Photon emission by ultra-relativistic positrons in crystalline undulators: the high-energy regime
W. Krause, A. V. Korol, A. V. Solov'yov, W. Greiner
备注：
submitted for the proceedings of the International Workshop on ``Electron-Photon Interaction in Dense Media'' in Nor-Hamberd, Armenia, 2001; 10 pages, 9 figures, LaTeX
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 destructive influence of the radiative losses on the frequency of the undulator radiation by the appropriate variation of the shape of the crystal channels. We also discuss a method by which, to our mind, it would be possible to prepare the crystal with the desired properties of its channels.
Optimization of a positron crystal undulator (CU) is addressed. The ways to assure both the maximum intensity and minimum spectral width of positron CU radiation are outlined. We claim that the minimum CU spectrum width of 3 -- 4% is reached at the positron energies of a few GeV and that the optimal bending radius of crystals planes in CU ranges from 3 to 5 critical bending radii for channeled particles. Following suggested approach a benchmark positron CU construction is devised and its functioning is illustrated using the simulation method widely tested by experimental data.
We study the influence of an imperfect structure of a crystalline undulator on the spectrum of the undulator radiation. The main attention is paid to the undulators in which the periodic bending in the bulk appears as a result of a regular (periodic) surface deformations. We demonstrate that this method of preparation of a crystalline undulator inevitably leads to a variation of the bending amplitude over the crystal thickness and to the presence of the subharmonics with smaller bending period. Both of these features noticeably influence the monochromatic pattern of the undulator radiation.
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 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 …
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…
The scheme for accurate quantitative treatment of the radiation from a crystalline undulator in presence of the dechanneling and the photon attenuation is presented. The number of emitted photons and the brilliance of electromagnetic radiation generated by ultra-relativistic positrons channeling in a crystalline undulator are calculated for various crystals, positron energies and different bending parameters. It is demonstrated that with the use of high-energy positron beams available at present in modern colliders it is possible to generate the crystalline undulator radiation with energies fr…
The design of the positron source for the International Linear Collider (ILC) is still under discussion. The baseline design plans to use the high-energy electron beam for the positron production before it goes to the IP. The electrons pass a long helical undulator and generate an intense circularly polarized photon beam which hits a thin conversion target to produce $e^+e^-$ pairs. The resulting positron beam is longitudinally polarized which provides an important benefit for precision physics analyses at the ILC. In this paper the status of the positron target design studies is presented. Fo…
The scattering of fast charged particles in a thin crystalline undulator is considered under conditions when all particles of the beam undergo above-barrier motion with respect to the bent crystalline atomic planes. The consideration is based on the analysis of the particles motion in the continuous potential field of the bent crystal atomic planes and on the simulation of the scattering process taking into account the influence of incoherent effects in scattering on the particles motion. The possibility of manifestation of the effect of multiple volume reflection from bent crystalline atomic …
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.
The design of the positron source for the International Linear Collider (ILC) is still under consideration. The baseline design plans to use the electron beam for the positron production before it goes to the IP. The high-energy electrons pass a long helical undulator and generate an intense circularly polarized photon beam which hits a thin conversion target to produce $e^+e^-$ pairs. The resulting positron beam is longitudinally polarized which provides an important benefit for precision physics analyses. In this paper the status of the design studies is presented with focus on ILC250. In pa…
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.
In the baseline design of the International Linear Collider (ILC) an undulator-based source is foreseen for the positron source. In this study the energy deposition in the pulsed flux concentrator (FC) of positron source is calculated for the ILC at 250 GeV center-of-mass energy. The peak energy of 33 J/g deposited by one beam pulse in the current design of the FC is above the limit for copper material. Several promising options were considered to solve the issue of overheating the FC: the quarter wave transformer (QWT) has a significantly bigger aperture and is considered as an valuable and s…
The positron source of the International Linear Collider is based on a superconducting helical undulator passed by the high-energy electron beam to generate photons which hit a conversion target. Since the photons are circularly polarized the resulting positron beam is polarized. At ILC250, the full undulator is needed to produce the required number of positrons. To keep the power deposition in the undulator walls below the acceptable limit of 1W/m, photon masks must be inserted in the undulator line. The photon mask design requires a detailed study of the power deposition in the walls and mas…
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…
In the future, International Linear Collider (ILC), a helical undulator based polarized positron source is expected to be chosen. A high energy electron beam passes through a superconducting helical undulator in order to create circularly polarized photons which will be directed to a conversion target, the result of which, will be electron-positron pairs. The resulting positron beam is longitudinally polarized. In order to produce the required number of positrons in ILC250 the full undulator length is needed. Since the photons are created with an opening angle and traveling through a 320 m lon…
