Betatron oscillation is a commonly known phenomenon in laser or beam-driven plasma wakefield accelerators. In the conventional model, the plasma wake provides a linear focusing force to a relativistic electron, and the electron oscillates in one transverse direction with the betatron frequency proportional to $1/\sqrt{\gamma }$, where $\gamma$ is the Lorentz factor of the electron. In this work, we extend this model to three-dimensional by considering the oscillation in two transverse and one longitudinal directions. The long-term equations, with motion in the betatron time scale averaged out, are obtained and compared with the original equations by numerical methods. In addition to the longitudinal and transverse damping due to radiation reaction which has been found before, we show phenomena including the longitudinal phase drift oscillation, betatron phase shift, and betatron polarization change based on our long-term equations. This work can be highly valuable for future plasma-based high-energy accelerators and colliders.

Achieving transparent Top-Up injection, characterized by stored beam position perturbations lower than 10% of the root mean square (rms) size of the stored beam, is very challenging for third-generation storage ring-based synchrotron light sources. The standard bump-based injection scheme used at SOLEIL 2.75-GeV storage ring for daily operation relies on two pulsed septum magnets and four pulsed dipole kickers installed in a 12-m-long straight section. Perfect tuning of the kickers to meet the perturbation tolerances is impossible since it would require at least four identical magnets, Ti-coated ceramic chambers, and electronics. On the way toward transparent injection, the four kickers can be replaced by a single pulsed magnet, benefiting from a field-free region in the stored beam path. This Multipole Injection Kicker (MIK), developed in the frame of a collaboration between SOLEIL and MAX IV, and currently installed in the MAX IV 3-GeV storage ring, has proven to meet the transparency specifications. A copy of the MIK has been installed in a short straight section of the SOLEIL storage ring in January 2021. Perturbations of less than 2% of the rms size of the stored beam were measured using the newly installed high-performance diagnostics. In this article, a start-to-end model of the MIK-based injection is presented as well as major challenges inherent in designing such an innovative magnet. Then, the results of the MIK commissioning are presented in depth along with the high-performance diagnostics, which are essential when such levels of beam stability are to be achieved.

In this article, the concept of a recently funded R&D project for the installation of a proof-of-concept cavity-based x-ray free electron laser (CBXFEL) demonstrator experiment at the European XFEL facility is presented, with the first results expected in 2024. It is composed of an x-ray cavity design in backscattering geometry with a 133 m round trip length using cryogenically cooled diamond crystals. It employs the concept of retroreflection to reduce the sensitivity to vibrations. The FEL radiation is produced in four undulator segments of 20 m total length. Simulations at 16 GeV beam energy and 250 pC bunch charge show that the expected x-ray pulses in saturation surpass state-of-the-art x-ray sources considering spectral flux and three-dimensional coherence. However, the stability of the proof of concept setup is severely challenged by the finite thermal transport in the diamond crystals. Therefore, suitable measures such as cooling the crystals to 70 K are explained in this paper and additional ones will have to be developed in the course of this project.

Next generation heavy ion therapy and research facilities require efficient accelerating structures. Particularly, at low beam energies, right after the standard scheme of the ion source, low-energy beam transfer, and radio-frequency quadrupole (RFQ), several options for accelerating structures are available including the classic drift-tube linac (DTL), the interdigital H-mode DTL (IH-DTL), and superconducting quarter-wave resonators. These structures need to integrate the beam acceleration with the focusing channel, nowadays typically provided by permanent-magnet quadrupoles (PMQs). The frequency of operation needs to be in line with that of the RFQ structure, and it has been chosen at 750 MHz for practical considerations for the Next Ion Medical Machine Study (NIMMS) that is the application focus of this manuscript. While classic DTL structures at low ion beam energies do not provide enough space for PMQs at that frequency within a single $\beta \lambda$ period, IH-DTL structures do not provide the regular focusing channel with consequences on the beam quality. For these reasons, quasi-Alvarez drift-tube linac (QA-DTL) structures are reevaluated in this manuscript as they might fill this gap. They have not received much attention in the literature so far and therefore their design is described in detail. The design procedure presented here may serve as a blueprint for DTL design in general. In addition to the overall rf design, axial field stabilization with a new technique and multiphysics studies of the rf structure are described. A cost estimation completes the NIMMS QA-DTL study.

Particle accelerators are complex facilities that produce large amounts of structured data and have clear optimization goals as well as precisely defined control requirements. As such they are naturally amenable to data-driven research methodologies. The data from sensors and monitors inside the accelerator form multivariate time series. With fast preemptive approaches being highly preferred in accelerator control and diagnostics, the application of data-driven time series forecasting methods is particularly promising. This review formulates the time series forecasting problem and summarizes existing models with applications in various scientific areas. Several current and future attempts in the field of particle accelerators are introduced. The application of time series forecasting to particle accelerators has shown encouraging results and promise for broader use, and existing problems such as data consistency and compatibility have started to be addressed.

