the channeling and undulator oscillations was found to be likely seen in the spectra in form of a splitting of the undulator lines into the sub-lines separated by the energies corresponding to the channeling peak. These theoretical results are important for experiments with the short-period small-amplitude silicon-based undulators.
In connection with the ongoing experiments at the SLAC facility carried out with the active participation of the UAAR team, the simulations of 1-10 GeV electron and positron channeling in Si(110) based crystalline short-period small-amplitude undulators were carried out. The undulators were assumed to have the bending periods and amplitudes varying from 200 to 600 nm and 0.2 to 0.6 Angstroms, respectively. The trajectories, both for the electrons and positrons, were found to exhibit short-period undulator oscillations with the amplitudes well distinguishable on the scale of the inter-planar sizes for the silicon crystals. The emission spectra were calculated as well. It was shown, that the energy separation between the channeling and undulator lines appears to be big enough not yielding a significance of the spectral interference between the channeling and undulator oscillations.
For the beam energy of 10 GeV, the short-period bending under study has been found to yield the undulator peaks in the gamma-ray energy region, where the effects of quantum recoil turned out to be significantly pronounced in the radiation spectra. The spectra have been therefore computed within the (quasi-classical) formalism accounting for the recoil. The quantitative significance of the recoil has been studied by comparison of the spectra with these computed for the same trajectories but within the (classical) formalism entirely neglecting the recoil.
Also in connection with the ongoing experiments at SLAC with active participation of the UAAR and SSL-FU teams, the planar channeling of 3-20 GeV electrons and positrons in bent Si(111) crystal was simulated by means of the MBN EXPLORER software package. The results of the simulations are ana-lyzed in terms of dechanneling length characterization, angular distribution of outgoing projectiles and radiation spectrum. The results of calculations were in good agreement with recently measured experi-mental data.
Channeling of 150GeV negatively charged pions in bent Si(110) channel was simulated. The analysis of the channeling fraction (with and without the rechanneling effect taken into account) as the function of the penetration distance was carried out for a L = 2mm thick crystal for several values of the bending radius. It was demonstrated that rechanneling is important to explain the dechanneling length recently measured experimentally.
The scheme of a coherent radiation source was developed which combines a conventional undulator and a crystalline undulator. The invention has been protected by a German patent.
Simple analytic codes for the purpose of analyzing experiments at MAMI have been developed at the University of Mainz. These are in particular de-convolution procedures for measured radiation spectra with NaI and Ge(i) detectors, and analytical models for the prediction of undulator radiation spectra.
A Monte-Carlo code to treat the radiation generation in bent crystals has been developed by the SSL-FU members. This approach, applicable to electrons or positrons of any energy, is based on the local straight-crystal approximation and Baier-Katkov quasi-classical operators method. For planar radiation case, the integration of Baier-Katkov formula is considerably facilitated by the fast Fourier transform method. This simulation code can be applied to compute the radiation emitted by electrons/positrons inside a crystalline undulator.
A toolkit for the simulation of coherent interactions between high-energy charged particles and complex crystal structures, called DYNECHARM++ has been developed by the SSL-FU. The code has been written in C++ language taking advantage of this object-oriented programing method. The code is capable to evaluating the electrical characteristics of complex atomic structures and to simulate and track the particle trajectory within them. Calculation method of electrical characteristics based on their expansion in Fourier series has been adopted. Two different approaches to simulate the interaction have been adopted, relying on the full integration of particle trajectories under the continuum potential approximation and on the definition of cross-sections of coherent processes. The code has proved to reproduce experimental results and to simulate interaction of charged particles with complex structures. Two extensions of the DYNECHARM++ code have been developed; one to compute the electromagnetic radiation emitted by ultrarelativistic electrons in crystals, named RADCHARM++ and a second one to take into account the contribution of crystal defects in the particle dynamics through coherent interactions with crystals.
The activities within the project constitute 4 work packages. Below, for each work package, as indicated, we present a summary description of the objectives as well as a description of the work performed since the beginning of the project (01.04.2011) accompanied by the description of the main results achieved.
