K. Heinemann, D. P. Barber
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.
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We give an overview of our current/future analytical and numerical work on the spin polarization in high-energy electron storage rings. Our goal is to study the possibility of polarization for the CEPC and FCC-ee. Our work is based on the so-called Bloch equation for the polarization density introduced by Derbenev and Kondratenko in 1975. We also give an outline of the standard approach, the latter being based on the Derbenev-Kondratenko formulas.
I extend and update earlier work, summarised in [1], whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.
In this paper we describe our work on spin polarization in high-energy electron storage rings which we base on the Bloch equation for the polarization density and which aims towards the e-/e+ option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The Bloch equation takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov-Ternov effect with its Baier-Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternati…
We present a set of notes, meant for quick reference, on radiative spin polarization, computer algorithms and spin matching in electron storage rings.
This article provides a unified introduction to the theory of electron and proton spin polarisation in storage rings and it provides a common starting point for the written versions of the four talks that I gave at Monterey
Laser cooling of nuclear beams in storage rings is discussed. The main properties of nuclei with isomeric levels in the range E<50 keV are presented.
Methods of particle beam cooling are reviewed.
Cooling methods are discussed in reference to the electron-positron, ion and muon beams.
Limits of applicability of the Robinson's damping criterion and the problem of enhanced cooling of particle beams in storage rings beyond the criterion are discussed.
Methods of enhanced laser cooling of particle beams in storage rings and Robinson's damping criterion are discussed. The dynamics of amplitudes of betatron oscillations and instantaneous orbits of electrons interacting with laser beams being displaced in the radial direction is investigated.
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.
A method of enhanced optical cooling (EOC) based on nonlinear selective interaction between particles and theirs amplified undulator radiation wavelets (URW) in storage rings is discussed. It leads to non-exponential fast damping. The selectivity is arranged by a moving screen located on the image plane of the optical system projecting URW there.
This paper presents a conceptual approach to phase modulation of the cavity field in storage ring RF systems. An implementation of the concept on Dimtel low-level RF controllers is also presented. The method is illustrated with the test results from a cavity simulator, as well as an electron storage ring KARA.
Physics of enhanced optical cooling of particle beams in storage rings, nonlinear features of cooling and requirements to ring lattices, optical and laser systems are discussed
This report summaries the workshop on accelerator R&D for ultimate storage ring, held in Huairou, Beijing, Oct. 30 to Nov. 1, 2012.
The problem of enhanced optical cooling (EOC) of particle beams in storage rings beyond the Robinson's damping criterion is discussed.
In this paper we propose an improved empirical equation for the bunch lengthening in electron storage rings. The comparisons are made between the analytical and experimental results, and the agreements are quite well. This improved equation can be equally applied to the case where a storage ring is very resistive (such as the improved SLC damping rings) instead of inductive as usual.
Currently there is significant interest in the use of storage rings to search for an electric dipole moment (EDM) in hadrons. This requires utilizing the storage ring as a precision measuring device. Part of understanding the detailed behavior of storage rings comes from careful analysis of fringe fields, but the various tracking codes available differ in their ability to model such behavior. It is the purpose of this paper to investigate these differences.
We have demonstrated a storage ring for ultra-cold neutral atoms. Atoms with mean velocities of 1 m/s corresponding to kinetic energies of ~100 neV are confined to a 2 cm diameter ring by magnetic forces produced by two current-carrying wires. Up to 10^6 atoms are loaded at a time in the ring, and 7 revolutions are clearly observed. Additionally, we have demonstrated multiple loading of the ring and deterministic manipulation of the longitudinal velocity distribution of the atoms using applied laser pulses. Applications of this ring include large area atom interferometers and cw monochromatic …
Central frequency is a key parameter of storage rings. This paper presents the measurement of central frequency of the HLS-II storage ring using the sextupole modulation method. Firstly, the basis of central frequency measurement of the electron storage ring is briefly introduced. Then, the error sources and the optimized measurement method for the HLS-II storage ring are discussed. The workflow of the self-compiled Matlab script used in central frequency measurement is also described. In the end, the results achieved by using two methods to cross-check each other are shown. The measured value…
We studied the coupled beam motion in a storage ring between the transverse and longitudinal directions introduced by crab cavities. Analytic form of the linear decoupling transformation is derived. The equilibrium bunch distribution in an electron storage ring with a crab cavity is given, including contribution to the eigen-emittance induced by the crab cavity. Application to the short pulse generation scheme using crab cavities is considered.