Longitudinal rf manipulation schemes have been widely employed for achieving various beam experiments and applications in heavy ion or proton (hadron) synchrotrons. For high-intensity hadron beams, longitudinal space charge and cavity beam loading play a key role in beam intensity limitations since they may cause beam oscillations and longitudinal emittance growth. Efficient schemes to compress such intense bunched beams and minimize the emittance blow-up during those manipulations are of practical concern. In this article, the behavior of the particle distribution in the presence of space charge and beam loading during bunch merging is investigated via a generalized elliptical bunch model and particle-in-cell (PIC) simulations. Possible schemes to minimize these intensity effects are discussed. As an application, parameters for the longitudinal rf manipulation scenario in the upcoming second phase of the China Spallation Neutron Sources (CSNS-II) are proposed. It is shown that for (slow cycling) storage rings, with an optimized set of longitudinal parameters, the emittance growth due to intensity effects can be largely dampened and a high compression efficiency is achieved. For rapid cycling synchrotrons, fast bunch merging can be achieved via a desynchronization method. The agreement between the analytical elliptical model and the PIC simulation results indicates that the extended model can be employed for the study of the intensity effects during longitudinal rf manipulations in hadron synchrotrons.

In electron coolers, under certain conditions, a circular attractor (CA) can appear in either a longitudinal or a transverse phase space of cooled ion bunches. In the presence of an attractor, ions with small amplitudes of synchrotron or betatron oscillations are getting excited rather than being damped. This effect was observed at several nonrelativistic electron coolers with a direct current electron beam. Experimental studies of circular attractors at electron coolers utilizing rf-accelerated electron bunches, where this effect becomes particularly important, are lacking. We report CA studies at the low energy RHIC electron cooler (LEReC)—the first rf-based relativistic electron cooler. We derive formulas defining conditions for a CA appearance, perform dedicated experiments, and compare the measurements’ results to the theoretical predictions.

The nonlinear space-charge effects in a high intensity or high brightness accelerator can have a significant impact on the beam properties through the accelerator. These effects are included in the accelerator design via self-consistent multiparticle tracking simulations. In order to study the sensitivity of the final beam’s properties with respect to the accelerator design parameters, one has to carry out the time-consuming space-charge simulation multiple times. In this paper, we propose a differentiable self-consistent space-charge simulation model that enables the study of such sensitivity through only one simulation. This model differs from previous applications of the truncated power series algebra by connecting the beam properties directly with the accelerator design parameters in the presence of collective space-charge effects so that the local derivative of the beam properties with respect to the design parameters can be computed during the simulation. Such a model can also be used with gradient-based numerical optimizers for accelerator design optimizations including the self-consistent space-charge effects.

In recent years, intense efforts have been devoted to studying how nonlinear effects can be used to shape the transverse beam distribution by means of an adiabatic crossing of nonlinear resonances. By this approach, it is possible to split the beams in the transverse plane so that the initial single-Gaussian beam is divided into several distinct distributions. This is at the heart of the multiturn extraction process that is successfully in operation at the CERN Proton Synchrotron. Nonlinear effects can also be used to cool a beam by acting on its transverse beam distribution. In this paper, we present and discuss the special case of a beam with an annular distribution, showing how its emittance can be effectively reduced by means of properly devised manipulations based on nonlinear effects.

Relativistic positron beams are required for fundamental research in nonlinear strong field QED, plasma physics, and laboratory astrophysics. Positrons are difficult to create and manipulate due to their short lifetime, and their energy gain is limited by the accelerator size in conventional facilities. Alternative compact accelerator concepts in plasmas are becoming more and more mature for electrons, but positron generation and acceleration remain an outstanding challenge. Here, we propose a new setup where we can generate, inject, and accelerate them in a single stage during the propagation of an intense laser in a plasma channel. The positrons are created from a laser-electron collision at 90°, where the injection and guiding are made possible by an 800-nC electron beam loading which reverses the sign of the background electrostatic field. We obtain a 17-fC positron beam, with GeV-level central energy within 0.5 mm of plasma.

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.

The electromagnetic design of a transition section consisting of couplers for extracting the 180-GHz ${\mathrm{TM}}_{01}$ accelerating mode and 190-GHz ${\mathrm{HE}}_{11}$ dipole mode of a cylindrical corrugated waveguide used as a collinear wakefield accelerator is presented. Extraction of the high power accelerating mode reduces the power dissipation in the corrugated accelerating structure and allows the much weaker ${\mathrm{HE}}_{11}$ mode to be isolated and used to monitor the stability of the 10-nC electron drive bunch. The final design demonstrates wide bandwidth and high coupling efficiency of two couplers. The design was also optimized to have the surface electric and magnetic fields that do not exceed those in the corrugated waveguide. Finally, coupling between the drive electron bunch and the ${\mathrm{HE}}_{11}$ dipole mode in the corrugated waveguide is considered and the utility of the ${\mathrm{TE}}_{11}$ coupler for detecting the electron beam oscillations in the wakefield accelerator is demonstrated using a few representative examples of oscillations below and above a threshold of the beam breakup instability.