WP1: Manufacture of periodically bent structures.
Objectives. (a) To produce graded composition strained layer superlattice crystals by Molecular Beam Epitaxy (MBE), by periodic doping of Chemical Vapour Deposition (CVD) grown diamond to be used in the experiments at the Mainz Microtron (MAMI).
(b) Production of CUs based on the methods of indentations and of film deposition. Characterization of the fabricated samples.
Descriptions of the work performed and of the main results achieved.
Various CUs were produced (by the UAAR team) using by means of femto-second laser ablation in both silicon and diamond crystals as well as by manufacturing of Si1-xGex graded composition strained layer superlatices using molecular beam epitaxy (MBE). Extensive characterization of samples via XRD and ion-beam analysis have been carried out in parallel to fabrication. The manufactured CUs were forwarded to the Institute for Nuclear Physics of the Mainz University and have been used in the experiments at the MAMI electron accelerator facility.
The achievement concerns the manufacture of a SiGe based crystalline undulators with small amplitude (0.2-0.6 Å) and short period (λu=400 nm). These undulators were further used in the experiments at MAMI with 855 MeV electron energies and at the SLAC facility at higher projectile energies.
The method of surface grooving, developed in last years by the SSL-FU team, has been refined and tested to manufacture periodically bent crystalline structures suitable to be used in electron channeling experiments at MAMI. Surface grooving produces permanent plastic deformation in the neighborhood of the grooves. Experiments based on x-ray diffraction showed that the crystalline structure of grooved samples is uniformly curved.
Characterization of a sample of a crystalline undulator with 400 GeV/c protons has been carried out. The experimental result on the profile of deflected beam after interaction with the sample is in good agreement with Monte-Carlo simulations performed for a perfect sinusoidal undulator.
An alternative method, based on deformations induced by tensile or compressive thin films has been under development. Preliminary results highlighted the possibility to deform, in a highly controllable and reproducible way, silicon substrates by deposition of thin films. The method allows one to keep intact both the crystalline quality of the crystal bulk and surface, increasing the volume of crystal available for channeling. White light interferometric charactherizations highlighted a perfect agreement between the crystal deformed shape and the shape predicted basing on the theory of elasticity.
The team from UJ performed a study of the bending of diamond by femto-second laser ablation method. A suite of diamonds for a systematic study was prepared which involved several similar synthetic diamonds with different crystallographic surfaces. The prepared samples were delivered to Aarhus (the location of the UAAR team) where the laser ablation was performed.
An innovative technique to produce thick self-standing bent crystals was developed by the SSL-FU team which utilizes depositing of a thick film composed of carbon fiber. Crystals up to 5 mm thick were bent with a radius of curvature up to 30 m. In order to demonstrate that the bending of crystals as thick as 5 mm is feasible, two self-standing bent silicon samples were produced. The two samples were shaped at the Sensor and Semi-conductor Laboratory (SSL) of Ferrara, Italy, through a high precision dicing saw. Then, the curvature of the samples was obtained by the deposition of a thick film of carbon fiber.
A graded Si1-xGex crystal has been manufactured by the SSL-FU team for operation with high-energy protons to excite coherent interactions of the particles with the crystal such as channeling and volume reflection. With current fabrication techniques, the curvature radius can be tailored up to some hundreds of meters and down to 15 m. Wafers 500 µm thick were cut from an ingot with the major surfaces of the wafer (111) oriented. Ge concentration was set to produce a cylindrical curvature on a small area. The crystal had the shape of a parallelepiped though its (111) atomic planes were curved at a radius of 25.6 m because of the graded Ge content.
A method for the fabrication of bent silicon crystals suited for steering electrons in the GeV energy range has been developed by the SSL-FU. Crystals are manufactured starting from a SOI wafer whose thickness is optimized for operations at the desired energy. Crystal bending in high-deformation regime exploits quasi-mosaic effect in order to obtain deformation of (111) planes, while strongly reducing unwanted anticlastic deformation. A full set of characterizations of the crystals was performed. Developed process allows manufacturing of crystals with thickness starting from a few tens of microns with no damaged surface layer, thus permitting to study coherent interactions with negatively charged particle beams in the GeV and sub-GeV energy range. In particular, two crystals were recently installed and tested at MAMI (MAinz MIcrotron) to steer a 855 MeV electrons beam (thickness 30.5 μm, bending angle 905 μrad), and at SLAC, to deflect an electron beam in the 1 to 10 GeV range (thickness 60 μm, bending angle 402 μrad), demonstrating for the first time efficient steering of negatively charged particle beams in the GeV-energy range.
