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This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$., Comment: 35 pages, 29 figures. Accepted by Phys. Rev. Accel. Beams

High-brightness electron bunches, such as those generated and accelerated in free-electron lasers (FELs), can develop small-scale structure in the longitudinal phase space. This causes variations in the slice energy spread and current profile of the bunch which then undergo amplification, in an effect known as the microbunching instability. By imposing energy spread modulations on the bunch in the low-energy section of an accelerator, using an undulator and a modulated laser pulse in the centre of a dispersive chicane, it is possible tomanipulate the bunch longitudinal phase space. This allows for the control and study of the instability in unprecedented detail. We report measurements and analysis of such modulated electron bunches in the 2Dspectro-temporal domain at the FERMI FEL, for three different bunch compression schemes. We also perform corresponding simulations of these experiments and show that the codes are indeed able to reproduce the measurements across a wide spectral range. This detailed experimental verification of the ability of codes to capture the essential beam dynamics of the microbunching instability will benefit the design and performance of future FELs., 12 pages, 14 figures

The compact linear accelerator for research and applications (CLARA) is an ultrabright electron beam test facility being developed at STFC Daresbury Laboratory. The ultimate aim of CLARA is to test advanced free electron laser (FEL) schemes that can later be implemented on existing and future short-wavelength FELs. In addition, CLARA is a unique facility to provide a high-quality electron beam to test novel concepts and ideas in a wide range of disciplines and to function as a technology demonstrator for a future United Kingdom x-ray FEL facility. CLARA is being built in three phases; the first phase, or front end (FE), comprises an S-band rf photoinjector, a linac, and an S-bend merging with the existing versatile electron linear accelerator beam line; the second phase will complete the acceleration to full beam energy of 250 MeV and also incorporate a separate beam line for use of electrons at 250 MeV; and the third phase will include the FEL section. The CLARA FE was commissioned during 2018, and the facility was later made available for user experiments. Significant advancements have been made in developing high-level software and a simulation framework for start-to-end simulations. The high-level software has been successfully used for unmanned rf conditioning and for characterization of the electron beam. This paper describes the design of the CLARA FE, performance of technical systems, high-level software developments, preliminary results of measured beam parameters, and plans for improvements and upgrades. © 2020 authors. Published by the American Physical Society.

In a fixed-field alternating-gradient (FFAG) accelerator, eliminating pulsed magnet operation permits rapid acceleration to synchrotron energies, but with a much higher beam-pulse repetition rate. Conceived in the 1950s, FFAGs are enjoying renewed interest, fuelled by the need to rapidly accelerate unstable muons for future high-energy physics colliders. Until now a 'scaling' principle has been applied to avoid beam blow-up and loss. Removing this restriction produces a new breed of FFAG, a non-scaling variant, allowing powerful advances in machine characteristics. We report on the first non-scaling FFAG, in which orbits are compacted to within 10 mm in radius over an electron momentum range of 12-18 MeV/c. In this strictly linear-gradient FFAG, unstable beam regions are crossed, but acceleration via a novel serpentine channel is so rapid that no significant beam disruption is observed. This result has significant implications for future particle accelerators, particularly muon and high-intensity proton accelerators. © 2012 Macmillan Publishers Limited. All rights reserved.

The need for real-time monitoring of beam losses, including evaluation of their intensity and localization of their exact position, together with the possibility to overcome the limitations due to the reduced space for the diagnostics, makes exploitation of the Cherenkov effect in optical fibres, one of the most suitable candidates for beam loss monitoring. In this article, we report on the first tests of an optical fibre beam loss monitor based on large numerical aperture pure silica fibres and silicon photomultipliers. The tests were carried out at the ALICE accelerator research and development facility, Daresbury Laboratories, UK. In contrast to the results already published where the fibres are longitudinally placed with respect to the accelerator beam path and the losses are multidirectional charged particle showers, for the first time a dedicated set-up with an incident accelerator beam impinging directly on the optical fibre was used for optimizing the collection efficiency of the Cherenkov effect as a function of the incident angle by changing the fibre direction. For this purpose large core fibres were used together with the latest generation silicon detector instead of the standard photomultiplier tubes commonly used for Cherenkov beam loss monitoring. The experiments described in this contribution aim to demonstrate the suitability of the optical fibre sensor for loss monitoring, to optimize the Collection Efficiency (CE) of the Cherenkov photons inside the fibre as a function of the particle incident angle, to calibrate the sensor and calculate its sensitivity, and to understand the limits of temporal resolution of losses from different bunches in the accelerator.

