Coherent Synchrotron Radiation can severely limit the performance of accelerators designed for high brightness and short bunch length. Examples include light sources based on ERLs or FELs, and bunch compressors for linear colliders. In order to better simulate Coherent Synchrotron Radiation, the established 1-dimensional formalism is extended to work at lower energies, at shorter bunch lengths, and for an arbitrary configuration of multiple bends. Wide vacuum chambers are simulated by means of vertical image charges. This formalism has been implemented in the general beam dynamics code "Bmad" and its results are here compared to analytical approximations, to numerical solutions of the Maxwell equations, and to the simulation code "elegant".
Coherent Synchrotron Radiation has been studied effectively using a 1-dimensional model for the charge distribution in the realm of small angle approximations and high energies. Here we use Jefimenko's form of Maxwell's equations, without such approximations, to calculate the exact wake-fields due to this effect in multiple bends and drifts. It has been shown before that the influence of a drift can propagate well into a subsequent bend. We show, for reasonable parameters, that the influence of a previous bend can also propagate well into a subsequent bend, and that this is especially importan…
We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to the situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmark…
Theory predicts that Coherent Synchrotron Radiation (CSR) in electron storage rings should appear in whispering gallery modes. In an idealized model these are resonances of the vacuum chamber that are characterized by their high frequencies and concentration of the field near the outer wall of the chamber. The resonant modes imply a series of sharp peaks in the frequency spectrum of CSR, and very long wake fields which lead to interbunch communication. Theory and experimental evidence for this behavior will be reviewed.
Beam quality preservation during transport of high-brightness electron beams is of general concern in the design of modern accelerators. Methods to manage incoherent synchrotron radiation (ISR) have been in place for decades; as beam brightness has improved coherent synchrotron radiation (CSR) and the microbunching instability (uBI) have emerged as performance limitations. We apply the compensation analysis of diMitri, Cornacchia, and Spampinati - as previously used by Borland - to the design of transport systems for use with low-emittance beams, and find that appropriately configured second o…
Coherent synchrotron radiation (CSR) occurs when short bunches travel on strongly bent trajectories. Its effects on high-quality beams can be severe and are well understood qualitatively. For quantitative results, however, one has to rely on numerical methods. There exist several simulation codes utilizing different approaches. We describe in some detail the code TraFiC4 developed at DESY for design and analysis purposes, which approaches the problem from first principles and solves the equations of motion either perturbatively or self-consistently. We present some calculational results and co…
Next generation accelerators will require a high current, low emittance beam with a low energy spread. Such accelerators will employ advanced beam conditioning systems such as emittance exchangers to manipulate high brightness beams. One of the goals of the Fermilab A0 photoinjector is to investigate the transverse to longitudinal emittance exchange principle. Coherent synchrotron radiation could limit high current operation of the emittance exchanger. In this paper, we report on the preliminary experimental and simulation study of the coherent synchroton radiation (CSR) in the emittance excha…
Most studies of Coherent Synchrotron Radiation (CSR) have only considered the radiation from independent dipole magnets. However, in the damping rings of future linear colliders, a large fraction of the radiation power will be emitted in damping wigglers. In this paper, the longitudinal wakefield and impedance due to CSR in a wiggler are derived in the limit of a large wiggler parameter $K$. After an appropriate scaling, the results can be expressed in terms of universal functions, which are independent of $K$. Analytical asymptotic results are obtained for the wakefield in the limit of large …
Generation of extreme bright coherent synchrotron radiation in a short wavelength range is of remarkable interest in the synchrotron light source community. In this paper, a novel technique is adopted to produce the coherent radiation which uses an angular dispersion to enhance the micro-bunch by a tiny amplitude of energy modulation. This scheme can be inserted in a long straight section of a storage ring. A lattice design of an extreme-low emittance storage ring with 3.5 GeV energy is presented in this paper, which employs a higher order achromat (HOA) concept. We show the design results for…
Coherent Synchrotron Radiation (CSR) can play an important role by not only increasing the energy spread and emittance of a beam, but also leading to a potential instability. Previous studies of the CSR induced longitudinal instability were carried out for the CSR impedance due to dipole magnets. However, many storage rings include long wigglers where a large fraction of the synchrotron radiation is emitted. This includes high-luminosity factories such as DAPHNE, PEP-II, KEK-B, and CESR-C as well as the damping rings of future linear colliders. In this paper, the instability due to the CSR imp…
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…
We investigate influence on the storage ring beam dynamics of the coherent Synchrotron Radiation (SR) self fields produced by an electron bunch. We show that the maximum energy gain in the RF cavity must far exceed the energy loss of electrons due to the coherent SR.
