We consider the maximum of the Wigner distribution (WD) of synchrotron radiation (SR) fields as a possible definition of SR source brightness. Such figure of merit was originally introduced in the SR community by Kim. The brightness defined in this way is always positive and, in the geometrical optics limit, can be interpreted as maximum density of photon flux in phase space. For undulator and bending magnet radiation from a single electron, the WD function can be explicitly calculated. In the case of an electron beam with a finite emittance the brightness is given by the maximum of the convolution of a single electron WD function and the probability distribution of the electrons in phase space. In the particular case when both electron beam size and electron beam divergence dominate over the diffraction size and the diffraction angle, one can use a geometrical optics approach. However, there are intermediate regimes when only the electron beam size or the electron beam divergence dominate. In this asymptotic cases the geometrical optics approach is still applicable, and the brightness definition used here yields back once more the maximum photon flux density in phase space. In these intermediate regimes we find a significant numerical disagreement between exact calculations and the approximation for undulator brightness currently used in literature. We extend the WD formalism to a satisfactory theory for the brightness of a bending magnet. We find that in the intermediate regimes the usually accepted approximation for bending magnet brightness turns out to be inconsistent even parametrically.
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.
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 …
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…
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.
A single electron circulating in a storage ring is a very peculiar object. Synchrotron radiation quantum fluctuation causes stohastic process in the synchrotron oscillation of an electron. The radiation from a undulator permits one to obtain discret moments of longitudional electron motion. Experiments with a single electron on on the VEPP-3 optical klystrons are described.
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…
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…
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…
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…
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.
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…
Generally, turn-to-turn power fluctuations of incoherent spontaneous synchrotron radiation in a storage ring depend on the 6D phase-space distribution of the electron bunch. In some cases, if only one parameter of the distribution is unknown, this parameter can be determined from the measured magnitude of these power fluctuations. In this Letter, we report an absolute measurement (no free parameters or calibration) of a small vertical emittance (5--15 nm rms) of a flat beam by this method, under conditions, when it is unresolvable by a conventional synchrotron light beam size monitor.
Undulator Radiation from a Single Electron: A Temporal Double-Slit Experiment
TU Dortmund University（多特蒙德工业大学）；Hiroshima University（广岛大学）；Institute for Molecular Science, National Institutes of Natural Sciences（国立自然科学研究所分子科学研究所）；SOKENDAI（综合研究大学院大学）；Helmholtz-Zentrum Berlin (HZB)（赫尔姆霍兹柏林中心）
We discuss radiation generated by positrons channeling in a crystalline undulator. The undulator is produced by periodically bending a single crystal with an amplitude much larger than the interplanar spacing. Different approaches for bending the crystal are described and the restrictions on the parameters of the bending are established. We present the results of numeric calculations of the spectral distributions of the spontaneous emitted radiation and estimate the conditions for stimulated emission. Our investigations show that the proposed mechanism provides an efficient source for high ene…
The 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 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 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…
A surprising small dechanneling length was observed at (111) channeling of ultrarelativistic electrons in a 60 $μ$m thick silicon single crystal with a bending radius of 0.15 m. The experiments were conducted at beam energies between 3.35 and 14 GeV at the Facility for Advanced Accelerator Experimental Tests (FACET at SLAC, USA). It is shown in this paper that the small dechanneling lengths can well be reproduced with a modified Fokker-Planck equation for plane crystals in which a crystal bending has been heuristically introduced. Encouraged by this result experiments have been reconsidered wh…
A recent "beam splitting" experiment at LCLS apparently demonstrated that after a microbunched electron beam is kicked on a large angle compared to the divergence of the FEL radiation, the microbunching wave front is readjusted along the new direction of motion of the kicked beam. Therefore, coherent radiation from an undulator placed after the kicker is emitted along the kicked direction without suppression. This strong emission of coherent undulator radiation in the kicked direction cannot be explained in the framework of conventional synchrotron radiation theory. In a previous paper we expl…
This paper describes a theory of transverse coherence properties of Undulator Radiation. Our study is of very practical relevance, because it yields specific predictions of Undulator Radiation cross-spectral density in various parts of the beamline. On the contrary, usual estimations of coherence properties assume that the undulator source is quasi-homogeneous, like thermal sources, and rely on the application of van Cittert-Zernike (VCZ) theorem, in its original or generalized form, for calculating transverse coherence length in the far-field approximation. The VCZ theorem is derived in the f…
Synchrotron radiation emitted by electrons passing through an undulator placed in a storage ring is decomposed in coherent modes. The case of ultimate storage rings where the electron emittance is comparable to the emittance of the photon fan is analyzed by means of the cross spectral density and the coherent mode spectrum. The proposed method permits naturally the statistical analysis and propagation of the cross spectral density along the beamline optics. The coherence properties of the X-ray beam at any point of the beamline are completely given in terms of the eigenvalues and coherent mode…
The laser-plasma accelerator has attracted great interest for constituting an alternative in the production of the relativistic electron beams of high peak current. But the generated electron beam has poor monochrome and emittance, which make it difficult to produce high brightness radiation. Here we propose a compact flexible laser undulator based on ponderomotive force to constitute a millimeter-sized synchrotron radiation source of X-ray. We demonstrate that it can produce bright radiation with tens of keV energies. This opens a new path to compact synchrotron source with high power laser.