WP2: Experiments on channeling and radiation production in crystalline undulators.
Objectives: Experimental investigation of the channeling phenomenon of electrons in straight and periodically bent crystals. Tools to be developed characterizing the crystals for their suitability as X-ray radiation sources. The focus to be made on the experiments with electrons at MAMI with the beam energy between 180 and 855 MeV.
Descriptions of the work performed and of the main results achieved within the reporting period.
The undulator crystals produced at UAAR (WP1) have been tested with 270, 375 and 855 MeV high quality electron beam of the MAMI. The experiments (with participation of the UAAR team) were performed with 4-period epitaxially grown strained layer Si1−xGex undulator with a period length λu = 9.9 micron in order (1) to characterize its bending features, and (2) to explore its radiation emission characteristics.
Basing on the analysis of the measured Ge-content profile of the undulator, model calculations yielded the value of 4.79 Å for the amplitude of the periodic bending, assuming a sinusoidal. This result is in accord with the analysis of the emitted high energy bremsstrahlung spectrum.
A broad excess yield around the theoretically expected photon energies of 0.069 0.132 and 0.62 MeV has been observed at (110) planar channeling for electron beam energies 270, 375 and 855 MeV, respectively. The analysis of the emission spectra for 270 MeV and 375 MeV beams indicates that a weak undulator effect originates from a small fraction of electrons which channel stably in the periodically bent channel. The observed peaks seem to be shifted to lower energies. The obtained experimental data need further detailed analysis by means of Monte Carlo simulations of the channeling process. Preliminary results of this analysis were reported by FIAS-GU group [48,53].
The experimental work at MAMI has led to a much improved understanding of the advantages and limitations related to crystalline undulator investigations at the facility, which has also resulted in new ideas to pursue the proposal of the gamma-ray klystron. The request for beam time at FACET (SLAC National accelerator laboratory, MS, USA) has been approved in 2012. The experiments (the designation E-212, the spokesman Urlik I. Uggerhøj (UAAR)) were carried out in 2013-2015. Many members of the current IRSES-CUTE consortium were the members of the experimental team at FACET.
The method of surface grooving has been applied to manufacture CUs with geometrical parameters optimized for studies at the MAMI accelerator facility. The dependence of the crystal plasticization on the size of the grain of the diamond blade and on the grooving parameters (blade rotating and feed speed, groove width and depth) has been analyzed by the SSL-FU team. The next step will be in investigation of the best parameters which lead to optimal crystal deformation and minimization of the plasticized region.
Regarding crystalline undulators obtained by means of silicon nitride deposition, an extensive characterization of thin films of silicon nitride and silicon oxide has been carried on. Such characterization highlighted the role of film deposition conditions on the stress imparted to the film.
A set of collaborative (UAAR, SSL-FU, Mainz-Uni) experiments were performed at MAMI. In particular an experiment where crystalline undulator radiation in the small amplitude, short period regime has been measured using a SiGe crystal with wavelength 400 nm. To investigate electron channeling in bent crystals, experiments were performed at the Mainz Microtron MAMI at a beam energy of 855 MeV. Various Si and Ge crystals were produced at the University of Ferrara using the quasimosaic effect for a bending of the (111) planes. Planar channeling and volume reflection were observed for the 30.5 µm Si crystal. Details of the results have been published. The tested crystal has also been used to investigate the radiation generated by 855 MeV electrons through the same coherent phenomena. The results obtained allow a better understanding of the dynamics and radiation generation of electrons subject to coherent interactions in a bent silicon crystal in the sub-GeV energy range, which is relevant for realization of a CU.
