E. G. Bessonov, R. M. Feshchenko, V. I. Shvedunov
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.
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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…
Spin dependencies of the intensity and polarization of the synchrotron radiation of the longitudinally polarized particle performing uniform circular motion in the magnetic field are investigated.
Investigation of neutrino oscillations and rare meson decays are main physics goals of Project X. The successful physics outcome relies on the feasibility of high-intensity neutrino and meson (K+ and μ) beams. In order to meet this goal we propose accelerator system dominated by the synchrotrons (Option A) as a technologically easier and significantly more cost-effective alternative to the accelerator system dominated by the linear accelerators (Option B). The synchrotron-based accelerator system and its main components are outlined and the expected proton beam power for the neutrino and meson…
The measurement of the longitudinal behavior of the accelerated particle beams at Fermilab is crucial to the optimization and control of the beam and the maximizing of the integrated luminosity for the particle physics experiments. Longitudinal measurements in the Tevatron and Main Injector synchrotrons are based on the analysis of signals from resistive wall current monitors. This article describes the signal processing performed by a 2 GHz-bandwidth oscilloscope together with a computer running a LabVIEW program which calculates the longitudinal beam parameters.
The low-level RF system (LLRF) generates the drive sent to the high-power equipment. In synchrotrons, it uses signals from beam pick-ups (radial and longitudinal) to minimize the beam losses and provide a beam with reproducible parameters (intensity, bunch length, average momentum and momentum spread) for either the next accelerator or the physicists. This presentation is the first of three: it considers synchrotrons in the lowintensity regime where the voltage in the RF cavity is not influenced by the beam. As the author is in charge of the LHC LLRF and currently commissioning it, much materi…
Longitudinal oscillations of bunched beams in synchrotrons have been analyzed by accelerator physicists for decades, and a closed theory is well-known [1]. The first modes of oscillation are the coherent dipole mode, quadrupole mode, and sextupole mode. Of course, these modes of oscillation are included in the general theory, but for developing RF control systems, it is useful to work with simplified models. Therefore, several specific models are analyzed in the paper at hand. They are useful for the design of closed-loop control systems in order to reach an optimum performance with respect to…
A longitudinal beam properties, data acquisition system has been commissioned to operate in the Fermilab booster ring. This system captures real time information including beam synchronous phase, bunch length, and coupled bunch instability amplitudes as the beam is accelerated from 400 MeV to 8 GeV in 33 ms. The system uses an off-the-shelf Tektronix oscilloscope running Labview software and a synchronous pulse generator. This paper describes the hardware configuration and the software configuration used to optimize the data processing rate.
In DAΦNE, the Frascati e+/e- collider, the crab waist collision scheme has been successfully implemented in 2008 and 2009. During the collision operations for Siddharta experiment, an unusual synchrotron damping effect has been observed. Indeed, with the longitudinal feedback switched off, the positron beam becomes unstable with beam currents in the order of 200-300 mA. The longitudinal instability is damped by bringing the positron beam in collision with a high current electron beam (~2A). Besides, we have observed a shift of \approx 600Hz in the residual synchrotron sidebands. Precise measur…
With respect to a "hot", non-crystallized beam the synchrotron radiation of a cold crystallized beam is considerably modified. We predict suppression of synchrotron radiation emitted by a crystallized beam in a storage ring. We also propose experiments to detect this effect.
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…
In present work we investigate the potential of a longitudinally focusing device to compress bunches passing an undulator for a synchrotron storage ring. If integrated into a storage ring similar to PETRAIII such device could potentially produce continuous $\sim$1ps pulses of photons in the $nm$ range with peak pulse powers of tens of GW. Even without operating in FEL saturation mode the longitudinal focusing can provide means to increase the brightness and shorten the photon pulse length.
