This paper develops a homogenized harmonic balance finite element method (HomHBFEM) to predict the dynamic behavior of magnets with fast excitation cycles, including eddy current and skin effects. A homogenization technique for laminated yokes avoids resolving the individual laminates and the skin depth in the finite element (FE) mesh. Instead, the yoke is represented by a bulk surrogate material with frequency-dependent parameters. The ferromagnetic saturation of the yoke at higher excitation currents is tackled by a harmonic balance method, which accounts for a coupled set of frequency components. Thereby, a computationally expensive time stepping of the eddy-current field problem and a convolution of the homogenized yoke model are avoided. The HomHBFEM enables, for the first time, nonlinear simulations of fast corrector magnets, which are embedded in a fast orbit feedback system to counteract orbit disturbances over a broad frequency spectrum, and thus guarantee stable light-source operation. The results show the impact of the nonlinearity on the phase lag and the field attenuation, as well as the eddy current losses at frequencies up to several tens of kilohertz. The numerical validation for a C-dipole magnet example shows that the HomHBFEM achieves a sufficient accuracy at an affordable computational effort, with simulation times of a few hours. In comparison, standard three-dimensional transient FE simulations need to resolve the lamination thickness and the skin depth in space and the largest relevant frequency in time, which leads to a 2 to 3 orders of magnitude larger mesh and prohibitive computational effort, with simulation times of a few weeks on a contemporary computer server.

Beam halo is one of the most crucial issues limiting the machine performance and causing radioactivation in high-intensity accelerators. Understanding halo formation is vital for high-luminosity colliders, advanced light sources, and spallation neutron sources to effectively mitigate beam loss through machine optimizations and tailored collimation systems. This article details numerical and experimental investigations of transverse and longitudinal halos at the KEK Accelerator Test Facility. Halo distributions are modeled incorporating operational beam parameters, synchrotron radiation, beam-gas scattering, and Touschek-scattering processes. A newly developed yttrium aluminum garnet/optical transition radiation monitor, positioned at the extraction line, enables direct imaging of transverse and longitudinal halo distributions. The general consistency between predictions and observations in various conditions indicates that the Touschek scattering is the dominant mechanism forming the horizontal and momentum halos.

The plasma photocathode has previously been proposed as a source of ultrahigh-brightness electron bunches within plasma accelerators. Here, the scheme is extended by using a radially-polarized ionizing laser pulse to generate high-charge, high-brightness electron bunches with symmetric transverse emittance. Efficient start-to-end modeling of the scheme, from ionization and trapping until drive bunch depletion, enables a multiobjective Bayesian optimization routine to be performed to understand the performance of the radially-polarized plasma photocathode, quantify the stability of the scheme, and explore the fundamental relation between the witness bunch charge and its emittance. Comparison of plasma photocathodes driven by radially- and linearly-polarized laser pulses shows that the former yields higher-brightness electron bunches when operating in the optimally-loaded regime.

For fourth-generation synchrotron light sources, the triple rf system has been proposed to achieve further bunch lengthening compared to the commonly used double rf system, as well as to meet specific requirements for longitudinal injection. In a previous study for the double rf system [T. He et al., Periodic transient beam loading effect with passive harmonic cavities in electron storage rings, Phys. Rev. Accel. Beams 25, 024401 (2022)], it was shown that the periodic transient beam loading (PTBL) effect, also referred to as mode 1 instability, could limit the maximum bunch lengthening. Intuitively, in the triple rf system, the harmonic cavity (HC) operating at a higher harmonic of the fundamental rf frequency is expected to help mitigate the mode 1 instability driven by the lower-order HC, as the two HCs are tuned in opposite directions. However, contrary to this intuition, both tracking simulations and semianalytical calculations presented in this paper show that the two HCs of the triple rf system together actually strengthen the PTBL effect. To better understand this unexpected behavior, we introduce a novel concept of steady-state response matrix of cavity voltage, which simplifies the semianalytical algorithm and directly links cavity voltage perturbations to the complex bunch form factor perturbations. Additionally, we propose a modified semianalytical method that efficiently and accurately determines the PTBL threshold for the triple rf system. Using the parameters of the Hefei Advanced Light Facility storage ring as a case study, we apply this modified method to explore the relationship between the threshold $R/Q$ values of the two HCs under different bunch lengthening scenarios. All results are well validated through tracking simulations. Our findings show that the $R/Q$ values of the two HCs must be sufficiently low to avoid the PTBL effect under the desired optimum bunch lengthening condition. This result provides valuable guidance for the design of the triple rf system.

