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 (111) crystallographic planes.
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.
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 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.
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 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 …
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…
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…
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…
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…
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 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）
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…
A simple analysis is given for optimum length of undulator in self-seeding free electron laser (FEL). The obtained relations show the correlation between the undulator length and the system parameters. The power required for the seeding in the second part undulator and overall efficiency to monochromatizating the seeding settle on the length of the first part undulator; the magnitude of seeding power dominates the length of the second part undulator; the whole length of the undulators in self-seeding FEL is determined by the overall efficiency to get coherent seed, it is about half as long aga…
We present measurements of slice energy spread growth due to quantum fluctuations of the undulator radiation at the European X-Ray Free-Electron Laser. The method uses a recently installed diagnostic wakefield structure, which enables measurements of the longitudinal phase space after the hard X-ray undulator. The effect of quantum diffusion in the undulator is measured for the first time, and the results are in good agreement with theoretical predictions.
The undulator is a critical component to produce synchrotron radiation and free electron laser. When a Bessel light beam carrying the orbit angular momentum co-propagates with an electron beam, a net transverse deflection force will be subjected to the electron beam. As a result of dephasing effect, the deflection force will oscillate acting as an undulator. For such a laser based undulator, the period length can reach sub-millimeter level, which will greatly reduce the electron energy for the required X-ray production.
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) …
Robb and Bonifacio (2011) claimed that a previously neglected quantum effect results in noticeable changes in the evolution of the energy distribution associated with spontaneous emission in long undulators. They revisited theoretical models used to describe the emission of radiation by relativistic electrons as a continuous diffusive process, and claimed that in the asymptotic limit for a large number of undulator periods the evolution of the electron energy distribution occurs as discrete energy groups according to Poisson distribution. We show that these novel results have no physical sense…
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 results of an experiment where, using a 200 GW CO2 laser seed, a 65 MeV electron beam was decelerated down to 35 MeV in a 54 cm long strongly tapered helical magnetic undulator, extracting over 30$\%$ of the initial electron beam energy to coherent radiation. These results demonstrate unparalleled electro-optical conversion efficiencies for a relativistic beam in an undulator field and represent an important step in the development of high peak and average power coherent radiation sources.
Free-electron lasers (FELs) over virtually the entire electromagnetic spectrum from microwaves through ultraviolet through hard x-rays that are either seeded or start from noise. FELs can produce a variety of different optical polarizations of the output radiation ranging from linear through elliptic to circular polarization depending upon the characteristics of the undulators used. For example, x-ray FELs use long undulator lines composed of a series of relatively short undulators. Most such FELs use linearly polarized undulators due to the ease of manufacture and tuning; hence the optical ou…
The angular drift of a laser beam is of particular concern in applications such as seeded free-electron lasers. A systematical study of the obliquely incident laser and electron beam interaction in an undulator is presented in this paper. Theoretical analysis and numerical simulations demonstrate that the interaction would imprint energy and angular modulations on the electron beam simultaneously. Compared with the normally incident pattern, the obliquely incident laser-electron interaction leads to reductions in the bunching factors of HGHG and EEHG. In the meanwhile, proactive applications o…
Besides the target to pursue the narrow bandwidth X-ray pulses, the large bandwidth free-electron laser pulses are also strongly demanded to satisfy a wide range of scientific user experiments. In this paper, using the transversely tilt beam enabled by deflecting cavity and/or corrugated structure, the potential of large bandwidth X-ray free-electron lasers generation with the natural gradient of the planar undulator are discussed. Simulations confirm the theoretical prediction, and X-ray free-electron laser bandwidth indicates an increase of one order of magnitude with the optimized parameter…
Besides the target to pursue the narrow bandwidth X-ray pulses, the large bandwidth free-electron laser pulses are also strongly demanded to satisfy a wide range of scientific user experiments. In this paper, using the transversely tilt beam enabled by deflecting cavity and/or corrugated structure, the potential of large bandwidth X-ray free-electron lasers generation with the natural gradient of the planar undulator are discussed. Theoretical predictions and numerical simulations demonstrated that X-ray bandwidth exceeding 5% can be observed with the optimized free-electron laser parameters.