We study the modifications of synchrotron radiation of charges in a storage ring as they are cooled. The pair correlation lengths between the charges are manifest in the synchrotron radiation and coherence effects exist for wavelengths longer than the coherence lengths between the charges. Therefore the synchrotron radiation can be used as a diagnostic tool to determine the state (gas, liquid, crystal) of the charged plasma in the storage ring. We show also that the total power of the synchrotron radiation is enormously reduced for crystallized beams. This opens the possibility of accelerating…
In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation modes, which belong to either the same or adjacent azimuthal modes, respectively. We show that both instability mechanisms exist in the SPS by applying the Oide-Yokoya approach to compute van Kampen modes for the realistic longitudinal impedance model of the SPS. The results agree with macroparticle simulations and are consistent with beam measurements. In pa…
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…
I describe a new scheme for selectively isolating high density low longitudinal emittance beam particles in a storage ring from the rest of the beam without emittance dilution. I discuss the general principle of the method, called longitudinal momentum mining, beam dynamics simulations and results of beam experiments. Multi-particle beam dynamics simulations applied to the Fermilab 8 GeV Recycler (a storage ring) convincingly validate the concepts and feasibility of the method, which I have demonstrated with beam experiments in the Recycler. The method presented here is the first of its kind.
Using Longitudinal Strong Focusing Principle to Lower Particle Beam Energy Spread Locally in a Storage Ring
本文提出利用纵向强聚焦原理在存储环中局部降低粒子束能量展宽，并通过可逆Echo SSMB在高功率EUV辐射生成中的应用示例展示了该方法的核心思想和主要贡献。
In this Letter, I report on a novel scheme for beam stacking without any beam emittance dilution using a barrier rf system in synchrotrons. The general principle of the scheme called longitudinal phase-space coating, validation of the concept via multi-particle beam dynamics simulations applied to the Fermilab Recycler, and its experimental demonstration are presented. In addition, it has been shown and illustrated that the rf gymnastics involved in this scheme can be used in measuring the incoherent synchrotron tune spectrum of the beam in barrier buckets and in producing a clean hollow beam …
The longitudinal dynamics of electron bunches with a large energy spread circulating in the storage rings with a small momentum compaction factor is considered. Also the structure of the longitudinal phase space is considered as well as its modification due to changes in the ring parameters. The response of an equilibrium area upon changes of the nonlinear momentum compaction factor is presented.
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.
Barrier rf buckets have brought about new challenges in longitudinal beam dynamics of charged particle beams in synchrotrons and at the same time led to many new remarkable prospects in beam handling. In this paper, I describe a novel beam stacking scheme for synchrotrons using barrier buckets without any emittance dilution to the beam. First I discuss the general principle of the method, called longitudinal phase-space coating. Multi-particle beam dynamics simulations of the scheme applied to the Recycler, convincingly validates the concepts and feasibility of the method. Then I demonstrate t…
Coherent synchrotron radiation instability in low-emittance electron storage rings
本文以Elettra 2.0和SuperKEKB低能环为例，系统研究低发射度电子储存环中由相干同步辐射等高频阻抗驱动的微波不稳定性，并分析其与宽带阻抗的相互作用。
The RF systems installed in synchrotrons can be used to change the longitudinal beam characteristics. 'RF gymnastics' designates manipulations of the RF parameters aimed at providing such non-trivial changes. Some keep the number of bunches constant while changing bunch length, energy spread, emittance, or distance between bunches. Others are used to change the number of bunches. After recalling the basics of longitudinal beam dynamics in a hadron synchrotron, this paper deals with the most commonly used gymnastics. Their principle is described as well as their performance and limitations.