Bunches of high charge (up to 10 nC) are compressed in length in the CTF II magnetic chicane to less than 0.2 mm rms. The short bunches radiate coherently in the chicane magnetic field, and the horizontal and longitudinal phase space density distributions are affected. This paper reports the results of beam emittance and momentum measurements. Horizontal and vertical emittances and momentum spectra were measured for different bunch compression factors and bunch charges. In particular, for 10 nC bunches, the mean beam momentum decreased by about 5% while the FWHM momentum spread increased from …
Spontaneous formation of spatial structures (patterns) occurs in various contexts, ranging from sand dunes and rogue wave formation, to traffic jams. These last decades, very practical reasons also led to studies of pattern formation in relativistic electron bunches used in synchrotron radiation light sources. As the main motivation, the patterns which spontaneously appear during an instability increase the terahertz radiation power by factors exceeding 10000. However the irregularity of these patterns largely prevented applications of this powerful source. Here we show how to make the spatio-…
Coherent fraction is a concept widely used in the synchrotron radiation community. Here I discuss the meaning of coherent fraction, an accurate way to define it, and the different formulations found in literature to calculate it. After several comparisons using values from the present and future ESRF lattices, an approximated way to quickly compute it is proposed.
A new model is presented for simulating coherent synchrotron radiation (CSR) in one dimension. The method is based on convolving an integrated Green function (IGF) with the longitudinal charge density. Since it is based on an IGF, the accuracy of this approach is determined by how well one resolves the charge density and not by resolving the single particle wake function. Since short-range wakefield effects are included analytically, the approach can be much more efficient than ordinary (non-IGF) approaches in situations where the wake function and charge density have disparate spatial scales.…
The coherent synchrotron radiation (CSR) effect in a bending path plays an important role in transverse emittance dilution in high-brightness light sources and linear colliders, where the electron beams are of short bunch length and high peak current. Suppression of the emittance growth induced by CSR is critical to preserve the beam quality and help improve the machine performance. It has been shown that the CSR effect in a double-bend achromat (DBA) can be analyzed with the two-dimensional point-kick analysis method. In this paper, this method is applied to analyze the CSR effect in a triple…
This paper theoretically proves that an electron storage ring can generate coherent radiation in THz region using a quick kicker magnet and an ac sextupole magnet. When the vertical chromaticity is modulated by the ac sextupole magnet, the vertical beam collective motion excited by the kicker produces a wavy spatial structure after a number of longitudinal oscillation periods. We calculate the radiation spectral distribution from the wavy bunch in Hefei Light Source(HLS). If we reduce electron energy to 400MeV, it can produce extremely strong coherent synchrotron radiation(CSR) at 0.115THz.
The transverse bunch spectrum and the transverse decoherence/recoherence following an initial bunch offset are important phenomena in synchrotrons and storage rings, and are widely used for beam and lattice measurements. Incoherent shifts of the particles betatron frequency and of the synchrotron frequency modify the transverse spectrum and the bunch decoherence. In this study we analyze the effects of transverse space charge and of the rf nonlinearity on the decoherence signals. The transverse bunch decoherence and the resulting coherent spectra are measured in the SIS18 synchrotron at GSI Da…
The coherent synchrotron radiation (CSR) of a high brightness electron beam traversing a series of dipoles, such as recirculation or transport arcs, may lead to the microbunching instability. We extend and develop a semi-analytical approach of the CSR-induced microbunching instability for a general lattice, based on the previous formulation with 1-D CSR model [Phys. Rev. ST Accel. Beams 5, 064401 (2002)] and apply it to investigate the physical processes of microbunching amplification for two example transport arc lattices. We find that the microbunching instability in transport arcs has a dis…
A compact damping ring with limited circumference of about 160 m is proposed for producing kilowatt-level coherent EUV radiation. The electron bunch in the ring is modulated by a 257nm wavelength laser with the help of the angular dispersion induced micro-bunching method [C. Feng and Z. Zhao, Sci. Rep. 7, 4724 (2017)]. Coherent radiation at 13.5 nm with an average power of about 2.5 kW can be achieved with the state-of-the-art accelerator and laser technologies.
