Synchrotron Motion Research Articles

Study on XiPAF-Upgrading Synchrotron Beam Loss

Xi’an 200MeV proton application Facility (XiPAF) is upgrading its proton synchrotron to a multi-ion synchrotron, which replaces H- stripping injection with multiturn injection scheme. New synchrotron’s vertical tune has been changed from 1.70 to 2.26, beam dynamics of new lattice is much different from the original proton lattice. Simulations has been performed with PyORBIT for beam loss study, with or without space charge effect. The main beam loss is caused by 3-order incoherent resonance νx + 2νy = 6, which is a structure resonance. Space charge and longitudinal synchrotron motion speed up the beam loss process.

Improvement of the longitudinal phase space tomography at the J-PARC synchrotrons

The longitudinal phase space tomography, which reconstructs the phase space distribution from the one-dimensional bunch profiles, is used in various accelerators to measure longitudinal beam parameters. At the J-PARC, an implementation of the phase space tomography based on the Convolution Back Projection method (CBP) has been used to measure the momentum spread of the injected beam. The method assumes that the beam distribution rotates without significant deformation during the synchrotron oscillation. Because of the nonlinearity of synchrotron motion with sinusoidal RF voltage, the method can be used only in limited situations such as small amplitude synchrotron oscillation. Algebraic Reconstruction Techniques (ART) in conjunction with particle tracking, which is implemented in the CERN’s tomography code, allows accurate reconstructions even for nonlinear large amplitude synchrotron oscillations. We present the overview of the application of the CERN’s tomography code to the J-PARC synchrotrons. The results of benchmarking are also reported.

Coherent dispersion effects in 2D and 3D high-intensity beams

Both space charge and dispersion have an effect on high-intensity beams in circular accelerators or transport sections with bending magnets and may lead to emittance growth and beam loss. In this paper, we present an investigation of the combined effect of dispersion and space charge on two-dimensional beams deepening the understanding of the 120° dispersion-induced instability. We also investigate the 90° envelope instability, which in the absence of the dispersion, mixes the confluent and parametric resonances. We show here that the presence of dispersion and high intensity breaks the overlapping and separates the two resonances. Furthermore, we study the beam dynamics of three-dimensional bunched beams and find the surprising result that the synchrotron motion can split the dispersion mode into two equally separated “sideband” modes according to the beam intensity and synchrotron frequency.

Longitudinal Tomography of Ion Bunches in the JINR Superconducting Booster Synchrotron

Methods for processing a digital signal proportional to the longitudinal intensity of ions in bunches during their acceleration in a synchrotron are discussed. Computer tomography is employed to reconstruct the longitudinal 2D ion distribution function in a bunch using data on its longitudinal profiles that depend on the bunch length and the synchrotron motion of particles. Presented are examples of tomographic reconstruction of the longitudinal distribution function of xenon ions in the JINR superconducting booster synchrotron prior to extraction (after acceleration) and on the injection plateau also with the activated electron cooling system.

Inertia modified by electromagnetic Abelian gauge transformations

This paper is about inertia modified by electromagnetic Abelian gauge transformations. We will establish an experiment proposal in order to control the gravitational acceleration constant near the surface of the planet. We will achieve this goal by establishing a change in electromagnetic gauge in a region of flat spacetime. The change in gauge will be generated by the Aharonov–Bohm effect through the use of a solenoid. The spacetime boosts outside the solenoid caused by the change in electromagnetic gauge will counteract the gravitational acceleration constant [Formula: see text] attenuating its local value as seen from the planet surface reference frames. Therefore, we will be able to establish local control of gravity on electrically charged particles like electrons in synchrotron motion outside the solenoid.

Spill ripple mitigation by bunched beam extraction with high frequency synchrotron motion

Slow extraction of bunched beams is widely used for mitigating the formation of temporal microstructures on the extracted beam due to ripples of the accelerator magnets power supplies. That helps in experiments with slow detectors or measurements with low event rates. Additionally, in ion cancer therapy machines, this technique is widely used for avoiding long gaps in the spill measured in ionization chambers which in turn would trigger interlocks. It is also well known that extraction of a bunched beam creates spill structures on time scales defined by the rf frequency which limits its usability for faster detectors. In this report, we show that further macroscopic spill structures of duration up to some hundred milliseconds can be created during bunched beam extraction for a sufficiently large synchrotron tune. The aim of this work is to study the influence of the synchrotron tune and its interplay with slow extraction settings on the slow extraction quality. Further dependencies on transverse emittance and longitudinal bunch area of the circulating beam are discussed.

