In the formulation of synchrotron radiation (SR), the Wigner function represents the photon flux density in the four-dimensional phase space, and thus defines the brilliance and coherence. Although we have to rely on a numerical method to evaluate the Wigner function for a realistic electron beam, a convolution approach is available under the assumption that each electron travels along a straight line apart from a sinusoidal motion driven by an undulator magnetic field. As a result, the computation of Wigner functions for typical SR sources is usually completed within an acceptable time. It should be noted, however, that the above assumption is violated in a multiple-beam-waist (MBW) configuration, in which the lattice function is designed to have more than one beam waist position where the vertical betatron function is optimized to accommodate a narrow-gap undulator. In such a case, we have to carry out a Monte Carlo simulation, which requires a huge amount of time to get a reliable result. To overcome this difficulty, we introduce a theoretical-numerical method aimed at reducing the cost of computing Wigner functions in the MBW configuration. We show that the computation time can be saved by 2–4 orders of magnitude by means of the proposed method.

Understanding and mitigating high-order nonlinearities is essential for ensuring long-term beam storage in high-energy colliders. The stability of particles at the Large Hadron Collider (LHC) is indeed strongly influenced by nonlinear effects, particularly at injection energy where the beam occupies a large fraction of the vacuum chamber. Among these effects, third-order chromaticity, primarily driven by decapolar fields, limits dynamic aperture and beam lifetime. Despite corrections based on magnetic measurements and model predictions, a discrepancy remains between the measured and expected third-order chromaticity, indicating the presence of residual decapolar components. In this study, the decapolar fields in the LHC at injection energy are investigated and their impact on beam dynamics assessed. Chromatic amplitude detuning and decapolar resonance driving terms are directly measured for the first time, using forced oscillations driven by an ac dipole. These measurements provide new insights into the source and impact of decapolar fields in the LHC and indicate that refined correction strategies could enhance beam lifetime, particularly for high-brightness operation in future runs.

In the SuperKEKB accelerator, higher-order-mode (HOM) power absorbed by the HOM dampers of the superconducting (SC) cavities limits the attainment of the design electron beam current of the High Energy Ring. As regards cylindrical ferrite dampers installed in the SC cavities, we observed that their effective loss factors considerably depended on the bunch fill pattern. To investigate this behavior in detail, wakefield simulations were conducted. HOM power is generally evaluated from the numerically calculated coupling impedance, which provides only the total beam power loss within the structure. However, when multiple absorbers are present, the absorbed power of each absorber remains unknown. To address this limitation, we introduce calculation methods that utilize the local electromagnetic fields to evaluate the absorbed power. In this study, the theoretical basis of the methods is presented and applied to the SuperKEKB SC cavity.

We demonstrate the first realization of electron beam and x-ray pulse shaping with a corrugated wakefield structure at a pulsed-mode megahertz-repetition-rate hard x-ray free-electron laser (XFEL). This is achieved by an L-shaped corrugated structure with low-beta optics and a collimator. Variable streaking direction and signature of quadrupole wakefield compensation are observed by controlling the position of the electron beam relative to the corrugated plates. Spectral analysis at 7 keV indicates a reduction of the reconstructed x-ray pulse duration by an approximate factor of 4 compared to the standard self-amplified spontaneous emission mode of the European x-ray free-electron laser. X-ray pulses with uniform properties along a train of 100 pulses at a 1.125 MHz repetition rate are generated under 10 Hz pulse mode. These results are a step toward tailoring the temporal and spectral domain of x-ray pulses at megahertz repetition rates with high flexibility and compatibility.

The Linac Coherent Light Source II (LCLS-II) is designed to generate 4 GeV electron bunches at an up-to-1-MHz-high repetition rate to drive x-ray free electron lasers. It has been in user operation since 2023 and has progressively ramped up the beam repetition rate to 93 kHz to date. The LCLS-II 1-MeV electron source was successfully commissioned between 2018 and 2020. The full-scale LCLS-II injector, operating above 75 MeV, began commissioning in 2022 and transitioned to operations a few months later. The LCLS-II injector has demonstrated the ability to deliver a high-brightness, low-emittance electron beam at high repetition rates, meeting key performance targets. However, several operational challenges have emerged during commissioning and early user operations. These include substantial gun dark current, the dependence of bunch charge generation and free-electron laser pulse intensity on the beam repetition rate, the formation of cathode quantum efficiency craters and bumps, significant emittance growth through the laser heater chicane, beam breakup, and the presence of beam halos. This paper presents recent progress in addressing these challenges, along with injector emittance measurements and optimizations, and the first demonstration of operating a laser heater undulator at the third-harmonic resonance.

