In an ideal accelerator, the single-particle dynamics can be decoupled into transverse motion -- the betatron oscillations -- and longitudinal motion -- the synchrotron oscillations. Chromatic and dispersive effects introduce a coupling between these dynamics, the so-called synchro-betatron coupling. We present an analysis of the fully coupled dynamics over a single synchrotron oscillation that leads to an averaged invariant with synchro-betatron coupling in a generic lattice. We apply this analysis to two problems: first, a toy lattice where the computations are analytically tractable, then a design for a rapid cycling synchrotron built using the integrable optics described by Danilov and Nagaitsev, showing that although there is fairly complex behavior over the course of a synchrotron oscillation, the Danilov-Nagaitsev invariants are nevertheless periodic with the synchrotron motion.
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…
Structural symmetries in the storage ring of synchrotrons are intentionally created during the design phase of the magnetic lattices, but they are not considered in the design of control algorithms that stabilize the beam of accelerated particles. The choice of control algorithm, however, is limited by the speed requirements of the synchrotron. Standard control algorithms for synchrotrons are based on a singular value decomposition (SVD) of the orbit response matrix. SVD controllers neither exploit the structural symmetries nor exhibit any speed advantages. Based on the periodicity and the ref…
We reinvestigate the gravitational waves (GWs) induced by charged particles in storage rings. There are two major components in such GWs. One is the gravitational synchrotron radiation (GSR), i.e., the direct emission by the bending of the trajectory of a relativistic charged particle, much like the conventional electromagnetic synchrotron radiation (EMSR), albeit with characteristic difference in their radiation spectra. While the conventional EMSR spectrum peaks at the critical frequency, $ω_c=γ^3ω_0\ggω_0$, the spectrum of GSR peaks at the storage ring fundamental frequency $ω_0$, which is …
We calculate equilibrium emittances and damping times due to the emission of synchrotron radiation for coupled storage ring lattices by evaluating the projections of the commonly used synchrotron radiation integrals onto the normal modes of the coupled motion. Orbit distortion is included by calculating off-axis contributions to the radiation integrals. We provide explicit formulae for fast forward calculation, which have been implemented into the interactive lattice design code OPA.
In order to improve the stability of synchrotron radiation, we developed a new method of machine learning-based closed orbit feedback and piloted it in the storage ring of the Shanghai Synchrotron Radiation Facility (SSRF). In our experiments, not only can the machine learning-based closed orbit feedback carry out horizontal, vertical and RF frequency feedback simultaneously, but it also has better convergence and convergence speed than the traditional Slow Orbit Feed Back (SOFB) system. What's more, the residual values of the correctors' currents variations after correction can be almost igno…
A techniques, describing electron dynamics for magnetic models closed to cyclical accelerators, is developed and applied to the analysis of electromagnetic radiation emitted by charged particles. Formulas for the angular characteristics of synchrotron emission, which take into account the electron vibrations in the lattices of accelerators and storage rings are derived. It is shown that both the degree of photon polarization, as well as the spectral and angular distributions of radiation intensity, exhibit an observable dependence on the vertical betatron oscillations.
At the Metrology Light Source (MLS), the compact electron storage ring of the Physikalisch-Technische Bundesanstalt (PTB) with a circumference of 48\,m, a specific operation mode with two stable closed orbits for stored electrons was realized by transverse resonance island buckets. One of these orbits is closing only after three turns. In combination with single-bunch operation, the new mode was applied for electron time-of-flight spectroscopy with an interval of the synchrotron radiation pulses which is three times the revolution period at the MLS of 160\,ns. The achievement is of significant…
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, …
We performed an analysis of coherence properties of the 4-th generation high-energy storage rings with emittance values of 10 pmrad. It is presently expected that a storage ring with these low emittance values will reach diffraction limit at hard X-rays. Simulations of coherence properties were performed with the XRT software and analytical approach for different photon energies from 500 eV to 50 keV. It was demonstrated that a minimum photon emittance (diffraction limit) reached at such storage rings is λ/2π. Using mode decomposition we showed that at the parameters of the storage ring consid…
In recent synchrotron radiation facilities, the use of short (picosecond) electron bunches is a powerful method for producing giant pulses of Terahertz Coherent Synchrotron Radiation (THz CSR). Here we report on the first direct observation of these pulse shapes with a few picoseconds resolution, and of their dynamics over a long time. We thus confirm in a very direct way the theories predicting an interplay between two physical processes. Below a critical bunch charge, we observe a train of identical THz pulses (a broadband Terahertz comb) stemming from the shortness of the electron bunches. …
The paper gives an overview of the particle dynamics in synchrotrons and storage rings. Both, transverse as well as the longitudinal plane are described in linear approximation. The main emphasis is to give an introduction into the basic concepts and to allow the reader to deduce the main parameters of the machine, based on some simple scaling laws.