Characterization and minimization of the half-integer stop band with space charge in a hadron synchrotron

In any hadron synchrotron, the half-integer resonance is among the strongest effects limiting the achievable maximum beam intensity. The heavy-ion superconducting synchrotron SIS100, currently under construction at GSI, should provide intense beams for the future FAIR experiments. Using SIS100 as an example, this paper develops a quantitative framework for characterizing the half-integer stop band for realistic, Gaussian-like distributed bunched beams. This study identifies the tune areas affected by the gradient-error-induced half-integer resonance for varying space charge strengths. A key insight of our analysis is that, for bunched beams a relatively small gradient error can result in a large half-integer stop band width. The achievable maximum bunch intensity, often referred to as space charge limit, is thus reduced significantly. This contrasts the findings in existing studies in literature based on more simplified beam distributions. The reason for discrepancy is identified in the increasing stop band width for Gaussian distributions when space charge becomes stronger, which appears on longer time scales as relevant for synchrotrons. The role of synchrotron motion in providing continuous emittance growth across the bunch is scrutinized. To minimize the half-integer stop band for a bunched beam, and hence increase the space charge limit, lattice corrections are applied: Including space charge in the optimization procedure recovers results equivalent to conventional lattice correction. Therefore, we find that conventional correction tools are well suited to increase the gradient-error-induced space charge limit of synchrotrons.

Single electron in a storage ring: a probe into the fundamental properties of synchrotron radiation and a powerful diagnostic tool

An experimental study of undulator radiation generated by a single electron was carried out at the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab. Photons were detected with a single-photon avalanche diode (SPAD) at an average rate of 20 kHz, corresponding to one detection every few hundred revolutions. Events were continuously recorded by a picosecond event timer for as long as 5 minutes at a time. The collected data were used to directly test the predictions of classical Poisson photostatistics. The study was motivated in part by a previous observation of sub-Poissonian statistics in a similar experiment with synchrotron radiation. In addition, we show that the time series of recorded events can be used to study the synchrotron motion of a single electron, yielding dynamical parameters such as the phase jitter of the radiofrequency cavity and the dependence of the synchrotron period on amplitude. Research plans for further experiments are also discussed.

Averaged invariants in storage rings with synchrotron motion

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.

Hadron beam evolution in microbunched electron cooling

The technique of microbunched electron cooling (MBEC) is a coherent cooling scheme with possible applications in high-energy hadron and electron-ion machines. In our previous work we analyzed the cooling of the hadron energy spread and transverse emittance using a one-dimensional (1D) technique that tracked the microscopic fluctuations in the hadron and electron beams. However, in order to obtain analytical expressions for our key quantities, we limited ourselves to calculating and optimizing only the initial values of the cooling rates. In this paper, we extend our approach so that it properly addresses the issue of the long-term, dynamic evolution of the hadron beam. In order to do so, it becomes necessary to consider the synchrotron motion of the hadron beam, in conjunction with the effects of diffusion and intrabeam scattering (IBS). With these modifications, our formalism allows us to develop a simple numerical tool that can effectively model the final state of hadron beam after many passages through the MBEC cooler.

Calculating the polarization lifetime from the Thomas-Bargmann-Michel-Telegdi equation

It was observed at the Relativistic Heavy Ion Collider that the polarization of the stored beam decays by 0.17 to 3% per hour. This effect could not be simulated up to now since the simulation time for an exact calculation exceeded the computer capacity. To solve this problem the action of the whole arc was considered as one element acting on the spin and not, as before, each optical element in the arc individually (called lattice independent integration). In addition to former simulations the coupling of synchrotron and betatron motions in the beam interaction regions and their action on the polarization were taken into account (called addition of longitudinal dynamics). It is shown that with these two changes the action on the polarization life time can be explained.

Computerized Tomography of Ion Bunches at the Nuclotron

Methods for processing a digital signal proportional to the longitudinal intensity of charged particles bunches during their acceleration in a synchrotron are discussed. Computerized tomography is used to reconstruct a longitudinal two-dimensional distribution function of particles in the bunch from its profiles depending on the synchrotron motion of particles. Examples of tomographic studies of ion bunches at the Nuclotron are given.