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…
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…
We study high efficiency, multi-terawatt peak power, few angstrom wavelength, X-ray Free Electron Lasers (X-ray FELs). To obtain these characteristics we consider an optimized undulator design: superconducting, helical, with short period and built-in strong focusing. This design reduces the length of the breaks between modules, decreasing diffraction effects, and allows using a stronger transverse electron focusing. Both effects reduce the gain length and the overall undulator length. The peak power and efficiency depend on the transverse electron beam distribution and on time dependent effect…
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 …
The Advanced Superconducting Test Accelerator (ASTA) facility is currently under construction at Fermilab. With a 1-ms macropulse composed of up to 3000 micropulses and with beam energies projected from 45 to 800 MeV, the need for non-intercepting diagnostics for beam size, position, energy, and bunch length is clear. In addition to the rf BPMs, optical synchrotron radiation (OSR), and optical diffraction radiation (ODR) techniques already planned, we propose the use of undulator radiation from a dedicated device for diagnostics. with a nominal period of 4-5 cm, a tunable field parameter K, an…
A dielectric laser accelerator, operating at optical frequencies and GHz pulse rate, is expected to produce attosec electron bunches with a moderate beam current at high energy. For relativistic electrons, the attosec bunch has a spatial length of a few nanometers, which is well suited for generating high-brightness superradiance in the VUV, EUV, and x-ray spectra. Our study shows that the brilliance of coherent undulator radiation driven by a short-bunch beam with 1~10 fC bunch charge from a dielectric laser accelerator is comparable to or higher than that of a synchrotron in the 0.1 ~ 3 keV …
The study presented here was initiated by a discussion to investigate the possibility of using synchrotron radiation as a source for the Next Generation Lithography (NGL) based on the EUV-concept (Extreme Ultra-Violet; here 13.5 nm or 11.3 nm radiation, respectively). The requirements are: 50 W, 2% bandwidth and minimal power outside this bandwidth. Three options were investigated. The first two deal with radiation from bending magnets and undulators. The results confirm the earlier work by Oxfords Instrument and others that these light-sources lack in-band power while emitting excessive out-o…
This paper is devoted to the investigation of the radiation energy losses of an ultra-relativistic charged particle channeling along a crystal plane which is periodically bent by a transverse acoustic wave. In such a system there are two essential mechanisms leading to the photon emission. The first one is the ordinary channeling radiation. This radiation is generated as a result of the transverse oscillatory motion of the particle in the channel. The second one is the acoustically induced radiation. This radiation is emitted because of the periodic bending of the particle's trajectory created…
Short period, high field undulators are used to produce hard X-rays on synchrotron radiation based storage ring facilities of intermediate energy and enable short wavelength Free Electron Laser. Cryogenic permanent magnet undulators take benefit from improved magnetic properties of RE2Fe14B (Rare Earth based magnets) at low temperatures for achieving short period, high magnetic field and high coercivity. Using Pr2Fe14B instead of Nd2Fe14B, which is generally employed for undulators, avoids the limitation caused by the Spin Reorientation Transition phenomenon, and simplifies the cooling system …
As an important measure of improving the efficiency and usability of X-ray free electron laser facilities, simultaneous operation of multiple undulator lines realized by a beam distribution system has become a standard configuration in the recent built XFEL facilities. In Shanghai, SXFEL-UF, the first soft X-ray free electron laser user facility in China, has finished construction and started commissioning recently. Electron beam from linac is alternately distributed between the two parallel undulator beam lines by a beam distribution system with a 6° deflection line. The beam distribution sys…
The electron cloud is a possible heat source in the superconducting undulator (SCU) designed for the Advanced Photon Source (APS), a 7-GeV electron synchrotron radiation source at Argonne National Laboratory. In electron cloud generation extensive research has been done, and is continuing, to understand the secondary electron component. However, little work has been done to understand the parameters of photoemission in the accelerator environment. To better understand the primary electron generation in the APS; a beamline at the Australian Light Source synchrotron was used to characterize two …
In this paper we analyze the image formation problem for undulator radiation through an optical system, accounting for the influence of the electron beam emittance. On the one hand, image formation with Synchrotron Radiation is governed by the laws of Statistical Optics. On the other hand, the widely used Gaussian-Shell model cannot be applied to describe the coherence properties of X-ray beams from third generation Synchrotron Radiation sources. As a result, a more rigorous analysis of coherence properties is required. We propose a technique to explicitly calculate the cross-spectral density …
This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert-Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical(geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four ord…
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 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…
China's first quasi-periodic undulator (QPU) has been developed for the Hefei Light Source (HLS). It uses a magnetic configuration with varied thicknesses of NdFeB blocks, based on the QPU of European Synchrotron Radiation Facility (ESRF). Depression of 3rd harmonic radiation is significantly improved over the ESRF QPU, as deduced from the measured magnetic fields. A method of configuring shims of different geometries and sizes, based on a symmetric principle to correct multi-pole field integrals, was demonstrated.