The synchrotron motion simulator is invented to simulate the longitudinal motion for particles under RF (Radio Frequency) voltage field in a ring accelerator. It is especially used to study the efficiency of adiabatic capture for a booster ring. The purpose of adiabatic capture is to optimize RF voltage settings during the ramping of beam energy and obtain the greatest efficiency of particle capture. In this paper we study the longitudinal (synchrotron) motion for particles in the TLS (Taiwan Light Source) booster. We compare the properties of TLS booster as a proton or electron accelerator, u…
Generalized threshold of longitudinal multi-bunch instability in synchrotrons
针对纵向耦合束团不稳定性与单束团朗道阻尼损失，提出数值求解稳定性问题的新方法并推导解析阈值，发现LLD会降低CBI阈值，解释了CERN SPS观测结果并适用于未来加速器设计。
Using calculations and mathematical modeling, we demonstrate the feasibility of constructing a synchrotron storage ring for neutral polar molecules. The lattice is a racetrack type 3.6 m in circumference consisting of two of 180-degree arcs, six bunchers, and two long straight sections. Each straight section contains two triplet focusing lenses and space for beam injection and experiments. The design also includes a matched injector and a linear decelerator. Up to 60 bunches can be loaded and simultaneously stored in the ring. The molecules are injected at 90 m/s but the velocity of the circul…
A pulsed electron lens produces a betatron tune shift along a hadron bunch as a function of the longitudinal coordinates, which is a longitudinal detuning. An example of transverse detuning are the tune shifts due to octupole magnets. This paper considers a pulsed electron lens as a measure to mitigate the head-tail instabilities. Using a detailed analytical description within a Vlasov formalism, the coherent properties of the longitudinal and transverse detuning are presented. The analytical predictions are compared with the results of the particle tracking simulations. A pulsed electron lens…
Recently a mechanism of storage ring operation based on the steady-state microbunching has been proposed and investigated, which contains a laser cavity modulator providing the longitudinal focusing for the circulating microbunches. In this paper we analyze the impact of the coherent undulator radiation on the longitudinal single-bunch multi-turn collective dynamics, exploring a new possible instability mechanism. We formulate the multi-turn equations of motion for the single microbunch as two sets of difference equations in the modulator and in the remaining storage ring. The dispersion equat…
Advanced storage ring lattice options based on hybrid six-bend achromat for Stanford Synchrotron Radiation Lightsource upgrade
本文为 SSRL 升级提出三种基于 H6BA 单元、适配 SPEAR3、SLAC 绿地及 PEP-II 场址的储存环晶格，通过透明匹配与数值优化实现超低发射度、优良非线性动力学、离轴注入及相当或更优束流寿命。
Longitudinal Localized Kick Driven Fast Extraction Method and Rapid Cycling Synchrotron Design for 3D PBS Proton FLASH Delivery
本文提出了一种用于三维铅笔束扫描质子FLASH输送的快速循环同步加速器设计，采用纵向局部激励驱动快速提取系统，通过动态调整激励区域提高提取精度和效率，确保在较短时间内完成扫描任务。
Time-Correlated Single-Photon Counting for versatile longitudinal diagnostics at the MAX IV Laboratory storage rings
MAX IV实验室利用时间相关单光子计数技术提升存储环中电子束团纵向诊断能力，增强同步辐射光源的运行效率。
We investigate the effects of a localized constant wake and a localized linear wake on the longitudinal beam distribution in equilibrium. We also examine the effects of the composite wake on the particle distribution when the constant wake and linear wake simultaneously exist in the ring. While moving around the parameter space, the system can show bifurcation phenomena and transition features between periodic states. We study the dynamical states in a beam, using the multi-particle tracking method in a Gaussian approximation. They show good qualitative agreement.