We propose to optimize the nonlinear beam dynamics of existing and future storage rings with direct online optimization techniques. This approach may have crucial importance for the implementation of diffraction limited storage rings. In this paper considerations and algorithms for the online optimization approach are discussed. We have applied this approach to experimentally improve the dynamic aperture of the SPEAR3 storage ring with the robust conjugate direction search method and the particle swarm optimization method. The dynamic aperture was improved by more than 5 mm within a short peri…
A new, hybrid design is proposed to eliminate the main systematic errors in the frozen spin, storage ring measurement of the proton electric dipole moment. In this design, electric bending plates steer the particles, and magnetic focusing replaces electric. The magnetic focusing should permit simultaneous clock-wise and counter-clock-wise storage to cancel systematic errors related to the out-of-plane dipole electric field. Errors related to the quadrupole electric fields can be eliminated by successive runs of magnetic focusing with different strengths.
The lifetime of a stored beam due to the Touschek effect is calculated for arbitrary ratios of beam height to beam width. A variation of the beam envelopes is taken into account, i.e. the derivatives of the horizontal and vertical amplitude functions and dispersions are included. The calculation is done for arbitrary energies in the rest frame of the colliding particles.
The lattice of laser-electron storage ring with controlled momentum compaction factor dedicated to generation of intense X-rays under Compton scattering is described. In such storage ring one can achieve the large energy acceptance and keep the long-term stable motion of electron beam with large energy spread. The intensity of X-rays may be very stable due to using of electron beam with steady-state parameters for Compton scattering. Parameters of the storage ring, electron beam and X-rays obtained by electron beam dynamics simulation involving Compton scattering are presented.
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.
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.
Third order tracking calculations show that a wavelength shifter on the basis of a commercially available 12 T split-pair solenoid is compatible with the ANKA storage ring
Precision searches for the electric dipole moment of protons in storage ring experiments call for beam-position monitoring in the picometer range. We present the relevant fully quantum mechanical derivation of radiofrequency-driven collective oscillations of a beam in a storage ring.
First Experimental Demonstration of Beam Storage by Three-Dimensional Spiral Injection Scheme for Ultra-Compact Storage Rings
本研究首次在超紧凑存储环中通过三维螺旋注入方案实现了电子束存储，验证了该方法在高精度测量中的应用潜力。
The upgrade project of Hefei Light Source storage ring is under way. In this paper, the wake fields of new designed vacuum chambers have been simulated by CST code, and then broadband impedances were obtained by FFT. Together with resistive wall wake fields, broadband impedance model for storage ring was established. Using theoretical formula, longitudinal and transverse single bunch instabilities were discussed. With carefully-designed vacuum chamber, the threshold of beam instabilities was higher than beam current goal.
A muon storage ring neutrino source uses an induction linac for muon capture, a 200 MHz copper cavity system for cooling, and 200 and 400 MHz superconducting rf systems for acceleration to a final energy of up to 50 GeV. These systems and their requirements are discussed in this paper.
Here, and in a sequel, we invoke the invariant spin field to provide an in--depth study of spin motion at and near low order orbital resonances in a simple model for the effects of vertical betatron motion in a storage ring with Siberian Snakes. This leads to a clear understanding, within the model, of the behaviour of the beam polarisation at and near so--called snake resonances in proton storage rings.