Electron coolers with high-density electron bunches obtained via rf acceleration provide a feasible path for extending electron cooling to high energies. In such coolers, the dispersive redistribution of cooling rates between the longitudinal and transverse directions is crucial and must be rigorously calculated. This paper presents exact formulas for cooling redistribution in high-energy electron coolers. The most general formulas are derived in terms of Carlson elliptic integrals, which are further reduced to elementary functions for a key special case. These formulas enable an efficient and accurate calculation of cooling rates and were instrumental in designing the electron coolers for the Electron-Ion Collider (EIC) by enabling rapid parameter identification and optimization. Consequently, these results offer a valuable tool for the design and development of future high-energy electron coolers.

The maximum secondary electron yield, ${\delta }_{\max }$, is a key parameter governing electron cloud buildup in high-intensity proton accelerators, yet its direct in situ determination under operational conditions remains challenging. This paper presents a novel method to estimate ${\delta }_{\max }$ in the Large Hadron Collider (LHC) using electron cloud measurements performed in the Vacuum Pilot Sector. The approach exploits the characteristic evolution of electron cloud intensity during beam injection, in particular the transition from an initial build-up regime to a linear scaling of electron flux with the number of injected bunches. Electron cloud currents measured with dedicated electron pickups are compared with PyECLOUD simulations performed for varying ${\delta }_{\max }$ values. The threshold number of injected bunches required to reach the linear regime provides a robust observable from which ${\delta }_{\max }$ can be extracted with limited sensitivity to other surface-emission parameters. The method is applied to multiple LHC fills and surface materials. For conditioned copper liners, ${\delta }_{\max }$ values between approximately 1.16 and 1.30 are obtained, in agreement with independent analyses and literature values. Applying the technique over extended operation periods enables the reconstruction of surface conditioning curves as a function of cumulative electron dose. These curves show a rapid initial decrease in ${\delta }_{\max }$ before approaching an apparent plateau, which may lie below the detection limit of the method depending on the beam pipe material and location. The method is compatible with routine LHC operation and enables systematic monitoring of vacuum-surface conditioning.

Superconducting magnets enable energy-frontier accelerators by generating strong magnetic fields to steer and focus the particles. Although high-temperature superconductors such as ${\text{REBa}}_2{\text{Cu}}_3{\mathrm{O}}_x$ (rebco, RE = rare earth) hold a strong potential for generating a higher magnetic field than Nb-Ti and ${\text{Nb}}_3\text{Sn}$, the associated magnet and conductor technology for accelerator applications is still in its infancy. The U.S. Magnet Development Program is developing rebco magnet technology in collaboration with industry. Here we report an experiment of making a dipole magnet called C3 using commercial high-temperature superconducting corc wires. The magnet, following a canted $\cos \theta$ design, generated a dipole field of 5.99 T at 4.2 K in its clear aperture of 65 mm at 6.795 kA when a resistive voltage of $105\mathrm{\mu }\mathrm{V}$ appeared across one of the coils in the magnet. The stored energy was 53 kJ at the peak field. The magnet showed no degradation in the current-carrying capability at 4.2 K after the thermal cycle. We report on the detailed design, fabrication, and performance of the C3 magnet that can be of interest to potential users of this emerging technology. We also discuss issues and research needs to inform future rebco magnet development. The experiment represented another step to addressing if the high-temperature superconducting accelerator magnet technology can increase the discovery capability of future particle accelerators.