Application of electron cooling at ion energies above a few GeV has been limited due to reduction of electron cooling efficiency with energy and difficulty in producing and accelerating a high-current high-quality electron beam. A high-current storage-ring electron cooler offers a solution to both of these problems by maintaining high cooling beam quality through naturally-occurring synchrotron radiation damping of the electron beam. However, the range of ion energies where storage-ring electron cooling can be used has been limited by low electron beam damping rates at low ion energies and hig…
Precision experiments, such as the search for electric dipole moments of charged particles using radiofrequency spin rotators in storage rings, demand for maintaining the exact spin resonance condition for several thousand seconds. Synchrotron oscillations in the stored beam modulate the spin tune of off-central particles, moving it off the perfect resonance condition set for central particles on the reference orbit. Here we report an analytic description of how synchrotron oscillations lead to non-exponential decoherence of the radiofrequency resonance driven up-down spin rotations. This non-…
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…
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…
A Monte-Carlo simulation of the equilibrium beam polarization in ultra-high energy electron (positron) storage rings
随着最近全球对建造下一代圆形电子-正电子对撞机以研究希格斯玻色子的性质以及粒子物理学中超高束能量的其他重要课题的兴趣，追求在该能量尺度上实现偏振束的可能性也很重要。因此，有必要建立模拟工具来评估这些超高光束能量下的光束偏振。本文利用多形跟踪码（PTC）（Schmidt et al.，2002年[1]。模拟是针对一个模型储存环，其参数类似于在该能量范围内提出的圆形对撞机的参数，并将其与建议（Derbenev等人，1978 [2]），在超高束能量的同步辐射存在下，存在作为束偏振基础的自旋动力学的不同状态。特别地，已经提出，在当前能量下的同步加速器振荡期间的自旋共振的所谓“相关”交叉在超高能量下演变成自旋共振的“不相关”交叉。
In order to improve the quality and stability of synchrotron light, Hefei Light Source has a major upgrade. Higher accuracy is necessary for installation and alignment of the storage ring magnets. It is not necessarily essential that the magnets are positioned exactly. In fact, the aim is to adjust neighboring magnets with a high accuracy to one another; in other words, these neighboring magnets are positioned on a smoothing curve. The paper presents an attempt to develop a reliable smoothing method based on curve fitting of least squares and iteration according to the structure characteristic…
We introduce a new application of measuring symplectic generators to characterize and control the linear betatron coupling in storage rings. From synchronized and consecutive BPM (Beam Position Monitor) turn-by-turn (TbT) readings, symplectic Lie generators describing the coupled linear dynamics are extracted. Four plane-crossing terms in the generators directly characterize the coupling between the horizontal and the vertical planes. Coupling control can be accomplished by utilizing the dependency of these plane-crossing terms on skew quadrupoles. The method has been successfully demonstrated…
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-…
In a lepton storage ring of very high energy (e.g. in the $e^+e^-$ Higgs factory) synchrotron radiation from quadrupoles constrains transverse dynamic aperture even in the absence of any magnetic nonlinearities. This was observed in tracking for LEP and the Future Circular $e^+e^-$ Collider (FCC-ee). Here we describe a new mechanism of instability created by modulation of the particle energy at the double betatron frequency by synchrotron radiation in the quadrupoles. Energy modulation varies transverse focusing strength at the same frequency and creates a parametric resonance of the betatron …
The Cornell Electron-positron Storage Ring (CESR) has been converted from a High Energy Physics electron-positron collider to operate as a dedicated synchrotron light source for the Cornell High Energy Synchrotron Source (CHESS) and to conduct accelerator physics research as a test accelerator, capable of studying topics relevant to future damping rings, colliders and light sources. Some of the specific topics that were targeted for the initial phase of operation of the storage ring in this mode, labeled CesrTA (CESR as a Test Accelerator), included 1) tuning techniques to produce low emittanc…
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…