In a superconducting linear accelerators (linacs), accurately monitoring beam dynamics is essential for minimizing beam losses and ensuring stable operations. However, destructive diagnostics must be avoided in superconducting sections to prevent the occurrence of particulates and outgassing, rendering direct measurements of the beam envelope particularly challenging. This study presents a nondestructive method that uses beam position monitors (BPMs) to estimate the transverse beam envelope based on measurements of the quadrupole moment of the beam distribution. Although this concept was originally proposed in the 1980s, its application, especially to hadron beams, has been limited because of low signal sensitivity and the accuracy constraints associated with conventional BPM geometries. To overcome these challenges, we employed $\cos 2\theta$-type BPMs, which offer improved sensitivity to quadrupole components and are well suited for low-$\beta$ heavy ion beams. This method was applied to the heavy ion beams in the superconducting RIKEN linac (SRILAC), for which data from eight BPMs were combined with transfer matrix calculations and supplemental wire scanner data. The resulting beam envelope estimates exhibited good agreement with conventional quadrupole scan results, demonstrating the feasibility of this technique for routine, nondestructive beam monitoring in superconducting accelerator sections.

High-repetition-rate free-electron laser (FEL) facilities such as LCLS-II rely on continuous-wave (cw) injectors to deliver high-quality electron beams to multiple undulator lines simultaneously. Ensuring injector reliability under nonideal conditions is critical for sustained user operations. In this work, we investigate the fault tolerance of a representative cw photoinjector by analyzing its performance under various degraded scenarios, including reduced gun energy, radio-frequency (rf) cavity failures, solenoid field constraints, and early-stage energy gain requirements. Using multiobjective optimization with a genetic algorithm framework (Xopt), we assess achievable beam quality—focusing on transverse emittance and bunch length—across a range of fault conditions. Our results reveal that while certain failures (e.g., buncher off) significantly impact emittance, coordinated adjustments to laser parameters, rf phases, and cavity gradients can still partially recover performance. The injector demonstrates resilience to a variety of perturbations, confirming its robustness for high-demand cw FEL operations.

A compact energy-recovery linac (cERL) has been under development at KEK to drive key accelerator technologies, demonstrate energy recovery under various conditions, and support beam applications. cERL began beam operations in 2013 to create stable, low-emittance, energy-recovered beams. The project focused on gradually increasing the current transported in a stepwise fashion while maintaining low beam losses at each step. However, the energy recovery of high-current beams is an issue that needs to be addressed. In this study, we propose a method for high-current beam tuning of approximately 1 mA under energy-recovery conditions with extremely small beam loss. We prepared a collimator and a local fast beam loss monitor to reduce the beam loss. We report successful results at approximately 1 mA, demonstrating 100.0% energy recovery with extremely small beam loss. The radiofrequency (rf) amplitude and phase varied by less than 0.02% and 0.02°, respectively. The study findings are expected to provide insights into steady beam operation for high-brightness beams and high-efficiency energy-recovery operations required for future extreme ultraviolet free-electron lasers.