The Super Tau-Charm Facility (STCF), a proposed high-luminosity electron-positron collider in China, requires a beam current of 2 A to achieve its design luminosity. Such intense current induces severe coupled-bunch instability driven by the rf cavity accelerating modes. This paper presents a systematic analysis of these instabilities across the STCF operational energy range of 1–3.5 GeV. Without active control, the low-order coupled-bunch modes, particularly the mode $-1$, exhibit growth rates significantly exceeding the radiation-damping rate. We demonstrate that the instability can be effectively suppressed using only the proportional-integral feedback loop of the baseline low-level rf system. The key lies in setting a unit proportional gain and a loop delay of approximately half the revolution period. This configuration creates a notch-filter response that attenuates the most dangerous mode $-1$. By combining analytical calculations with particle-tracking simulations, we show that this simple and robust approach maintains beam stability for the baseline design parameters across all design energies, thereby enabling reliable high-current operation without requiring additional dedicated feedback measures, such as direct or one-turn-delay feedback. A stability assessment based on the Nyquist criterion confirms the closed-loop stability of the system and indicates sufficient gain margins. These results provide a reliable foundation for the STCF rf and feedback system design, enabling stable high-current operation under realistic constraints. The proposed approach and the associated analysis framework also offer a practical reference for other high-current storage rings facing similar instability challenges.

We present the baseline design of the electron ring collimation system for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory (BNL). The system addresses beam losses in a high-current electron storage ring with superconducting (SC) final-focus magnets and sensitive detectors, where uncontrolled losses can generate heat loads, radiation, and detector backgrounds and damage. The proposed collimation insertion localizes halo particle losses through reducing interaction region beam losses from beam-gas and Touschek scattering by several orders of magnitude while keeping detector backgrounds and cryostat heat loads within acceptable limits. Multiturn particle-tracking simulations show that the collimators do not significantly impact machine acceptance or beam lifetime, and their positions and apertures can be reoptimized for future lattice configurations. Ongoing work includes incorporating crab cavities and solenoid fields into simulations, refining vacuum conditions, and optimizing collimator geometry and materials. This design establishes a robust baseline for the EIC electron ring collimation system and supports continued lattice optimization for machine operations.

The future circular electron-positron collider will provide collisions at four interaction points (IPs) along a 91-km ring, with beam energies ranging from 45.6 GeV (Z pole) to 182.5 GeV ($\mathrm{t}\overline{\mathrm{t}}$ threshold). Several processes, induced by both the collisions at the IPs and the circulating beams, contribute to the radiation environment of the experimental insertion regions, exposing the detector, machine equipment, and electronics. Quantifying these radiation fields and their effects is essential to guide design strategies. In this work, the Monte Carlo code fluka is employed to simulate the propagation of radiation showers from both IP-driven and beam-driven sources, including radiative Bhabha scattering, incoherent pair creation, beamstrahlung, synchrotron radiation, and beam-gas interactions. Power deposition, equivalent fluences, and total ionizing dose are estimated to assess the exposure of sensitive components and to characterize tunnel radiation levels at the Z-pole and $\mathrm{t}\overline{\mathrm{t}}$-threshold modes. The results show that incoherent pairs dominate the detector environment, particularly in the tracker, while radiative Bhabha losses in the superconducting final-focus quadrupoles (FFQs) require shielding to ensure safe magnet operation. Tunnel radiation levels exceed the tolerance of standard equipment at both operational modes, being dominated by radiative Bhabha and collimation losses at the Z pole, and by synchrotron radiation at the $\mathrm{t}\overline{\mathrm{t}}$ threshold. While a tungsten layer is shown to effectively protect the FFQs, the high radiation levels elsewhere indicate the need for additional shielding in dipoles and drifts, as well as dedicated absorbers downstream of the IPs and collimators.

We propose a new approach for a high-density free-neutron target, primarily aimed at nuclear astrophysics reaction studies in inverse kinematics with radioactive ions circulating in a storage ring. The target concept integrates four key subsystems: a neutron production source driven by a supercompact cyclotron utilizing ${}^9\mathrm{Be}$($p,xn$) reactions, an optimized moderator/reflector assembly using either heavy water or beryllium oxide with a graphite reflector shell to thermalize fast neutrons, a cryogenic liquid hydrogen moderator to maximize thermal neutron density in the interaction region, and beam pipe geometries that enable neutron-ion interactions while maintaining vacuum conditions for ion circulation. This integrated approach focuses on feasibility by incorporating readily available technologies. Using a commercial supercompact cyclotron delivering a proton beam of $130\mathrm{\mu }\mathrm{A}$, the design achieves thermal neutron areal densities of $\sim 3.4\times {10}^6\mathrm{n}/{\mathrm{cm}}^2$ for a proof-of-concept demonstrator at the CRYRING ion-storage ring at GSI Darmstadt. This autonomous accelerator-target assembly design enables deployment at both in-flight and ISOL facilities to exploit their complementary production mechanisms. Potential upgrades based on higher-energy and/or higher-current cyclotrons will enable an increase in areal density to $\sim {10}^9\mathrm{n}/{\mathrm{cm}}^2$. In combination with a customized low-energy storage ring and a radioactive ion-beam facility, the proposed solution could deliver luminosities above ${10}^{23}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, thereby enabling neutron capture measurements of $\sim \mathrm{mb}$ cross sections within a few days of experiment. The proposed system represents a significant milestone toward enabling large neutron-capture surveys on short-lived nuclei, thereby opening a new avenue for understanding the synthesis of heavy elements in our universe.