An experiment performing channeling and volume reflection of a high-energy electron beam using a quasimosaic, bent silicon (111) crystal was carried out at the End Station A Test Beam at SLAC with. 3.35 and 6.3 GeV electron beams. These are the first quantitative measurements of channeling and volume reflection using a primary beam of multi-GeV electrons. The crystal was manufactured by SSL-FU, the UAAR team participated on the data taking on the beam.
A graded Si1-xGex crystal was exposed to a 400 GeV/c proton beam at the external lines of CERN Super Proton Synchrotron to probe its capability to steer high-energy particles in the experiment carried out with the participation of the SSL-FU team. Measured deflection efficiency was 62% under planar channeling and 96% under volume reflection. Such values were critically compared to their counterparts for a standard bent Si crystal under peer conditions. A Monte Carlo simulation of the dynamics of channeled and volume reflected particles in a graded crystal including the effect of Ge impurities and of lattice dislocations has been carried out.
WP3: Theoretical study of physical processes involved in crystal bending.
Objectives. To develop theoretical models of a quantitative description of physical phenomena accompanying the process of crystal bending. It is aimed to achieve a better control over the parameters of periodically bent crystals obtained in various technological processes. The ultimate goal of the WP is in attaining the ability to calculate technological conditions for obtaining bent crystals with pre-assigned shape of channels.
Descriptions of the work performed and of the main results achieved.
A model based on the theory of anisotropic bent plates has been developed (the SSL-FU team) to foresee and adjust the curvature of grooved samples. The model relies on the assumption that plasticized layer behaves as a compressive film on the substrate. Hence, the Stoney approach is used to determine the curvature of grooved crystals. The same approach has been applied to the design and calculation of stress and strain parameters in periodically bent crystals.
A numerical code capable to predict stress and strain fields in crystals uniformly bent by means of patterned thin films has been developed and experimentally validated. The same code is being applied to the calculation of stress and strain fields arising in periodically bent crystals.
The code has been developed and tested which allows one to carry out large-scale molecular dynamic simulations of the structure deformation in the bulk of a crystalline material under the surface stress. A theoretical study on quasimosaic effect in anomalous directions such has been performed. The results were in agreement with experiments performed at ESRF for diffraction of hard X rays.
A theoretical model for qualitative and quantitative analysis of the influence of imperfect structure of a crystalline undulator (in particular, the influence of the variation of the bending amplitude over the crystal thickness due to the stress applied to its surface) on the spectral distribution of the radiation has been developed by the FIAS-GU team. Based on the developed formalism the Fortran code has been constructed and tested which allows one to compute (a) the variation of the bending amplitude over the crystal thickness as well as of the presence of the subharmonics with smaller bending period, (b) the spectral and spectral-angular distribution of the emitted the radiation emitted in imperfect undulator.
A code has been developed for the molecular-dynamics simulation of the crystalline structure of a crystal doped with atoms of another element. The first numerical results, obtained with the code, were reported in 2014 [79]. They concern modelling of the binary SixGe1-x crystal as well as simulation of the trajectories of ultra-relativistic electrons and positrons channeling through the crystal. The structure modelling was carried out by applying the methods and algorithms of the molecular dynamics. The molecular dynamic approach was applied to study the deformation of an ideal Si crystal due to its doping with germanium atoms. To simulate the crystalline structure the bond-ordered potential due to Stillinger and Weber (Phys. Rev. B 31 (1984) 5262) was used. This potential accounts not only for pairwise interaction forces between the atoms but also for the angles of bonds between neighbouring particles. Numerical calculations were performed for the whole range of the dopant concentration, x: 0≤x≤1, where x=0 corresponds to a pure Silicon monocrystal, and x=1 to the Germanium monocrystal. Special attention was paid to the range x≈0.05 which corresponds to the dopant concentration used in the manufacturing process of Si1-xGex graded composition strained layer superlattices using molecular beam epitaxy (see WP1).
WP4: Development of the theory, codes, computer simulations of particle channeling through periodically bent structures and of the radiation emission.