Turkish Accelerator Center) project is aimed to build an accelerator center in Turkey. The first step of the project is to construct IR-FEL facility. The second stage is to build a synchrotron radiation facility named TURKAY, which is the third generation synchrotron radiation light source that aimed to achieve high brilliance photon beam from low emittance electron beam at 3 GeV. The electron beam parameters highly depend on the magnetic lattice of the storage ring. In this paper a low emittance storage ring for TURKAY is proposed and beam dynamic properties of the magnetic lattice are invest…
In the fourth-generation storage ring light sources (4GLSs), associated with the extremely strong nonlinearities inherent in the multi-bend achromat design, the dynamic acceptance is usually small and it is difficult to implement traditional off-axis local-bump injection. To release the requirement on dynamic acceptance, on-axis longitudinal injection schemes have been explored. In this paper, we present a multi-objective optimization of longitudinal injection with a multi-frequency RF system, based on the parameters of the Southern Advanced Photon Source, a 4GLS proposed in China. We show tha…
Electron storage rings used for the production of synchrotron radiation (SR) have an output photon brightness that is limited by the equilibrium beam emittance. By using interleaved injection and ejection of bunches from a source with repetition rate greater than 1 kHz, we show that it is practicable to overcome this limit in rings of energy ~1 GeV. Sufficiently short kicker pulse lengths enable effective currents of many milliamperes, which can deliver a significant flux of diffraction-limited soft X-ray photons. Thus, either existing SR facilities may be adapted for non-equilibrium operation…
In DAFNE, the Frascati $e^+e^-$ collider operating since 1998, an innovative collision scheme, the crab waist, has been successfully implemented during the years 2008-09. During operations for the Siddharta experiment an unusual synchrotron oscillation damping effect induced by beam-beam collisions has been observed. Indeed, when the longitudinal feedback is off, the positron beam becomes unstable with currents above 200-300 mA due to coupled bunch instability. The longitudinal instability is damped by colliding the positron beam with a high current electron beam (of the order of 2 A). A shift…
In the Brazilian synchrotron light source, we observed that modulating the phase of the accelerating fields at approximately twice the synchrotron frequency suppressed remarkably well a longitudinal coupled-bunch mode of the beam driven by a higher order mode (HOM) in one of the radiofrequency (RF) cavities. In this work, we present the results of a set of systematic measurements, in single and multibunch mode, aimed at characterizing the effects of RF phase modulation on the beam. We compare those experiments with the results of tracking simulations and of a theoretical model in which Landau …
Equilibrium of longitudinal bunch distributions in storage rings with arbitrary impedance sources and generic filling patterns
提出一种计算储存环中任意填充模式与阻抗源下稳态束流感应电压的自洽半解析方法，经SIRIUS参数验证，并用于评估宽带阻抗影响及被动高次谐波腔对Touschek寿命的改善。
The course gives a summary of longitudinal beam dynamics for both linear and circular accelerators. After discussing different types of acceleration methods and synchronism conditions, it focuses on the particle motion in synchrotrons.
Various effects of intense synchrotron radiation on the performance of particle accelerators, especially for storage rings, are discussed. Following a brief introduction to synchrotron radiation, the basic concepts of heat load, gas load, electron emission, and the countermeasures against these effects are discussed.
Optimization of the injection beam line at the Cooler Synchrotron COSY using Bayesian Optimization
本研究将贝叶斯优化应用于COSY储存环注入束流线，通过有限观测调节15个四极磁铁和28个校正磁铁，提升了环内束流强度，且效果优于手动优化。
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…
Reinforcement Learning applied to Optimization of LHC beams in the CERN Proton Synchrotron
本研究将卷积神经网络与Soft-Actor-Critic强化学习智能体结合，实现CERN PS纵向三重分裂的自动化优化，其2025年部署的自主控制器为CERN注入器复合体首批强化学习束流质量优化系统之一。
To understand and control the dynamics in the longitudinal phase space, time-resolved measurements of different bunch parameters are required. For a reconstruction of this phase space, the detector systems have to be synchronized. This reconstruction can be used e.g. for studies of the micro-bunching instability. It occurs if the interaction of the bunch with its own radiation leads to the formation of sub-structures on the longitudinal bunch profile. These sub-structures can grow rapidly -- leading to a sawtooth-like behaviour of the bunch. At KARA, we use a fast-gated intensified camera for …