The generation and capture of polarized positrons at a source with a superconducting helical undulator having 4.3 cm period and 500 GeV electron drive beam have been simulated. The positron polarization has been calculated for the different undulator K values (up to K = 2.5). Without applying a photon collimator, the maximal polarization of positrons is about 25% for 231 meters active magnet length of undulator with K = 0.7. Using an undulator with K = 2.5 and a collimator with an aperture radius of 0.9 mm results in increase of positron polarization to 54%. The energy deposition, temperature …
We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic micro-scratches (trenches) by means of a diamond blade. The X-ray tests of the crystal deformation due to given periodic pattern of surface scratches have shown that a sinusoidal shape is observed on both the scratched surface and the opposite (unscratched) face of the crystal, that is, a periodic sinusoidal deformation goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in crystalline …
In the future the International Linear Collider (ILC), a helical undulator-based polarized positron source, is expected to be chosen. A high energy electron beam passes through a superconducting helical undulator in order to create circularly polarized photons which will be directed to a conversion target, resulting in electron-positron pairs. The resulting positron beam is longitudinally polarized. Since the photons are produced with an opening angle and pass through a long superconducting helical undulator, some of these photons will strike the undulator walls. Therefore photon masks must be…
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…
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…
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…
From Simulation to Fabrication: Realizing Silicon Crystalline Undulators with Silicon Nitride Stressor Layer Patterning
INFN, Sezione di Ferrara（意大利国家核物理研究所费拉拉分部）；CNR - IMM, Bologna（意大利国家研究委员会材料研究所博洛尼亚分部）；Università degli Studi di Padova（帕多瓦大学）；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）；Università degli Studi di Ferrara（费拉拉大学）；MBN Research Center, Frankfurt（MBN研究中心）
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…
A periodically bent Si crystal is shown to efficiently serve for producing highly monochromatic radiation in a gamma-ray energy spectral range. A short-period small-amplitude bending yields narrow undulator-type spectral peaks in radiation from multi-GeV electrons and positrons channeling through the crystal. Benchmark theoretical results on the undulator are obtained by simulations of the channeling with a full atomistic approach to the projectile-crystal interactions over the macroscopic propagation distances. The simulations are facilitated by employing the MBN Explorer package for molecula…
The ILC baseline design for the positron source is based on radiation from a helical undulator to produce positrons in a thin target. Since the photon beam created in the helical undulator is circularly polarized, the generated positron beam is longitudinally polarized. Using a photon collimator upstream the positron target the positron polarization can be enhanced. However, the photon beam intensity yields a huge thermal load in the collimator material. In this paper the thermal load and heat dissipation in the photon collimator is discussed and design solutions are suggested.
The impact of experimental conditions on the observation of channeling and crystalline undulator radiation
Instituto Superior de Tecnologías y Ciencias Aplicadas, University of Havana (InSTEC-UH)（哈瓦那大学应用技术和高等科学研究院）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；MBN Research Center（MBN研究中心）
Full exploitation of the physics potential of a future International Linear Collider will require the use of polarized electron and positron beams. Experiment E166 at the Stanford Linear Accelerator Center (SLAC) has demonstrated a scheme in which an electron beam passes through a helical undulator to generate photons (whose first-harmonic spectrum extended to 7.9MeV) with circular polarization, which are then converted in a thin target to generate longitudinally polarized positrons and electrons. The experiment was carried out with a one-meter-long, 400-period, pulsed helical undulator in the…
When a high-energy electrons move in a crystal along one of the crystallographic planes the phenomenon of planar channeling is possible, in which the particles move in channels formed by the continuous potential of crystalline planes. Such particle motion in a crystal is conserved for most particles even for weak bending of crystalline planes of atoms. In [1-3] the process of channeled electrons radiation in such a device was considered. It was shown that the radiation spectrum of particles in the crystal in this case contains maxima associated with the period of oscillation of the channeled p…
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…
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…
To achieve the extremely high luminosity for colliding electron-positron beams at the future International Linear Collider (ILC) an undulator-based source with about 230 meters helical undulator and a thin titanium-alloy target rim rotated with tangential velocity of about 100 meters per second are foreseen. The very high density of heat deposited in the target has to be analyzed carefully. The energy deposited by the photon beam in the target has been calculated in FLUKA. The resulting stress in the target material after one bunch train has been simulated in ANSYS.
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 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…
The design of the conversion target for the undulator-based ILC positron source is still under development. One important issue is the cooling of the target. Here, the status of the design studies for cooling by thermal radiation is presented.
The propagation of a modulated positron beam in a planar crystal channel is investigated. It is demonstrated that the beam preserves its modulation at sufficiently large penetration depths which opens the prospect of using a crystalline undulator as a coherent source of hard x-rays. This finding is a crucial milestone in developing a new type of lasers radiating in the hard x-ray and gamma-ray range.