The procedure for calculating the resistive wall impedance is simplified using Gaussian elimination with a sufficiently large floating point precision. This procedure generalises readily to the multilayer beam pipe wall. We apply this to investigate the effect of NEG coating on the transverse wake field coupling between electron bunches in the ILC damping ring. For a 5 GeV electron beam and 3 cm radius aluminium beam pipe, a 1 μm thick NEG coating is found to increase the impedance around 10 GHz. The wake field over a distance of 300 km around the ring is required for the study of the multi-bunch instabilities. This has to be obtained by Fourier transforming over a very wide range of frequencies. To overcome the computation problem, we developed a way of splitting up the frequencies into three overlapping ranges, and then joining the transforms together to obtain the overall wake field. The results for a few NEG coating thicknesses are presented.

We demonstrate that the normalised phase space can be used to improve the quality of the reconstructed image in phase space tomography. This study uses the Filtered Back Projection (FBP) for reconstruction. We simulate the tomographic projections of a Gaussian phase space distribution in real phase space and in normalised phase space. The reconstruction can be carried out in real phase space directly. It can also be done first in normalised phase space, and then the co-ordinates can be transformed to real phase space. Using FBP, we show that the latter procedure produces images that agree well with the original distribution even when there are only three angles. It also gives better resolution for a more complex distribution, which we simulate with a random collection of Gaussian spots.

Fringe fields in multipole magnets can have a variety of effects on the linear and nonlinear dynamics of particles moving along an accelerator beamline. An accurate model of an accelerator must include realistic models of the magnet fringe fields. Fringe fields for dipoles are well understood and can be modelled at an early stage of accelerator design in such codes as MAD8, MADX or ELEGANT. However, usually it is not until the final stages of a design project that it is possible to model fringe fields for quadrupoles or higher order multipoles. Even then, existing techniques rely on the use of a numerical field map, which will usually not be available until the magnet design is well developed. Substitutes for the full field map exist but these are typically based on expansions about the origin and rely heavily on the assumption that the beam travels more or less on axis throughout the beam line. In some types of machine (for example, a non-scaling FFAG such as EMMA) this is not a good assumption. In this paper, a method for calculating fringe fields based on analytical expressions is presented, which allows fringe field effects to be included at the start of an accelerator design project. The magnetostatic Maxwell equations are solved analytically and a solution that fits all orders of multipoles derived. Quadrupole fringe fields are considered in detail as these are the ones that give the strongest effects. Two examples of quadrupole fringe fields are presented. The first example is a magnet in the LHC inner triplet, which consists of a set of four quadrupoles providing the final focus to the beam, just before the interaction point. Quadrupoles in EMMA provide the second example. In both examples, the analytical expressions derived in this paper for quadrupole fringe fields provide a good approximation to the field maps obtained from a numerical magnet modelling code., Comment: 27 pages, 39 figures. The figures are new with respect to the previous version, Several mistakes also corrected

We describe a new technique for low-emittance tuning of electron and positron storage rings. This technique is based on calibration of the beam position monitors (BPMs) using excitation of the normal modes of the beam motion, and has benefits over conventional methods. It is relatively fast and straightforward to apply, it can be as easily applied to a large ring as to a small ring, and the tuning for low emittance becomes completely insensitive to BPM gain and alignment errors that can be difficult to determine accurately. We discuss the theory behind the technique, present some simulation results illustrating that it is highly effective and robust for low-emittance tuning, and describe the results of some initial experimental tests on the CesrTA storage ring.