Diagnostics of polarization purity of x rays by means of Rayleigh scattering

The synchrotron radiation is commonly known to be completely linearly polarized when observed in the orbital plane of the synchrotron motion. Under actual experimental conditions, however, the degree of polarization of the synchrotron radiation may be lower than the ideal 100%. We demonstrate that even tiny impurities of polarization of the incident radiation can drastically affect the polarization of the elastically scattered light. We propose to use this effect as a precision tool for the diagnostics of the polarization purity of the synchrotron radiation. Two variants of the diagnostics method are proposed. The first one is based on the polarization measurements of the scattered radiation and relies on theoretical calculations of the transition amplitudes. The second one involves simultaneous measurements of the polarization and the cross sections of the scattered radiation and is independent of theoretical amplitudes.

New Feature of the Oscillating Synchrotron Motion Derived from the Hamiltonian Composed of Three Motions

Equations for the synchrotron motion are derived from the Hamiltonian, which was composed of coasting, betatron and synchrotron motions. The synchrotron oscillation is not only an oscillation of the revolution frequency but also an oscillation of the average radius. The synchrotron oscillation, which is both longitudinal and horizontal oscillations, can exchange energy with the betatron oscillation, which is a horizontal oscillation. The synchrotron oscillation occurs under a constant particle velocity and the s description is equivalent to the t description. Coriolis like force acting on its horizontal oscillation brings out its longitudinal oscillation.

Elaborated Modeling of Synchrotron Motion in Vlasov-Fokker-Planck Solvers

Solving the Vlasov-Fokker-Planck equation is a well-tested approach to simulate dynamics of electron bunches self-interacting with their own wake-field. Typical implementations model the dynamics of a charge density in a damped harmonic oscillator, with a small perturbation due to collective effects. This description imposes some limits to the applicability: Because after a certain simulation time coherent synchrotron motion will be damped down, effectively only the incoherent motion is described. Furthermore – even though computed – the tune spread is typically masked by the use of a charge density instead of individual particles. As a consequence, some effects are not reproduced. In this contribution, we present methods that allow to consider single-particle motion, coherent synchrotron oscillations, non-linearities of the accelerating voltage, higher orders of the momentum compaction factor, as well as modulations of the accelerating voltage. We also provide exemplary studies - based on the KIT storage ring KARA (KArlsruhe Research Accelerator) - to show the potentiality of the methods.

Electron cooling of a bunched ion beam in a storage ring

A combination of electron cooling and rf system is an effective method to compress the beam bunch length in storage rings. A simulation code based on multiparticle tracking was developed to calculate the bunched ion beam cooling process, in which the electron cooling, intrabeam scattering (IBS), ion beam space-charge field, transverse and synchrotron motion are considered. Meanwhile, bunched ion beam cooling experiments have been carried out in the main cooling storage ring (CSRm) of the Heavy Ion Research Facility in Lanzhou, to investigate the minimum bunch length obtained by the cooling method, and study the dependence of the minimum bunch length on beam and machine parameters. The experiments show comparable results to those from simulation. Based on these simulations and experiments, we established an analytical model to describe the limitation of the bunch length of the cooled ion beam. It is observed that the IBS effect is dominant for low intensity beams, and the space-charge effect is much more important for high intensity beams. Moreover, the particles will not be bunched for much higher intensity beam. The experimental results in CSRm show a good agreement with the analytical model in the IBS dominated regime. The simulation work offers us comparable results to those from the analytical model both in IBS dominated and space-charge dominated regimes.

Single-particle dynamics in a nonlinear accelerator lattice: attaining a large tune spread with octupoles in IOTA