The self-interaction of short electron bunches with their own radiation field can have a significant impact on the longitudinal beam dynamics in a storage ring. While higher bunch currents increase the power of the emitted CSR which can be provided to dedicated experiments, it simultaneously amplifies the strength of the self-interaction. Eventually, this leads to the formation of dynamically changing micro-structures within the bunch and thus fluctuating CSR emission, a phenomenon that is generally known as micro-bunching or micro-wave instability. The underlying longitudinal dynamics can be …
A novel polarimeter based on the asymmetry in the spacial distribution of synchrotron radiation will make for a fine addition to the existing Møller and Compton polarimeters. The spin light polarimeter consists of a set of wiggler magnet along the beam that generate synchrotron radiation. The spacial distribution of synchrotron radiation will be measured by ionization chambers. The up-down (below and above the wiggle) spacial asymmetry in the transverse plain is used to quantify the polarization of the beam. As a part of the design process, effects of a realistic wiggler magnetic field and an …
The development of fast detection methods for comprehensive monitoring of electron bunches is a prerequisite to gain comprehensive control over the synchrontron emission in storage rings with their MHz repetition rate. Here, we present a proof-of-principle experiment with at detailed description of our implementation to detect the longitudinal electron bunch profiles via single-shot, near-field electro-optical sampling at the Karlsruhe Research Accelerator (KARA). Our experiment is equipped with an ultra-fast line array camera providing a high-throughput MHz data stream. We characterize statis…
Theoretical models for longitudinal coupled-bunch instabilities driven by harmonic cavities in electron storage rings
本文提出统一理论框架分析双射频系统纵向耦合束团不稳定性，推导Lebedev方程，首次实现mode-1阈值与实验数据极好吻合，揭示PTBL不稳定性抗Landau阻尼机制，并在pycolleff中实现。
This paper gives an introduction of longitudinal beam dynamics for circular accelerators. After briefly discussing some types of circular accelerators, it focuses on particle motion in synchrotrons. It summarizes the equations of motion, discusses phase-space matching during beam transfer, and introduces the Hamiltonian of longitudinal motion.
The first attainment of longitudinal spin polarisation in a high energy electron (positron) storage ring is described.
The J-PARC Main Ring (MR) has achieved the delivery of the 30 GeV proton beam with the beam power of 500 kW to the neutrino experiment in May 2018. The longitudinal coupled-bunch instabilities have been observed in the MR for the beam power beyond 470 kW. Since more significant coupled-bunch oscillation was observed in higher beam power, the mitigation of the coupled-bunch instabilities is necessary for the stable beam delivery with the beam power beyond 500 kW. A new feedback system was developed to suppress the coupled-bunch instabilities. The feedback system consists of a wall current monit…
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…
We show how, beginning with the Fokker--Planck equation for electrons emitting synchrotron radiation in a storage ring, the corresponding equation for spin motion can be constructed. This is an equation of the Bloch type for the polarisation density.
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…
The dipole mode synchrotron frequency is a basic beam parameter; it and a few similarly basic quantities measured at small time intervals serve to characterize the longitudinal beam dynamics throughout the acceleration cycle. The effective accelerating voltage, in conjunction with the amount of rf voltage required for the acceleration, is important for the estimate of the beam energy loss per turn. The dipole mode frequency can be used to obtain the effective accelerating rf voltage, providing that it can be measured precisely. The synchrotron frequency measured from the synchrotron phase dete…
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.
ANKA is a 2.5 GeV synchrotron radiation storage ring under construction at the Forschungszentrum Karlsruhe in Germany. The injector system will consist of a pre-injector with an end energy of 20 to 50 MeV and a 0.5 GeV booster synchrotron. In the following three different concepts for designing the booster synchrotron are compared.
Injection performance of storage ring is one of the important factors for the light efficiency and quality of Synchrotron Radiation Facility when it is in top-up mode. To evaluate the injection performance of storage ring at SSRF, we build a bunch-by-bunch position measuring system based on oscilloscope IOC. Accurate assessment of energy mismatching, distribution of residual oscillation and angle error of injection kickers can be achieved by this system.
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