Injection of fresh bunches into a storage ring can induce jitter in the stored bunches. For machines demanding beams of very low emittance and high stability, such as the damping rings of a future linear collider or the storage rings of a super flavor factory, this could be a potential performance limitation. We present an analysis, for the International Linear Collider (ILC) damping rings, of the transverse jitter induced on the extracted bunches from the jitter on the injected bunches, with the coupling between bunches mediated by the resistive-wall wakefield of the vacuum chamber. We find that it is important to include details of the local transverse focusing around the ring. We consider the impact of the finite thickness of the beam pipe wall, and of nonevaporable getter coating on the inside surface: in the parameter regime of the ILC damping rings, we find that the results are only slightly modified compared to an approximation to the resistive-wall wakefield based on a single-layer wall of infinite thickness. The results from our simulations indicate a tight specification on the jitter of the injected bunches.

The damping rings of a future linear collider will have demanding alignment and stability requirements in order to achieve the low vertical emittance necessary for high luminosity. The Accelerator Test Facility (ATF) at KEK has successfully demonstrated the vertical emittance below 5 pm that is specified for the GLC/NLC Main Damping Rings. One contribution to this accomplishment has been the use of Beam Based Alignment (BBA) techniques. The mode of operation of the ATF presents particular challenges for BBA, and we describe here how we have deduced the offsets of the BPMs with respect to the quadrupoles. We also discuss a technique that allows for direct measurements of the beam-to-quad offsets.

The consequences of beam conditioning in four example cases [VISA, a soft x-ray free-electron laser (FEL), LCLS, and a “Greenfield” FEL] are examined. It is shown that in emittance limited cases, proper conditioning reduces sensitivity to the transverse emittance and, furthermore, allows for stronger focusing in the undulator. Simulations show higher saturation power, with gain lengths reduced by a factor of 2 or more. The beam dynamics in a general conditioning system are studied, with “matching conditions” derived for achieving conditioning without growth in the effective emittance. Various conditioning lattices are considered, and expressions derived for the amount of conditioning provided in each case when the matching conditions are satisfied. These results show that there is no fundamental obstacle to producing beam conditioning, and that the problem can be reduced to one of proper lattice design. Nevertheless, beam conditioning will not be easy to implement in practice.

We present an overview of collective effects in a proposed ultrafast X-ray facility, based on a recirculating linac. The facility requires a small vertical emittance of 0.4 mm-mrad and is designed to operate with a "flat bunch" with a large emittance ratio. Emittance control from the electron source at the RF photocathode to the photon production chain of undulators, including understanding and mitigation of collective effects, is critical to successful machine operation. Key aspects of accelerator physics involved in beam break-up, coherent synchrotron radiation, resistive wall impedance and other effects have been addressed and reported here.

We derive two formulae relating the variation in closed orbit in a storage ring to variations in quadrupole strength, neglecting nonlinear and dispersive effects. These formulae correct results previously reported [1,2,3]. We compare the results of the formulae applied to the ATF with simulations using MAD, and consider their application to beam-based alignment.

LOCO is a computer code for analysis of the linear optics in a storage ring based on the closed orbit response to steering magnets. The analysis provides information on focusing errors, BPM gain and rotation errors, and local coupling. Here, we discuss the details of the LOCO implementation at the KEK-ATF Damping Ring, and report the initial results. Some of the information obtained, for example on the BPM gain and coupling errors, has not previously been determined. We discuss the possibility of using the data provided by the LOCO analysis to reduce the vertical emittance of the ATF beam.

The consequences of beam conditioning in four example cases (VISA, a Soft X-Ray FEL, LCLS and a ''Greenfield'' FEL) are examined. It is shown that in emittance limited cases, proper conditioning reduces sensitivity to the transverse emittance, and allows stronger focusing in the undulator. Simulations show higher saturation power, with gain lengths reduced up to a factor of two. The beam dynamics in a general conditioning system are studied, with ''matching conditions'' derived for achieving conditioning without growth in effective emittance. Various conditioners are considered, and expressions derived for the amount of conditioning provided in each case when the matching conditions are satisfied. We discuss the prospects for conditioners based on laser and plasma systems.