X-ray free-electron lasers (XFELs) of high brightness have opened new opportunities for exploring ultrafast dynamical processes in matter, enabling imaging and movies of single molecules and particles at atomic resolution. In this paper, we present a straightforward method for multiframe diffraction imaging, using the whole electron beam to generate four-color XFEL pulses with adjustable wavelength separation and time delay. The optical klystron scheme is introduced to enhance the FEL intensity and reduce the total length of the undulators. The time delay is tuned via a magnetic chicane between the undulators for different colors. Using parameters of SHINE, start-to-end simulations demonstrate the effectiveness and tunability of our method, achieving representative results such as time delays of hundreds of femtoseconds and four-color XFEL pulses spanning 1.8 to 2.7 nm with 0.3 nm intervals. The proposed scheme enables the recording of multiframe diffraction images in a single exposure, providing a new perspective for ultrafast molecular and atomic dynamics studies.

The survival of charged particles in synchrotrons requires avoiding setting the beam on machine resonances, the most dangerous of which are the integer and half-integer. Nevertheless, operationally, the transverse tunes may change dynamically, crossing these resonances and resulting in unwanted beam quality degradation and beam loss. For high-intensity beams, the process of resonance crossing is even more critical, as space charge, in addition to the incoherent effects, may also generate coherent effects. The interplay of the speed of resonance crossing, the space charge incoherent tune spread, and the half-integer resonance width is fundamental for the beam behavior. In this paper, we study the crossing of the half-integer resonance $2Q_y=9$ in the CERN Proton Synchrotron Booster (PSB) for a range of parameters using a coasting beam. We take advantage of the newly commissioned PSB to investigate the beam response experimentally. The experimental findings are also discussed with the support of simulations.

Bunch shaping in electron linear accelerators is of critical importance, as it enables the realization of prescribed projection profiles along specific coordinates of the bunch distribution for linac-based x-ray free-electron laser (XFEL) applications. It is evident that temporally flattop electron bunches yield more uniform slice properties, reduced emittance growth, and enhanced FEL gain compared to conventional Gaussian profiles. In this work, we present a data- and model-guided framework that consists of a physics-informed model and an inverse emittance model for minimizing the bunch emittance through laser pulse shaping and the control of laser and accelerator parameters in high-brightness photoinjectors. With a temporal flattop laser shape selected, a flat slice emittance distribution along the bunch has been experimentally obtained at the European XFEL. A measured central slice emittance of about $\text{0.4\hspace{0.17em}\hspace{0.17em}}\mathrm{\mu }\mathrm{m}$ at 250 pC is achieved using a 20 ps flattop laser pulse at the photocathode. Here we present the results of a commissioning experiment, marking a practical application of temporally flattop-shaped electron bunches for stable photon delivery in a user experiment week at the facility. Within limited tuning time, a pulse energy of 1.7 mJ has been achieved at photon energies of 7.1 and 7.6 keV for the two hard x-ray undulator beamlines, surpassing the user requirements. Such a data- and model-driven framework opens up new opportunities for end-to-end optimization of machine parameters, thereby enhancing the capabilities of large-scale FEL facilities.

In heavy-ion accelerators used for radioactive isotope production, the accelerated beam is typically directed onto a target and then discarded in a beam dump. To make more efficient use of the beam, recycling of the beam passed through the target is proposed in the framework of the so-called energy recovery internal target (ERIT). In the ERIT system, the target is irradiated by a circulating beam, while the energy lost in the target is recovered using rf cavities. So far, such a system has been realized only for proton beams. Here, an ERIT system for heavy-ion beams is demonstrated for the first time. A major challenge is the circulation of ions with multiple atomic charge states. After passing through the target, ions rapidly reach an equilibrated charge-state distribution, independent of the initial charge state. This stochastic charge-state conversion (SCSC) leads to rapid beam-emittance growth. To mitigate this effect, we develop a method to match the closed orbits and betatron functions of different charge states at the target location, based on a scaling fixed-field alternating-gradient (FFA) lattice. We present the design of such an FFA ring and show, through 6D beam-tracking simulations, that the transverse emittance growth induced by SCSC can be significantly reduced over a practical number of turns, whereas longitudinal emittance growth remains significant and is discussed separately.