Laser wakefield accelerators have emerged as a promising candidate for compact synchrotron radiation and even x-ray free electron lasers. Today, to make the electrons emit electromagnetic radiation, the trajectories of laser wakefield accelerated electrons are deflected by transverse wakefield, counter-propagating laser field or external permanent magnet insertion device. Here, we propose a novel type of undulator which has a few hundred microns of period and tens of Tesla of magnetic field. The undulator consists of a bifilar capacitor-coil target which sustains strong discharge current that …
All-optical ideas provide a potential to dramatically cut off the size and cost of x-ray light sources to the university-laboratory scale, with the combination of the laser-plasma accelerator and the laser undulator. However, the large longitudinal energy spread of the electron beam from laser-plasma accelerator may hinder the way to high brightness of these all-optical light sources. In this paper, the beam energy spread effect is proposed to be significantly compensated by the natural transverse gradient of a laser undulator when properly transverse-dispersing the electron beam. Theoretical …
In a free-electron laser equipped with variable-gap undulator modules, the technique of undulator tapering opens up the possibility to increase the radiation power beyond the initial saturation point, thus enhancing the efficiency of the laser. The effectiveness of the enhancement relies on the proper optimization of the taper profile. In this work, a multidimensional optimization approach is implemented empirically in the x-ray free-electron laser FLASH2. The empirical results are compared with numerical simulations.
An x-ray regenerative amplifier free-electron laser with a step-tapered-undulator
University of Maryland（马里兰大学）；NoVa Physical Science and Simulations（诺瓦物理科学与模拟研究所）；MESA+ Institute, University of Twente（特温特大学MESA+研究所）；Department of Electrical Engineering, University of Maryland（马里兰大学电气工程系）
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 show that a short relativistic electron beam propagating in a plasma with a density gradient perpendicular to the direction of motion generates a wakefield in which a witness bunch experiences a transverse force. A density gradient oscillating along the beam path would create a periodically varying force---an undulator, with an estimated strength of the equivalent magnetic field more than ten Tesla. This opens an avenue for creation of a high-strength, short-period undulators, which eventually may lead to all-plasma, free electron lasers where a plasma wakefield acceleration is naturally co…
A model of a Free Electron Laser operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate a generalised Bessel function scaling factor, similar to that of planar undulator FEL theory. Comparison between simulations of the averaged model with those of an unaveraged model show very good agreement in the linear regime. Two unexpected results were found. Firstly, an increased coupling to harmonics for elliptical rather than planar polarisarised undu…
We demonstrate that the output radiation characteristics of the European XFEL sources at nominal operation point can be easily made significantly better than what is currently reported in the TDRs of scientific instruments and X-ray optics. In fact, the output SASE characteristics of the baseline European XFEL have been previously optimized assuming uniform undulators at a nominal operating point of 5 kA peak current, without considering the potential of udulator tapering in the SASE regime. In order to illustrate this point, we analyze the case of an electron bunch with nominal parameters. Ba…
In this paper we discuss the design choices and construction strategy of the tapered undulator system designed for a high energy extraction efficiency experiment in the ultraviolet region of the electromagnetic spectrum planned for installation at the Argonne National Laboratory Linac Extension Area (LEA) beamline. The undulator is comprised of 4 sections pure permanent magnet Halbach array separated by short break sections, each one of them housing a focusing quadrupole doublet and a phase shifter. The quadrupoles use a novel hybrid design which allows one to vary the gradient and match the b…
It is reported that [Z. Huang et al., Phys. Rev. Lett. 109, 204801 (2012)], high-gain free-electron laser (FEL) can be generated by transverse-dispersed electron beams from laser-plasma accelerators (LPAs) using transverse-gradient undulator (TGU) assuming an ideal constant dispersion function without focusing optics. The constant dispersion function keeps electrons beyond the resonant energy bandwidth still being on resonant with the FEL radiation. Instead, in this paper, the case with focusing optics in an LPA-driven FEL using TGU is numerically studied, in which the dispersion function shou…
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…
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 baseline parameters are optimized for the ILC at sqrt(s)=500 GeV, that means an electron drive beam of 250 GeV. Precision measurements in the Higgs sector, however, require measurements at sqrt(s)=250 GeV, i.e. running with the electron drive beam only at 125 GeV, which imposes a challenge for achieving a high yield. Therefore the baseline undulator parameters have to be optimized as much as possible within their technic…