Objectives: To develop a microscopic theory of projectiles channeling in periodically bent crystals and of the accompanying photon emission. On its basis to construct computer codes for numerical analysis of the phenomena, and to carry out systematic computations of dechanneling lengths and the emission spectra. On the basis of this study, to produce suggestions for the experimentalists on the range of parameters of crystals, beams, bending shapes which are to be considered in the experiments.
Descriptions of the work performed and of the main results achieved.
A novel code has been developed to simulate trajectories of ultra-relativistic projectiles in a crystalline medium. For this purpose the approaches and algorithms used in modern molecular dynamics codes were applied. The motion of a projectile is treated classically by integrating the relativistic equations of motion with account for the interaction between the projectile and crystal atoms. The probabilistic element is introduced by a random choice of transverse coordinates and velocities of the projectile at the crystal entrance as well as by accounting for the random positions of the atoms due to thermal vibrations.
The calculated dependencies of the coordinates and velocities of the projectile on time were used as the input data to generate spectral and spectral-angular distributions of the emitted radiation.
Initial approbation and verification of the codes has been carried out by simulating the trajectories and calculating the radiation emitted by 6.7 GeV electrons and positrons in straight oriented Si(110) crystal and in amorphous silicon. The calculated spectra were compared with the experimental data and with predictions of the Bethe-Heitler theory for the amorphous environment.
By means of the developed code the electron channeling along Si(110) crystallographic planes was studied for the beam energies 195-855 MeV and for different curvatures of the bent crystal. Quantitative analysis was performed of the channel acceptance, dechanneling and rechanneling length and their dependence on the curvature, the evolution of the fraction of the channeling particles with penetration distance. This work was performed with active participation of the PTU team.
Another set of numerical simulations of electron and positron channeling and of calculation of the emission spectra were performed for straight, uniformly bent and periodically bent silicon crystal. The electron and positron channeling along Si(110) and Si(111) crystallographic planes was studied for the projectile energies 270-855 MeV. The emission spectra were computed for two distinct apertures. The first one, equal to 0.21 mrad (which is much smaller than the natural cone of the emission), corresponds to the experimental setup at MAMI. This aperture collects the radiation emitted primarily in the forward direction. The second aperture, equal to 2 mrad, exceeds greatly the natural cone, thus, it collects nearly all radiation.
The quantitative analysis of the channeling motion and of the emitted radiation was carried out for electron- and positron-based Crystalline Undulators (CU) with the parameters used in the experiments at the Mainz Microtron MAMI. A comparison theory-vs-experiment was carried out.
Numerical simulations of the channeling and the radiative processes have been carried out and reported for straight and uniformly bent silicon and diamond crystals. The electron channeling along Si(110) and Si(111) crystallographic planes was studied for the projectile energy 855 MeV. In the case of the planar channeling in diamond along the (110) plane the calculations were performed for electrons and positrons of the same energy. The calculations were performed for several values of the crystal thickness and in a wide range of the bending radius R, starting from the mm range up to the straight crystal limit (R=∞). The influence of the crystal bending on the dechanneling and rechanneling processes as well as on the spectral distribution of the radiation emitted within different apertures was analyzed quantitatively. This work was carried out with an active participation of the PTU team. Similar calculations and analysis were performed for 855 MeV electrons and positrons channeling in straight and bent Germanium (for (100), (110) and (111) planes) and Tungsten (for (100) and (110) ) monocrystals. The calculations were made in late 2014 in collaboration with the CNST-BNU and WIPM teams, and the results are currently being prepared for publication.
Simulation of axial channeling of sub-GeV electrons and positrons in straight and periodically bent Si crystals were carried out for different crystallographic axes. The numerical analysis of the channeling fraction (with and without rechanneling effect taken into account) was carried out providing one with the estimated values of the dechanneling lengths for both types of the projectile.