Pump-probe experiments using x-ray pulses or MeV ultrafast electrons as probes are important for studying ultrafast dynamic processes at the atomic level. Increasing demand is being focused on ultrashort x-ray pulses and electron pulses to research processes down to a few femtoseconds. Due to the limitation of the space charge force, only low charge electron bunches with critical synchronization can achieve such short pulses. A high-precision beam arrival-time monitor for the low charge is especially important. In this paper, a low $Q_l$ cavity with high sensitivity is designed to measure the arrival time of charges below 1 pC. The pickup is particularly optimized with high $R/Q$ at 4.76 GHz to provide the maximum signal, and the cold test results are in good agreement with the simulations. An IQ demodulation scheme is developed for the readout electronics. In the beam tests, the measured resolution of the beam arrival-time monitor is 33.46 fs at 0.5 pC.

The current designs of future electron-positron linear colliders incorporate large and complex damping rings to produce asymmetric beams for beamstrahlung suppression. Here, we present the design of an electron injector capable of delivering flat electron beams with phase-space partition comparable to the electron-beam parameters produced downstream of the damping ring in the proposed International Linear Collider (ILC) design. Our design does not employ a damping ring but is instead based on cross-plane phase-space manipulation techniques. The performance of the proposed configuration, its sensitivity to jitter along with its impact on spin-polarization are investigated. The proposed paradigm could be adapted to other linear collider concepts under consideration and offers a path toward significant cost and complexity reduction.

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 particular, we see that the uncontrolled longitudinal emittance blowup of single bunches observed before the recent impedance reduction campaign (2018–2021) is due to the radial mode-coupling instability. Unexpectedly, this instability is as strong as the azimuthal mode-coupling instability, which is possible in the SPS for other combinations of bunch length and intensity. We also demonstrate the significant role of rf nonlinearity and potential-well distortion in determining these instability thresholds. Finally, we discuss the effect of the recent impedance reduction campaign on beam stability in single- and double-rf configurations.

The EicC (The highly polarized Electron-ion collider in China) project proposes a scheme with different numbers of bunches in the two rings, which leads to an asymmetric beam-beam effect, also known as the gear-change effect. In order to investigate the feasibility of asymmetric collision in EicC, a self-consistent simulation program named athenagpu, which uses GPU for high-performance computing, was developed. A linearized matrix model is used to account for the dipole instability that occurs in the simulation. The simulation results in different collision modes show that asymmetric collision can lead to instability, and the beam can be stabilized by adjusting the nominal tunes. In the process of scanning the beam intensity, instability may occur as the beam intensity decreases, and this instability can be suppressed by compensating the nominal tunes. Offset collision simulations show that the decoherence time of the displaced bunch is shorter in the asymmetric collision than in the symmetric collision. The study in this paper suggests that asymmetric collision is promising for EicC when only the beam-beam effect is considered.

In linear induction accelerators, high-brightness electron beams are accelerated by voltages applied at gaps at discrete locations along the accelerator. At high currents, the beam itself induces wakefields in the accelerating gaps which can then feedback and distort the beam. The coupling of the gap-cavity modes and the beam can be characterized by frequency-dependent quantities known as the parallel and perpendicular gap impedances. Assessing the effects of instabilities resulting from these interactions requires accurate knowledge of these quantities. In this paper, we describe how a 3D finite-difference time-domain particle-in-cell code can be used to calculate both parallel and perpendicular gap impedances. We also demonstrate good agreement between full particle-in-cell simulations and results from a beam transport code making use of gap impedances to model beam centroid deflections. In practice, ferrite materials are often used in accelerating gaps to dampen cavity modes and reduce the severity of the resulting instabilities. We describe an implicit recursive convolution algorithm used to model the linear response of dispersive ferrite materials.

The study of the approach to the quantum ground state and the possibility to detect displacements of macroscopic bodies close to the quantum limit represent pressing challenges in modern physics. In the recent experiment of the JEDI Collaboration at the COSY storage ring, the coherent oscillations of a deuteron beam were detected with an amplitude of only one order of magnitude above the limit of the Heisenberg uncertainty principle of about 40 nm for the one-particle betatron motion. On the other hand, the much discussed search for the permanent electric dipole moment of the proton with an ultimate sensitivity of ${10}^{-29}\mathrm{e}\mathrm{cm}$ requires control of the position of the beam center of gravity with an accuracy of $\approx 5\mathrm{pm}$. In this paper, we develop the full quantum mechanical treatment of the coherent beam oscillations with ultrasmall amplitudes. In agreement with the Ehrenfest theorem, we find a continuity of the description of the coherent betatron motion from the large classical amplitudes down to the deep quantum region below the one-particle Heisenberg limit. We argue that quantum mechanics does not preclude control of the beam center with subpicometer accuracy.