Laser-plasma accelerators (LPAs) offer an attractive alternative to conventional accelerators for the development of compact electron sources and next-generation light sources. Due to orders-of-magnitude larger accelerating gradients, LPAs enable the acceleration of high-brightness electron beams to ultrarelativistic energies in millimeter- to centimeter-scale distances. However, LPA stability is limited by shot-to-shot fluctuations of the driving laser system. Specifically, fluctuations in the final-focus longitudinal position result in correlated instability in LPA electron beam qualities, including total beam charge, average beam energy, and energy spread. We demonstrate active stabilization of the longitudinal focal position for a 100 TW-class laser system. This repetition-rate scalable stabilization system leverages noninvasive wave front monitoring of a copropagating, unamplified kHz pulse train to guide corrective adjustments to the focal position of a 1 Hz amplified drive laser via an upstream telescope on millisecond timescales. In this demonstration, the approach limits standard deviation fluctuations of the amplified drive beam’s longitudinal focal position to $\pm 0.22\mathrm{mm}$ (representing at least a 53% reduction), achieved with a correction bandwidth that reaches the Nyquist frequency limit. Consequently, we observe marked improvements in both long-term and shot-to-shot LPA stability in terms of charge and spectrum.

In low-energy beam transport of pulsed, high-perveance ion beams operating under neutralized space-charge conditions, understanding the time required for the compensation process to develop—known as the build-up time—is critically important for ensuring efficient beam transmission and maintaining beam quality. This study presents a comprehensive investigation into the dynamics and optimization of space-charge compensation (SCC) in the low-energy beam transport line of a high-perveance proton beam, integrating numerical simulations with time-resolved experimental measurements. A detailed 3D numerical simulation has been developed, which takes into account both secondary electron and ion dynamics to evaluate the temporal evolution of the beam potential and its dependence on various parameters. Additionally, experimental measurements complement the numerical results, providing validation of SCC dynamics. These measurements analyze the effects of injected gas properties, pressure levels, and beam current on build-up time, while also considering nonlinear space-charge effects that influence SCC efficiency and the beam’s transverse emittance evolution. A correlation between SCC and radio-frequency quadrupole matching conditions is also examined, demonstrating the necessity of adjusting solenoid magnet settings to maintain optimal transmission efficiency.

Beams designated for the LHC are injected into the SPS in multiple batches. Given the tight spacing of 200 ns between these batches, the injection kickers have to be precisely synchronized with the injected beam to minimize injection oscillations. Due to machine drift, the optimal settings for the kickers vary. This paper presents an active controller trained by reinforcement learning that counteracts the machine drifts by adjusting the settings. The agent was exclusively trained in a simulation environment and directly transferred to the accelerator. Although its results are slightly worse than those obtained by an explicit numerical optimizer, the BOBYQA algorithm, the agent attains these results much faster since it requires far less computation.

The focus-scan scheme has been adopted to diagnose the emittance of the electron beams produced from laser wakefield accelerators. The spot size of the electron beam has an energy dependence after propagating through a beamline consisting of two or more quadrupoles, which can be used to fit the beam emittance and the Courant-Snyder (C-S) parameters. We use the concept of the principal planes to unify the analysis of the focus-scan scheme. The fitting procedures and the effects of the length variation between the source, magnets, and screen on the diagnostic are presented. Particle-in-cell simulations using plasmas with different downramp lengths are conducted to study their effects on the measurements of the emittance and C-S parameters. Our analysis provides a unified understanding of the focus-scan scheme and can be applied to beamlines consisting of more quadrupoles.

Radio frequency (rf) bunchers are often utilized to control a longitudinal bunch length in low- and medium-energy transport lines. However, nonlinear rf fields in the bunchers deform a longitudinal phase space distribution, which causes emittance growth leading to beam quality degradation and unexpected beam losses. This paper describes a decrease in the longitudinal rms emittance in a high-intensity deuteron linac, where the longitudinal phase space deformed by a nonlinear rf field in the buncher is self-linearized by a longitudinal nonlinear space charge force. To quantitatively explain this phenomenon, we develop two formulas to express deformations of phase space and forces acting on the beam. We perform particle tracking simulations with the tracewin code using a 125 mA, 5 MeV deuteron beam at the Linear IFMIF Prototype Accelerator (LIPAc) and validate the two formulas by applying them to LIPAc. The quantitative evaluations of the deformations with the formulas lead to a deeper understanding of beam physics and are also expected to be useful in mitigating phase space deformation.