We study coherent synchrotron radiation (CSR) in a perfectly conducting vacuum chamber of rectangular cross section, in a formalism allowing an arbitrary sequence of bends and straight sections. We apply the paraxial method in the frequency domain, with a Fourier development in the vertical coordinate but with no other mode expansions. A line charge source is handled numerically by a new method that rids the equations of singularities through a change of dependent variable. The resulting algorithm is fast compared to earlier methods, works for short bunches with complicated structure, and yiel…
We investigate the effect of shear in the flow of charged particle equilibria that are unstable to the Coherent Synchrotron Radiation (CSR) instability. Shear may act to quench this instability because it acts to limit the size of the region with a fixed phase relation between emitters. The results are important for the understanding of astrophysical sources of coherent radiation where shear in the flow is likely.
The electromagnetic radiation of a rotating relativistic electron layers is studied numerically using particle-in-cell simulation. The results of the simulation confirm all relevant scaling properties predicted by theoretical models. These models may turn out to be important for the understanding of the coherent synchrotron radiation (CSR) instability that may occur in systems as diverse as particle accelerators radio pulsars.
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…
NA60+ is a fixed target experiment proposed in the framework of the Physics Beyond Colliders programme at CERN. It aims to precisely measure the hard and electromagnetic probes in nuclear collisions. Initially proposed for the underground cavern ECN3 with very high beam intensities, the experiment now foresees a location in the EHN1 surface hall which was shown to have a limited impact on the physics performance in spite of a significant reduction of beam intensity and detector size. The potential installation and operation of the experiment with the ion beams from the Super Proton Synchrotron…
We report on high resolution measurements of resonances in the spectrum of coherent synchrotron radiation (CSR) at the Canadian Light Source (CLS). The resonances permeate the spectrum at wavenumber intervals of $0.074 ~\textrm{cm}^{-1}$, and are highly stable under changes in the machine setup (energy, bucket filling pattern, CSR in bursting or continuous mode). Analogous resonances were predicted long ago in an idealized theory as eigenmodes of a smooth toroidal vacuum chamber driven by a bunched beam moving on a circular orbit. A corollary of peaks in the spectrum is the presence of pulses …
An understanding of collective effects is of fundamental importance for the design and optimisation of the performance of modern accelerators. In particular, the design of an accelerator with strict requirements on the beam quality, such as a free electron laser (FEL), is highly dependent on a correspondence between simulation, theory and experiments in order to correctly account for the effect of coherent synchrotron radiation (CSR), and other collective effects. A traditional approach in accelerator simulation codes is to utilise an analytic one-dimensional approximation to the CSR force. We…
Each successive generation of x-ray machines has opened up new frontiers in science, such as the first radiographs and the determination of the structure of DNA. State-of-the-art x-ray sources can now produce coherent high brightness keV x-rays and promise a new revolution in imaging complex systems on nanometre and femtosecond scales. Despite the demand, only a few dedicated synchrotron facilities exist worldwide, partially due the size and cost of conventional (accelerator) technology. Here we demonstrate the use of a recently developed compact laser-plasma accelerator to produce a well-coll…
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.
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…
The self-consistent nonlinear dynamics of a relativistic charged particle beam interacting with its complete self-fields is a fundamental problem underpinning many of the accelerator design issues in high brightness beam applications, as well as the development of advanced accelerators. Particularly, synchrotron radiation induced effects in a magnetic dispersive beamline element can lead to collective beam instabilities and emittance growth. A novel beam dynamic code is developed based on a Lagrangian method for the calculation of the particles' radiation near-fields using wavefront/wavelet me…
In recent and future synchrotron radiation facilities, relativistic electron bunches with increasingly high charge density are needed for producing brilliant light at various wavelengths, from X-rays to terahertz. In such conditions, interaction of electrons bunches with their own emitted electromagnetic fields leads to instabilities and spontaneous formation of complex spatial structures. Understanding these instabilities is therefore key in most electron accelerators. However, investigations suffer from the lack of non-destructive recording tools for electron bunch shapes. In storage rings, …
The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses OpenCL to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of c…
Nonlinear waves have been observed in synchrotrons for years but have received little attention in the literature. While pathological, these phenomena are worth studying on at least two accounts. First, the formation of solitary waves may lead to droplet formation that causes significant beam halo to develop. Secondly, a variety of nonlinear processes are likely involved in the normal saturation of unstable oscillations, leading to the possibility that low-level, but potentially broadband fluctuation spectra may develop. Both features carry indirectly the signature of the machine impedance. In…
In the presence of longitudinal coherent electron cooling, the evolution of the line-density profile of a circulating ion bunch can be described by the 1-D Fokker-Planck equation. We show that, in the absence of diffusion, the 1-D equation can be solved analytically for certain dependence of cooling force on the synchrotron amplitude. For more general cases with arbitrary diffusion, we solved the 1-D Fokker-Planck equation numerically and the numerical solutions have been compared with results from macro-particle tracking.
SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
Particle accelerators support a wide array of scientific, industrial, and medical applications. To meet the needs of these applications, accelerator physicists rely heavily on detailed simulations of the complicated particle beam dynamics through the accelerator. One of the most computationally expensive and difficult-to-model effects is the impact of Coherent Synchrotron Radiation (CSR). As a beam travels through a curved trajectory (e.g. due to a bending magnet), it emits radiation that in turn interacts with the rest of the beam. At each step through the trajectory, the electromagnetic fiel…
The propagation of hard X ray beam from partially coherent synchrotron source is simulated by using the novel method based on the coherent mode decomposition of Gaussian Schell model and wave front propagation. We investigate how the coherency properties and intensity distributions of the beam are changed by propagation through optical elements. Here, we simulate and analyze the propagation of the partially coherent radiation transmitted through an ideal slit. We present the first simulations for focusing partially coherent synchrotron hard X ray beams using this novel method. And when compare…
Dedicated optics with extremely short electron bunches enable synchrotron light sources to generate intense coherent THz radiation. The high degree of spatial compression in this so-called low-alpha optics entails a complex longitudinal dynamics of the electron bunches, which can be probed studying the fluctuations in the emitted terahertz radiation caused by the micro-bunching instability ("bursting"). This article presents a "quasi-instantaneous" method for measuring the bursting characteristics by simultaneously collecting and evaluating the information from all bunches in a multi-bunch fil…
Emission of light by a single electron moving on a curved trajectory (synchrotron radiation) is one of the most well-known fundamental radiation phenomena. However experimental situations are more complex as they involve many electrons, each being exposed to the radiation of its neighbors. This interaction has dramatic consequences, one of the most spectacular being the spontaneous formation of spatial structures inside electrons bunches. This fundamental effect is actively studied as it represents one of the most fundamental limitations in electron accelerators, and at the same time a source …
Although microbunching-instability (MBI) based synchrotron-radiation facilities do not exist yet, the prominent presence of this space-charge driven instability in the high-brightness accelerator facilities promotes the ongoing worldwide effort to mastering it. Thereby not only the possible countermeasures but also the applications of MBI are in focus of the research. So far, the observed microbunching wavelengths are in IR or optical regime. Shifting the microbunching towards shorter wavelengths seems to require either very high-bunch peak currents or extremely small emittances. These extreme…
The notion of brightness is efficiently conveyed in geometric optics as density of rays in phase space. Wigner has introduced his famous distribution in quantum mechanics as a quasi-probability density of a quantum system in phase space. Naturally, the same formalism can be used to represent light including all the wave phenomena. It provides a natural framework for radiation propagation and optics matching by transferring the familiar `baggage' of accelerator physics (beta-function, emittance, phase space transforms, etc.) to synchrotron radiation. This paper details many of the properties of…
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 …
We study the stability of a collisionless, relativistic, finite-strength, cylindrical layer of charged particles in free space by solving the linearized Vlasov-Maxwell equations and compute the power of the emitted electromagnetic waves. The layer is rotating in an external magnetic field parallel to the layer. This system is of interest to understanding the high brightness temperature of pulsars which cannot be explained by an incoherent radiation mechanism. Coherent synchrotron radiation has also been observed recently in bunch compressors used in particle accelerators. We consider equilibri…
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）
In order to meet requirements of the synchrotron radiation users, a fully coherent VUV free electron laser (FEL) has been preliminarily designed. One important goal of this design is that the radiation wavelength can be easily tuned in a broad range (70-170 nm). In the light of the users' demand and our actual conditions, the self-seeding scheme is adopted for this proposal. Firstly, we attempt fixing the electron energy and only changing the undulator gap to varying the radiation wavelength, but the analysis implies that it is difficult because of the great difference of the power gain length…
Since their discovery in 1896, x-rays have had a profound impact on science, medicine and technology. Here we show that the x-rays from a novel tabletop source of bright coherent synchrotron radiation can be applied to phase contrast imaging of biological specimens, yielding superior image quality and avoiding the need for scarce or expensive conventional sources.