The luminosity performance of a future linear collider (LC) will depend critically on the performance of the damping rings. The design luminosities of the current LC proposals require rings with very short damping times, large acceptance, low equilibrium emittance and high beam intensity. We discuss the design strategies for lattices achieving the goals of dynamical stability, examine the challenges for alignment and coupling correction, and consider a variety of collective effects that threaten to limit beam quality. We put the design goals in context by referring to the experience of operating facilities, and outline the further research and development that is needed.

One of the major challenges facing the proposed high-energy linear e/sup +/e/sup c/olliders is the preservation of the extremely small vertical emittance from the damping rings to the interaction point (IP). This emittance must be transported through bunch compression sections, the main linac and finally through the beam delivery system to the IP. Historically, the beam dynamics issues of each subsystem have been studied quasi-independently, with the beam conditions and tolerances being specified at the boundaries. As part of the recent International Linear Collider Technical Review Committee, new simulation tools have been developed to simulate the beam transport through the integrated system, including static and dynamic errors, stabilization systems, and tuning algorithms.

For synchrotron light sources and for damping rings of linear colliders it is important to be able to minimize the vertical emittance and to correct the spurious vertical dispersion. This allows one to maximize the brightness and/or the luminosity. A commonly used tool to measure the skew error distribution is the analysis of orbit response matrices using codes like LOCO. Using the new Matlab version of LOCO and 18 newly installed power supplies for individual skew quadrupoles at the ALS the emittance ratio could be reduced below 0.1% at 1.9 GeV yielding a vertical emittance of about 5 pm. At those very low emittances, additional effects like intra beam scattering become more important, potentially limiting the minimum emittance for machine like the damping rings of linear colliders

To achieve the required damping time in the main damping rings for the Next Linear Collider (NLC), a wiggler will be required in each ring with integrated squared field strength up to 110 T^2m. There are concerns that nonlinear components of the wiggler field will damage the dynamic aperture of the ring, leading to poor injection efficiency. Severe effects from an insertion device have been observed and corrected in SPEAR 2. In this paper, we describe a model that we have developed to study the effects of the damping wiggler, compare the predictions of the model with actual experience in the case of the SPEAR 2 wiggler, and consider the predicted effects of current damping wiggler design on the NLC main damping rings.

The KEK Accelerator Test Facility (ATF) damping ring is a prototype low emittance source for the NLC/JLC linear collider. To achieve the goal normalized vertical emittance {gamma}{var_epsilon}{sub y} = 20 nm-rad, magnet placement accuracy better than 30 mm must be achieved. Accurate beam-based alignment (BBA) is required. The ATF arc optics uses a FOBO cell with two horizontally focusing quadrupoles, two sextupoles and a horizontally defocusing gradient dipole, all of which must be aligned with BBA. BBA at ATF uses the quadrupole and sextupole trim windings to find the trajectory through the center of each magnet. The results can be interpreted to assess the accuracy of the mechanical alignment and the beam position monitor offsets.

The Next Linear Collider (NLC) injector system is designed to produce low emittance 8 GeV electron and positron beams at 120 hertz for injection into the NLC main linacs. Each beam consists of a 265 ns train of bunches (190 bunches spaced by 1.4 ns or 95 bunches spaced by 2.8 ns); each bunch has a population of up to 1.6/spl times/10/sup 10/ particles for 2.8 ns (or 0.8/spl times/10/sup 10/ particles for 1.4 ns). Horizontal and vertical emittances are specified to be /spl gamma//spl epsi//sub x/=3/spl times/10/sup -6/ m-rad and /spl gamma//spl epsi//sub y/=2/spl times/10/sup -8/ m-rad; bunch length at injection is variable from 90-140 /spl mu/m. Electron polarization of greater than 80% is required. Electron and positron beams are generated in separate accelerator complexes each of which contains the source, damping ring systems, linacs, bunch length compressors, and collimation regions. Investigation into the feasibility of polarized positrons for the NLC has begun; operations at 180 Hz and the centralization of the injector complex have been studied. The need for affordable, low technical risk, reliable injector subsystems is a major consideration in the design effort. This paper presents an overview of the NLC injector systems with an emphasis on changes in the design since 1999 and discusses the planned R&D.