We show that radiation pulses from an X-ray Free-Electron Laser (XFEL) with a planar undulator, which are mainly polarized in the horizontal direction, exhibit a suppression of the vertical polarization component of the power at least by a factor $λ_w^2/(4 πL_g)^2$, where $λ_w$ is the length of the undulator period and $L_g$ is the FEL field gain length. We illustrate this fact by examining the XFEL operation under the steady state assumption. In our calculations we considered only resonance terms: in fact, non resonance terms are suppressed by a factor $λ_w^3/(4 πL_g)^3$ and can be neglected.…
In a previous paper we discussed the physics of a microbunched electron beam kicked by the dipole field of a corrector magnet by describing the kinematics of coherent undulator radiation after the kick. We demonstrated that the effect of aberration of light supplies the basis for understanding phenomena like the deflection of coherent undulator radiation by a dipole magnet. We illustrated this fact by examining the operation of an XFEL under the steady state assumption, that is a harmonic time dependence. We argued that in this particular case the microbunch front tilt has no objective meaning…
Free-electron lasers (FELs) have been built ranging in wavelength from long-wavelength oscillators using partial wave guiding through ultraviolet through hard x-ray that are either seeded or start from noise (SASE). In addition, FELs that produce different polarizations of the output radiation ranging from linear through elliptic to circular polarization are currently under study. In this paper, we develop a three-dimensional, time-dependent formulation that is capable of modeling this large variety of FEL configurations including different polarizations. We employ a modal expansion for the op…
The effects of a correlated linear energy/velocity chirp in the electron beam in the FEL, and how to compensate for its effects by using an appropriate taper (or reverse-taper) of the undulator magnetic field, is well known. The theory, as described thus far, ignores velocity dispersion from the chirp in the undulator, taking the limit of a `small' chirp. In the following, the physics of compensating for chirp in the beam is revisited, including the effects of velocity dispersion, or beam compression or decompression, in the undulator. It is found that the limit of negligible velocity dispersi…
Various methods have been proposed to condition an electron beam in order to reduce its emittance effect and to improve the short-wavelength free electron laser (FEL) performance. In this paper, we show that beam conditioning does not result in a complete elimination of the emittance effect in an alternating-gradient focusing FEL undulator. Using a one-dimensional model and a three-dimensional simulation code, we derive a criteria for the emittance limitation of a perfectly conditioned beam that depends on the focusing structure.
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…
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…
Free Electron Lasers (FEL) are commonly regarded as the potential key application of laser wakefield accelerators (LWFA). It has been found that electron bunches exiting from state-of-the-art LWFAs exhibit a normalized 6-dimensional beam brightness comparable to those in conventional linear accelerators. Effectively exploiting this beneficial beam property for LWFA-based FELs is challenging due to the extreme initial conditions particularly in terms of beam divergence and energy spread. Several different approaches for capturing, reshaping and matching LWFA beams to suited undulators, such as …
The possibility of constructing terawatt (TW) x-ray free-electron lasers (FELs) has been discussed using novel superconducting helical undulators [5]. In this paper, we consider the conditions necessary for achieving powers in excess of 1 TW in a 1.5 Å FEL using simulations with the MINERVA simulation code [7]. Steady-state simulations have been conducted using a variety of undulator and focusing configurations. In particular, strong focusing using FODO lattices is compared with the natural, weak focusing inherent in helical undulators. It is found that the most important requirement to reach …
In a previous work we proposed a scheme for polarization control at the LCLS baseline, which exploited the microbunching from the planar undulator. After the baseline undulator, the electron beam is transported through a drift by a FODO focusing system, and through a short helical radiator. The microbunching structure can be preserved, and intense coherent radiation is emitted in the helical undulator at fundamental harmonic. The driving idea of this proposal is that the background linearly-polarized radiation from the baseline undulator is suppressed by spatial filtering. Filtering is achieve…
Generally, turn-to-turn fluctuations of synchrotron radiation power in a storage ring depend on the 6D phase-space distribution of the electron bunch. This effect is related to the interference of fields radiated by different electrons. Changes in the relative electron positions and velocities inside the bunch result in fluctuations in the total emitted energy per pass in a synchrotron radiation source. This effect has been previously described assuming constant and equal electron velocities before entering the synchrotron radiation source. In this paper, we present a generalized formula for t…
The (spectral) brightness for partially transverse coherent sources as Synchrotron Radiation (SR) and Free-Electron Laser (FEL) sources can be defined as the maximum of the Wigner distribution. Then, the brightness includes information on both coherence and wavefront characteristics of the radiation field. For undulator sources, it is customary to approximate the single-electron electric field at resonance with a Gaussian beam, leading to great simplifications. Attempts to account for the modified spatial and angular profile of the undulator radiation in the presence of detuning due to energy …