Fermilab is constructing the Integrable Optics Test Accelerator (IOTA) as the centerpiece of the Accelerator R&D Program towards high-intensity circular machines. One of the factors limiting the beam intensity in present circular accelerators is collective instabilities, which can be suppressed by a spread of betatron frequencies (tunes) through the Landau damping mechanism or by an external damper, if the instability is slow enough. The spread is usually created by octupole magnets, which introduce the tune dependence on the amplitude and, in some cases, by a chromatic spread (tune dependence on particle's momentum). The introduction of octupoles usually has both beneficial (improved Landau damping) and harmful properties, such as a resonant behavior and a reduction of the dynamic aperture. One of the research goals at the IOTA ring is to achieve a large betatron tune spread, while retaining a large dynamic aperture, using conventional octupole magnets in a special but realistic accelerator configuration. The configuration, although not integrable by design, approximates an autonomous 2D Hamiltonian system. In this paper, we present results of computer simulations of an electron beam in the IOTA by particle tracking and the Frequency Map Analysis. The results show that the ring's octupole magnets can be configured to provide a betatron tune shift of 0.08 (for particles at large amplitudes) with the dynamical aperture of over 20 beam sigma for a 150-MeV electron beam. The influence of the synchrotron motion, lattice errors, and magnet imperfections is insignificant for the parameters and levels of tolerances set by the design of the ring. The described octupole insert could be beneficial for enhancing Landau damping in high intensity machines.

Synchrobetatron resonant coupling mechanism in a storage ring

A clear synchrobetatron resonant coupling of Mg ion beam was observed experimentally in the horizontal laser beam cooling experiment in small laser equipped storage ring. Synchrotron and horizontal betatron motions were intentionally coupled in a rf cavity. Using the Hamiltonian which is composed of coasting, synchrotron and betatron motions, physical mechanism of the coupling is analyzed to explain the observed horizontal betatron tune jump near the synchrobetatron resonant coupling point. There energy exchange between the synchrotron oscillation and the horizontal betatron oscillation was mediated by coasting particles and the freedom of the horizontal direction is connected with the freedom of the longitudinal direction.

Study on application of independent component analysis in the CSNS/RCS

The China Spallation Neutron Source (CSNS) accelerators consist of a low energy H− linac and a high energy proton Rapid Cycling Synchrotron (RCS). The proton beam is accumulated in the RCS and accelerated from 80 MeV to 1.6 GeV with a repetition of 25 Hz. Independent component analysis (ICA) is a robust method for processing the collected data (samples) recorded by the turn-by-turn beam position monitor (BPM), which was recently applied to the accelerator. The samples are decomposed to source signals, or the so-called independent components, which correspond to the inherent motion of samples, such as betatron motion and synchrotron motion. A study on the application of the ICA method to CSNS/RCS has been made. It shows that the beta function, phase advance, and dispersion can be well reconstructed by using ICA in CSNS/RCS. The effects of BPM errors on the ICA results are also studied. By comparing the different solving methods in ICA, the so-called SOBI has more advantages for isolating the independent components on the application of ICA to CSNS/RCS. Beam emittance dilution in the process of exciting the turn-by-turn samples is considered, and thus an RF kicker is adopted to avoid such emittance growth.

Synchrotron oscillation effects on an rf-solenoid spin resonance

New measurements are reported for the time dependence of the vertical polarization of a 0.97 GeV/c deuteron beam circulating in a storage ring and perturbed by an rf solenoid. The storage ring is the cooler synchrotron (COSY) located at the Forschungszentrum Jülich. The beam polarization was measured continuously using a 1.5 cm thick carbon target located at the edge of the circulating deuteron beam and the scintillators of the EDDA detector. An rf solenoid mounted on the ring was used to generate fields at and near the frequency of the 1−Gγ spin resonance. Measurements were made of the vertical beam polarization as a function of time with the operation of the rf solenoid in either fixed or continuously variable frequency mode. Using rf-solenoid strengths as large as 2.66×10−5 revolutions/turn, slow oscillations (∼1 Hz) were observed in the vertical beam polarization. When the circulating beam was continuously electron cooled, these oscillations completely reversed the polarization and showed no sign of diminishing in amplitude. But for the uncooled beam, the oscillation amplitude was damped to nearly zero within a few seconds. A simple spin-tracking model without the details of the COSY ring lattice was successful in reproducing these oscillations and demonstrating the sensitivity of the damping to the magnitude of the synchrotron motion of the beam particles. The model demonstrates that the characteristic features of measurements made in the presence of large synchrotron oscillations are distinct from the features of such measurements when made off resonance. These data were collected in preparation for a study of the spin coherence time, a beam property that needs to become long to enable a search for an electric dipole moment using a storage ring.15 MoreReceived 14 September 2012DOI:https://doi.org/10.1103/PhysRevSTAB.15.124202This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society