The ALICE tomography section at Daresbury is a diagnostic setup in the injection line of EMMA, the world's first non-scaling FFAG accelerator. We present our measurements and analysis of the transverse emittance, Twiss parameters and phase space distribution of the electron beam that is injected into EMMA. The measurements are carried out at 12 MeV, for bunch charges from 20 to 80 pC. Quadrupole scans and tomography are used. The results show that space charge effect does not change the beam emittance significantly over the length of the tomography section. Starting from projections of the beam images, the quadrupole scan technique can be applied to give the emittance and Twiss parameters. The same projections can be processed using tomography to give the phase space distribution. A careful treatment of the background noise is required to produce consistent emittances between quadrupole scans at different locations. Extending this in a natural way to tomography, we are also able to remove most of the the streaking artefacts from reconstructions obtained using the Filtered Back Projection technique.

We present a method to measure and reconstruct the full 4D transverse phase space of a particle beam. The method assumes that it is possible to freely and independently rotate the separate 2D transverse phase spaces in the horizontal and vertical directions. Using images of the beam that would be captured on a screen, we develop a mathematical procedure that will reconstruct the full 4D particle distribution. We simulate this procedure for a hypothetical distribution and show that the reconstruction agrees with the actual distribution. Finally, we demonstrate for the practical case of a two-quadrupole setup that it is indeed possible to adjust the quadrupole strengths so that the separate 2D transverse phase spaces can be rotated independently. However, in this setup, the rotation angles are restricted to smaller ranges. Even so, the reconstructed results reproduce the actual distribution clearly.

We report on impedance calculations and single-bunch and multi-bunch instabilities in the NLC damping rings. Preliminary designs of vacuum chambers and major components have addressed beam impedance issues, with the desire to increase instability current thresholds and reducing growth rates. MAFIA calculations of short-range and long-range wakefields have allowed computations of growth rates and thresholds, which are presented here. Resistive wall instability dominates long-range effects, and requires a broadband feedback system to control coupled-bunch motion. Growth rates are within the range addressable by current feedback system technologies. Single-bunch instability thresholds are safely above nominal operating current.

In low emittance synchrotron light sources the main source of beam loss is intrabeam or Touschek scattering. In most cases the Touschek scattered particles get lost on the vacuum chamber with the narrowest vertical gap. The particles reach the vertical chamber from either diffusion or coupling of the particle motion from the horizontal to the vertical plane. The beam lifetime can be very sensitive to the size of the vertical chamber that can limit the dynamic momentum aperture. The reduction in lifetime limits the minimum size of the chamber that can be installed in the ring. In this paper we examine the effect of the size of the vertical apertures on the beam lifetime at the ALS under various different machine conditions. We show that there are conditions where one can make the beam lifetime much less sensitive to the size of the vertical aperture.

Intra-beam scattering (IBS) potentially limits the minimum emittance of low-energy storage rings, and this effect strongly influences the choice of energy of damping rings for linear colliders. The Advanced Light Source (ALS) is a third-generation synchrotron light source operating with high-intensity, low-emittance beams at energies up to 2 GeV. It can operate with an emittance coupling of below 1%. We present measurements of the beam growth in three dimensions as a function of current, for normalized natural horizontal emittances of approximately 1-10 mm-mrad at energies of 0.7-1.5 GeV, values comparable to the parameters in an NLC damping ring. Using a dedicated diagnostic beamline with an X-ray scintillator imaging system, measurements of the transverse beamsize are made, simultaneously with bunch length measurements using an optical streak camera. The bunch volume growth as a function of bunch current is compared with theoretical estimates, for a parameter space of IBS, where very little experimental data exists so far.