A novel cooling mechanism for heavy-ion beams, termed charge-exchange cooling (CEC), is proposed. Phase-space-dependent zoned charge exchange combined with charge-state-dependent closed-orbit distortions (CODs) enables rapid, autonomous, turn-by-turn contraction of the phase-space distribution for continuous-wave heavy-ion beams. The resulting dynamics forms a stochastic affine-map system with state-dependent switching and a net negative drift. CEC is implemented in the charge stripper ring 1 (CSR1), under development at the RIKEN RI Beam Factory, where zoned charge exchange and charge-state-specific CODs are readily incorporated. Proof-of-principle studies based on two- and multicharge-state models, together with realistic CSR1 simulations, demonstrate fast turn-by-turn cooling under practical machine conditions and establish CEC as a new beam-cooling principle with potential implications for future accelerator design and applications.

We consider the radiation emitted by a purely longitudinally accelerated relativistic electron bunch and find, contrary to the usual expectation of negligible emission, that for ultrashort compact bunches within reach of current experiments, a significant and measurable radiation pulse is produced. The underlying mechanism for the enhanced emission is coherence in the single-electron emission over $\mathcal{O}({10}^8)$ electrons. We derive analytic descriptions of the emission spectrum and energy for acceleration fields and bunch conditions encountered in rf-driven particle accelerators, and in the extreme high-gradient conditions of plasma-driven acceleration. Both the bunch duration and the duration of the acceleration have a role in describing a phase-matching limitation to the coherence, with the latter dependent on the acceleration field strength and the initial energy of the electrons. In extremely compact bunches, just beyond those currently realized in the laboratory, the radiation losses approach the Larmor radiation for a massively charged particle ($Q\sim {10}^{9}e$). In such conditions, the implied energy of the longitudinal acceleration radiation may approach the energy available from the electric field driving the acceleration, raising questions about a connection to mechanisms of field depletion.

SuperKEKB collimator system protects the superconducting final focusing magnets (QC1 and QC2) from quenching caused by beam halo particles. For effective shielding, the minimum aperture of vertical collimators is set smaller than the physical aperture of QC1. However, such collimators become dominant sources of beam coupling impedance, which can limit the maximum beam current due to impedance-driven instabilities. To address this issue, a nonlinear collimator (NLC) was introduced in February 2024. NLC is designed to reduce both beam backgrounds and collimator impedance, thereby suppressing beam instabilities caused by short-range wakefields. In this paper, we describe the results on impedance effects, beam background reduction, and beam lifetime when the nonlinear collimation system is turned on and off. These results validate the NLC concept and offer a promising approach for future high-luminosity colliders.

Since the emergence of laser-plasma accelerators (LPAs), substantial work has been dedicated to using LPAs to drive free-electron lasers (FELs) for a broad range of applications. Despite recent breakthroughs, which have proven the fundamental feasibility of operating FELs with an LPA source, stable FEL operation over multiple hours without operator input had yet to be achieved. In this work, we report significant improvements to the stability of a hundred terawatt laser system, resulting in successful demonstration of reliable, long-term operation of an LPA-driven FEL in the self-amplified spontaneous emission (SASE) regime at 420 nm. The LPA source delivered 100 MeV electron beams at 1 Hz with high stability over more than 10 h, enabling over 8 h of continuous FEL operation without operator input. The acquired data were subsequently used to investigate correlations between the measured undulator radiation and parameters of the drive laser, plasma source, and electron beam. The revealed connections between LPA and FEL performance gave important additional insights into ways to further improve and stabilize the system, thus demonstrating the capability of our setup to serve as a powerful platform for future studies of LPA-driven FEL operation. The one-of-a-kind integration of multiple stabilization concepts onto the LPA facility discussed in this manuscript yielded significant accelerator and light source improvements (with residual correlations suggesting even more is possible), which will positively impact LPA applications at large.