Theoretical simulations of the channeling and emergent radiation for the sub-GeV electrons and positrons in a periodically bent silicon crystal were carried out in collaboration with the FIAS-GU and PTU teams. A short-period small-amplitude bending has been addressed and shown to be promising for producing highly monochromatic undulator radiation in the spectral range well above the energies of the channeling radiation from the straight crystal. The incident beam energy of 855 MeV is relevant for the MAMI experimental facilities. The emergent radiation displays the undulator lines at the energies exceeding the energies of the spectral maxima in the channeling radiation from the straight crystals. The interference between the channeling and undulator oscillations was found to be likely seen in the spectra in form of a splitting of the undulator lines into the sub-lines separated by the energies corresponding to the channeling peak. These theoretical results are important for experiments with the short-period small-amplitude silicon-based undulators.
In connection with the ongoing experiments at the SLAC facility carried out with the active participation of the UAAR team, the simulations of 1-10 GeV electron and positron channeling in Si(110) based crystalline short-period small-amplitude undulators were carried out. The undulators were assumed to have the bending periods and amplitudes varying from 200 to 600 nm and 0.2 to 0.6 Angstroms, respectively. The trajectories, both for the electrons and positrons, were found to exhibit short-period undulator oscillations with the amplitudes well distinguishable on the scale of the inter-planar sizes for the silicon crystals. The emission spectra were calculated as well. It was shown, that the energy separation between the channeling and undulator lines appears to be big enough not yielding a significance of the spectral interference between the channeling and undulator oscillations.
For the beam energy of 10 GeV, the short-period bending under study has been found to yield the undulator peaks in the gamma-ray energy region, where the effects of quantum recoil turned out to be significantly pronounced in the radiation spectra. The spectra have been therefore computed within the (quasi-classical) formalism accounting for the recoil. The quantitative significance of the recoil has been studied by comparison of the spectra with these computed for the same trajectories but within the (classical) formalism entirely neglecting the recoil.
Also in connection with the ongoing experiments at SLAC with active participation of the UAAR and SSL-FU teams, the planar channeling of 3-20 GeV electrons and positrons in bent Si(111) crystal was simulated by means of the MBN EXPLORER software package. The results of the simulations are ana-lyzed in terms of dechanneling length characterization, angular distribution of outgoing projectiles and radiation spectrum. The results of calculations were in good agreement with recently measured experi-mental data.
Channeling of 150GeV negatively charged pions in bent Si(110) channel was simulated. The analysis of the channeling fraction (with and without the rechanneling effect taken into account) as the function of the penetration distance was carried out for a L = 2mm thick crystal for several values of the bending radius. It was demonstrated that rechanneling is important to explain the dechanneling length recently measured experimentally.
The scheme of a coherent radiation source was developed which combines a conventional undulator and a crystalline undulator. The invention has been protected by a German patent.
Simple analytic codes for the purpose of analyzing experiments at MAMI have been developed at the University of Mainz. These are in particular de-convolution procedures for measured radiation spectra with NaI and Ge(i) detectors, and analytical models for the prediction of undulator radiation spectra.
A Monte-Carlo code to treat the radiation generation in bent crystals has been developed by the SSL-FU members. This approach, applicable to electrons or positrons of any energy, is based on the local straight-crystal approximation and Baier-Katkov quasi-classical operators method. For planar radiation case, the integration of Baier-Katkov formula is considerably facilitated by the fast Fourier transform method. This simulation code can be applied to compute the radiation emitted by electrons/positrons inside a crystalline undulator.
A toolkit for the simulation of coherent interactions between high-energy charged particles and complex crystal structures, called DYNECHARM++ has been developed by the SSL-FU. The code has been written in C++ language taking advantage of this object-oriented programing method. The code is capable to evaluating the electrical characteristics of complex atomic structures and to simulate and track the particle trajectory within them. Calculation method of electrical characteristics based on their expansion in Fourier series has been adopted. Two different approaches to simulate the interaction have been adopted, relying on the full integration of particle trajectories under the continuum potential approximation and on the definition of cross-sections of coherent processes. The code has proved to reproduce experimental results and to simulate interaction of charged particles with complex structures. Two extensions of the DYNECHARM++ code have been developed; one to compute the electromagnetic radiation emitted by ultrarelativistic electrons in crystals, named RADCHARM++ and a second one to take into account the contribution of crystal defects in the particle dynamics through coherent interactions with crystals.