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…
This work contains a systematic treatment of single particle Synchrotron Radiation and some application to realistic beams with given cross section area, divergence and energy spread. Standard theory relies on several approximations whose applicability limits and accuracy are often forgotten. We begin remarking that on the one hand, a paraxial approximation can always be applied without loss of generality and with ultra relativistic accuracy. On the other hand, dominance of the acceleration field over the velocity part in the Lienard-Wiechert expressions is not always granted and constitutes a…
The parameters for a 30 GeV test beam are outlined for use with an undulator in the FFTB tunnel where the LCLS will eventually be housed. It is proposed to use the SLAC linac and damping rings in their present mode of operation for PEP II injection, where 30 GeV beams are also delivered at 10 Hz to the FFTB. High peak currents are obtained with the addition of a second bunch compressor in the linac. In order to minimize the synchrotron radiation induced emittance growth in the bunch compressor it is necessary to locate the new bunch compressor at the low-energy end of the linac, just after the…
In this paper we discuss a method for nondestructive measurements of the longitudinal profile of sub-picosecond electron bunches for X-Ray Free Electron Lasers (XFELs). The method is based on the detection of the Coherent Synchrotron Radiation (CSR) spectrum produced by a bunch passing a dipole magnet system. This work also contains a systematic treatment of synchrotron radiation theory which lies at the basis of CSR. Standard theory of synchrotron radiation uses several approximations whose applicability limits are often forgotten: here we present a systematic discussion about these assumptio…
Synchrotron light sources and X-ray free-electron laser (FEL) facilities are unique tools providing extremely brilliant X-rays that allow the observation of matter with atomic spatial resolution. On the one hand, synchrotron light sources consist of electron circular accelerators and produce synchrotron radiation in bending magnets and undulators. On the other hand, X-ray FEL facilities are based on electron linear accelerators and generate more coherent and shorter pulses suitable for time-resolved experiments. In this contribution we will qualitatively describe synchrotron and X-ray FEL faci…
Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsytem critical to the OSC scheme is the focusing optics used to image radiation from the upstream "pickup" undulator to the downstream "kicker" undulator. In this paper, we present simulation results using wave-optics calculation carried out with the {\sc Synchrotron Radiation Wor…
In anticipation of the increased use of coherent x-ray methods and the need to upgrade beamlines to match improved source quality, we have characterized the coherence properties of the x-rays delivered by beamline 12ID-D at the Advanced Photon Source. We compare the measured x-ray divergence, beam size, brightness, and coherent flux at energies up to 26 keV to the calculated values from the undulator source, and evaluate the effects of beamline optics such as a mirror, monochromator, and compound refractive lenses. Diffraction patterns from slits as a function of slit width are analyzed using …
The performance of synchrotron light facilities are strongly influenced by the photon beam bright- ness, that can be further increased by reducing the beam emittance. A Robinson Wiggler can be installed in a non-zero dispersion straight section to reduce the horizontal beam emittance. It is composed of an array of magnets of alternated polarities, whose both magnetic field and gradient are of opposite signs. It provides a compact solution to reduce by 50% the horizontal emittance. How- ever, it increases the energy spread by 40%. The concept of the Robinson Wiggler (RW) is described here, the …
Undulator radiation from synchrotron light sources must be transported down a beamline from the source to the sample. A partially coherent photon beam may be represented in phase space using a Wigner function, and its transport may use some similar techniques as is familiar in particle beam transport. We describe this process in the case that the beamline is composed of linear focusing and defocusing sections as well as apertures. We present a compact representation of the beamline map involving linear transformations and convolutions. We create a 1:1 imaging system (4f system) with a single s…
Synchrotron radiation of relativistic electrons in storage rings naturally leads to the process of damping of betatron oscillations. Damping time and transverse beam emittance can be reduced by wigglers or undulators while the beam parameters are still well defined by the common radiation integrals, based on the properties of synchrotron radiation. However, the quantum excitation of betatron oscillations in principle can be considerably reduced if an electron radiation occurs due to the Thomson scattering in the periodic electromagnetic field. After a brief introduction we compare radiation pr…
We represent results of calculations of coherent synchrotron radiation (CSR) of the relativistic bunch in an undulator with a vacuum chamber of arbitrary cross section with a new algorithm. This algorithm associated with direct calculations of electric field rather than the vector potential. CSR normalized to the incoherent one and compared with analytical calculations for a free space.