No Abstract of this Colloquium
A method for reversing the laser modulation in a Storage ring
针对储存环激光调制会降低电子束品质且受结构限制难以实现调制解调的问题，提出无需特殊储存环结构的可逆激光调制方法，模拟显示可大幅恢复束流品质，助力高重频相干储存环光源实现。
In the trial \cite{BNL} of measuring the proton electric moment, storage rings with electrostatic lattice have been considered. Here an overview is given about the main parameters regarding such a kind of focusing. Beyond confirming all the issues regarding this subject, a non-null element $M_{31}$ is introduced in all the $3\times 3$ matrices which deal with the vector $(x,x',Δp/p)$ and its role is discussed.
Fast ion instability has been observed in the early commissioning and operation of the Shanghai Synchrotron Radiation Facility (SSRF) storage ring. In this paper, a weak-strong code is used to simulate the fast ion instability in SSRF storage ring. Various fill patterns and gas pressures are investigated. The results show that the mini-train fill patterns are very effective to suppress the growth of the fast ion instability.
A kinetic equation for the joint probability distribution for fixed values of the classical action, momentum and density has been derived. Further, the hydrodynamic equations of continuity and balance of momentum density have been transformed into a Schroedinger-like equation, describing particle motion in an effective electro-magnetic field and an expression for the gauge potentials has been obtained.
HLS (Hefei Light Source) is a second generation synchrotron radiation source. After injected into the storage ring at energy of 200MeV, the electrons will be ramped to 800MeV. During ramping, the magnetic fields of the bend, quadruple and sextuple magnets are ramped up synchronously to keep the working point of the storage ring unchanged. This process is carefully controlled by HLS control system, which is built under EPICS. Several measures are taken to insure the synchronization and linearity of the ramping.
We give the geralized expression of spin precession of extended bunch particles having both anomalous magnetic and electric dipole moments in storage ring. The transversal betatron oscillation formula of the bunch is also given. The latter is the generalization of the Farley's pitch correction \cite{Farley}, including radial oscillation as well as vertical one. Some useful formulae for muon storage ring are discussed in appendix.
Specific velocities of particles circulating in a storage ring can lead to betatron resonances at which static perturbations of the particles' orbit yield large transverse (betatron) oscillations. We have observed betatron resonances in an ultracold-atom storage ring by direct observation of betatron motion. These resonances caused a near-elimination of the longitudinal dispersion of atomic beams propagating at resonant velocities, an effect which can improve the performance of atom interferometric devices. Both the resonant velocities and the strength of the resonances were varied by delibera…
Conceptual Design of a Low-Energy Ion Beam Storage Ring and a Recoil Separator to Study Radiative Neutron Capture by Radioactive Ions
本文提出了一种低能离子存储环及回收分离器的概念设计，用于通过离子光学计算和粒子跟踪模拟研究放射性离子的辐射中子捕获反应。
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.
Storage rings have been employed over three decades in various kinds of nuclear and atomic physics experiments with highly charged ions. Storage ring operation and precision physics experiments benefit from the availability of beam cooling which is common to nearly all facilities. The basic aspects of the storage ring components and the operation of the ring in various ion-optical modes as well as the achievable beam conditions are described. Ion storage rings offer unparalleled capabilities for high precision experiments with stable and radioactive beams. The versatile techniques and methods …
Electric Dipole Moments (EDMs) of subatomic particles, are considered as one of the most powerful tools to study CP-violation beyond the Standard Model. Such CP-violating mechanisms are searched for to explain the dominance of matter over anti-matter in our universe. This paper discusses EDM searches of charged hadrons in storage rings. The document focuses on activities at the existing storage ring COSY at Forschungszentrum Jülich, Germany and the design of a 100\,m circumference prototype ring able to demonstrate key technologies and components. These include simultaneous clockwise and count…
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.
We calculate the corrections for constant radial magnetic field in muon g--2 and electric-dipole-moment experiments in storage rings. While the correction is negligible for the current generation of g--2 experiments, it affects the upcoming muon electric-dipole-moment experiment at Fermilab.
We explore the possibility of operating a SASE FEL with a Storage Ring. We use a semi-analytical model to obtain the evolution inside the undulator by taking into account the interplay on the laser dynamics due to the induced energy spread and to the radiation damping. We obtain the Renieri's limit for the stationary output power and discuss the possibility of including in our model the effect of the beam instabilities.