Most bright sources of the radiation in hard x-ray and gamma--ray regions are undulator sources and Compton based ones. These sources are ultimate for production of polarized positrons necessary for future linear colliders ILC, CLIC. We developed a novel method for evaluating the energy spectrum of electrons emitting the undulator- and the inverse Compton radiation. The method based on Poisson weighted superposition of electron states is applicable for whole range of the emission intensity per electron pass through the driving force, from much less than unity emitted photons (Compton sources) …
In the baseline design of the International Linear Collider (ILC) an undulator-based source is foreseen for the positron source in order to match the physics requirements. The recently chosen first energy stage with sqrt(s)=250 GeV requires high luminosity and imposes an effort for all positron source designs at high-energy colliders. In this paper we perform a simulation study and adopt the new technology of plasma lenses to capture the positrons generated by the undulator photons and to create the required high luminosity positron beam.
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…
A series of Silicon crystal undulator samples were produced based on the approach presented in PRL 90 (2003) 034801, with the periods of undulation from 0.1 mm to 1 mm, and the number of periods on the order of 10. The samples were characterized by X-rays, revealing the sine-like shape of the crystal lattice in the bulk. Next step in the characterization has been the channeling tests done with 70 GeV protons, where good channeling properties of the undulated Silicon lattice have been observed. The photon radiation tests of crystal undulators with high energy positrons are in progress on severa…
High energy e+e- linear colliders are the next large scale project in particle physics. They need intense sources to achieve the required luminosity. In particular, the positron source must provide about 10E+14 positrons per second. The positron source for the International Linear Collider (ILC) is based on a helical undulator passed by the electron beam to create an intense circularly polarized photon beam. With these photons a longitudinally polarized positron beam is generated; the degree of polarization can be enhanced by collimating the photon beam. However, the high photon beam intensity…
Radiation of charged particles passing through a set of equidistant ridges on the surface of a single crystal is calculated. The ridges are rectangular in shape, each of thickness of half of the particle trajectory period at planar channeling in a thick crystal. Positively charged particle entering the first ridge with angle smaller than the critical channeling angle is captured into channeling and changes the direction of its transversal velocity to reversed. Between the half-wave ridges the particle moves along a straight line. Passing through such set of half-wave crystal plates the particl…
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…
The evolution of a modulated positron beam in a planar crystal channel is investigated within the diffusion approach. A detailed description of the formalism is given. A new parameter, the demodulation length, is introduced, representing the quantitative measure of the depth at which the channelling beam preserves its modulation in the crystal. It is demonstrated that there exist crystal channels with the demodulation length sufficiently large for using the crystalline undulator as a coherent source of hard X rays. This finding is a crucial milestone in developing a new type of lasers radiatin…
The radiation damage of the positron source target for the International Linear Collider (ILC) has been studied. The displacement damage in target material due to multi-MeV photons has been calculated by combining FLUKA simulations for secondary particle production, SPECTER data for neutron displacement cross-sections and the Lindhard model for estimations of displacement damage by ions. The radiation damage of a stationary Ti6Al4V target in units of displacements per atom (dpa) has been estimated for photons from an undulator with strength 0.92 and period 1.15 cm. The calculated damage is 7 d…
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…
An unprecedented positron average current is required to fit the luminosity demands of future $e^+e^-$ high energy physics colliders. In addition, in order to access precision-frontier physics, these machines require positron polarization to enable exploring the polarization dependence in many HEP processes cross sections, reducing backgrounds and extending the reach of chiral physics studies beyond the standard model. The ILC has a mature plan for the polarized positron source based on conversion in a thin target of circularly polarized gammas generated by passing the main high energy e-beam …
Various methods of obtaining longitudinally polarized positrons for future linear colliders are reviewed. Special attention is paid to the schemes using circularly polarized high-energy photons for positron production. Most effectively such photons are obtained from electrons passing through a helical undulator or colliding with a circularly polarized laser wave. Spectrum and polarization of radiation emitted during helical motion of electrons are considered in detail. A new simple presentation of known formulas is used to account for the influence of the wave intensity, of the electron-beam a…
Simple formulas for the probability of radiation of twisted photons by scalar and Dirac particles with quantum recoil taken into account are derived. We show that the quantum recoil does not spoil the selection rule for the forward radiation of twisted photons in the planar undulator: $m+n$ is an even number, where $n$ is the harmonic number and $m$ is the projection of the total angular momentum of the radiated twisted photon. The explicit formulas for the radiation probability of twisted photons produced in the planar wiggler are obtained with account for the quantum recoil. The radiation of…
An intense positron sources is a demanding element in the design of future lepton colliders. A crystal-based hybrid positron source could be an alternative to a more conventional scheme based on the electron conversion into positron in a thick amorphous target. The conceptual idea of the hybrid source is to have two separate objects, a photon radiator and a photon-to-positron converter target. In such a scheme an electron beam crosses a thin axially oriented crystal with the emission of a channeling radiation, characterized by a considerably larger amount of photons if compared to Bremsstrahlu…
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…