A multi-objective genetic algorithm is developed for optimizing nonlinearities in diffraction limited storage rings. This algorithm determines sextupole and octupole strengths for chromaticity correction that deliver optimized dynamic aperture and beam lifetime. The algorithm makes use of dominance constraints to breed desirable properties into the early generations. The momentum aperture is optimized indirectly by constraining the chromatic tune footprint and optimizing the off-energy dynamic aperture. The result is an effective and computationally efficient technique for correcting chromatic…
We propose a method to simultaneously correct linear optics errors and linear coupling for storage rings using turn-by-turn (TbT) beam position monitor (BPM) data. The independent component analysis (ICA) method is used to isolate the betatron normal modes from the measured TbT BPM data. The betatron amplitudes and phase advances of the projections of the normal modes on the horizontal and vertical planes are then extracted, which, combined with dispersion measurement, are used to fit the lattice model. The fitting results are used for lattice correction. The method has been successfully demon…
The sensitivity much better than $10^{-24} e$ cm may be expected in the searches for electric dipole moments (EDM) of $β$-active nuclei at ion storage rings. It would be a serious progress in studies of the CP-violation problem.
We improve the algorithm to noninvasively update the response matrix using information from the orbit-feedback system, described in [1]. The new version is capable of adapting to slow changes of the lattice, albeit at the expense of limiting the accuracy.
Estimated AC power consumption ranges from ~280 MW (1) to 416 MW (2) for a 350 GeV E_cm 80 km circumference colliding beam storage ring complex with parameters given in (1). The difference between the two estimates is from differing assumptions concerning heat removal, cryo-plant efficiency, klystron operation etc. The purpose of this note is to list and explain these. (1) Mike Koratzinos, et al, IPAC13 (2) Marc Ross, Higgs Quo Vadis Workshop, March 2013.
In the SSRF Phase-II beamline project, a Superconducting Wiggler (SW) will be installed in the electron storage ring. It may greatly impact on the beam dynamics due to the very high magnetic field. The emittance growth becomes a main problem, even after a well correction of the beam optics. A local achromatic lattice is studied, in order to combat the emittance growth and keep the good performance of the SSRF storage ring, as well as possible. Other effects of the SW are simulated and optimized as well, including the beta beating, the tune shift, the dynamic aperture, and the field error effec…
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…
The general theoretical description of the influence of oscillating horizontal magnetic and quasimagnetic fields on the spin evolution in storage rings is presented. Previous results are generalized to the case when both of the horizontal components of the oscillating field are nonzero and the vector of this field circumscribes an ellipse. General equations describing a behavior of all components of the polarization vector are derived and the case of an arbitrary initial polarization is considered. The derivation is fulfilled in the case when the oscillation frequency is nonresonant. The gener…
The Storage Ring at the Advanced Light Source is capable of being filled in selectable buckets. Typically, 276 consecutive buckets out of 328 possible are selected. It has been found that the amount of charge injected is not uniform bucket-to-bucket, sometimes varying by 100% or more. This variability causes problems with beam stability, and it may shorten the beam lifetime. We have devised a feedback system that allows for beam filling in an orderly manner, yielding bunch heights uniform to within 17%. At fill time, multiple bunches are injected into the Storage ring first, then, using feedba…
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 injection control system of Hefei Light Source (HLS) storage ring is a subsystem of the upgraded HLS control system, which is based upon EPICS. Three programmable logic controllers (PLCs) are used as device controllers, which control one septum modulator and four kicker modulators of HLS storage ring. An Industrial PC is used as Input/Output Controller (IOC) and it connects the PLCs with serial communication (RS232 mode) over fibre. A PC with Linux is used as operator interface (OPI), operator application are running on it. The control system was completed in July 2000. The commissioning s…
Analysis of spin dynamics in storage ring electric-dipole-moment (EDM) experiments ascertains that the use of initial vertical beam polarization allows to cancel spin-dependent systematical errors imitating the EDM effect. While the use of this polarization meets certain difficulties, it should be considered as an alternative or supplementary possibility of fulfilling the EDM experiment.
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