Beam loss monitors (BLMs) and beam current monitors (BCMs) are ubiquitous at particle accelerators around the world. These simple devices provide noninvasive high-level beam measurements but give no insight into the detailed 6D $(x,y,z,p_x,p_y,p_z)$ beam phase-space distributions or dynamics. We show that generative conditional latent diffusion models can learn intricate patterns to solve the extreme inverse problem of mapping waveforms of tens of BLMs or BCMs along an accelerator to detailed 2D projections of a charged particle beam’s 6D phase-space density. This transformational method can be used at any particle accelerator to transform simple noninvasive devices into detailed beam phase-space diagnostics. We demonstrate this concept via multiparticle simulations of the high-intensity beam in the kilometer-long Los Alamos Neutron Science Center linear proton accelerator.

The High Energy Photon Source (HEPS) Linac is a normal-conducting electron linear accelerator capable of producing high bunch charge beam. Its bunching system includes two subharmonic bunchers (SHBs), one prebuncher, one buncher, and one accelerating structure. The SHB is commonly used in the low-energy section for longitudinal bunching to increase the bunch charge. The phase and voltage of the SHB are crucial for obtaining a high-quality electron beam in Linac. This paper presents a method for calibrating the phase and voltage of the SHB using the time-of-flight technique. Experiments were conducted at the HEPS Linac using two beam position monitors. According to the simulations, we found that bunch length and space charge effect have a significant impact on the results, and we propose corrective measures to address them. To enhance experimental efficiency, we propose a data processing method called the truncated averaging technique that eliminates the need for corrective measures, which has been validated through both simulations and experiments, yielding outstanding results. This paper presents detailed insights into both the simulation and experimental procedures.

To investigate the internal spin structure of nucleons and explore fundamental phenomena such as parity and time-reversal symmetry violations, polarized deuteron beams are pivotal because they serve as a unique alternative to polarized neutron beams and allow for the exploration of tensor polarization—a critical feature of spin-1 systems that offers distinct insights beyond vector polarization. This study advances the understanding of tensor-polarized deuteron beam dynamics in synchrotrons, with direct relevance to the Electron-Ion Collider in China (EicC). By deriving spin tensor transfer matrices and validating their accuracy through numerical simulations, we demonstrate the tensor polarization evolution in bending magnets, solenoids, and quadrupoles. The analysis of depolarizing resonances during acceleration reveals negligible polarization losses under the EicC’s design parameters, ensuring the feasibility of high-precision spin experiments without dedicated polarization maintenance. Furthermore, the planar-constrained translational dynamics of spin tensors, fundamentally distinct from the rotational mechanisms governing spin vectors, offer novel strategies for spin manipulation in future accelerators. These results provide theoretical and computational foundations for spin tensor control in the EicC and broader applications in spin-correlation experiments.

As the ring-based light source community is moving toward fourth-generation light sources, many facilities plan to upgrade their boosters in parallel to meet the more demanding beam properties for the storage ring, especially in terms of a much lower emittance. Concerns over collective effects have, therefore, risen, particularly in the transverse planes, since the vacuum chamber dimensions tend to be reduced as a way to achieve a stronger focusing force on the beam. In this article, we present numerical studies on transverse beam instabilities, both in the single- and multibunch regimes, in the SOLEIL II booster as an example of a low-emittance booster. We show that Landau damping is an efficient mechanism for suppressing both transverse single-bunch and coupled-bunch instabilities. We also prove that the damping in the longitudinal plane can diffuse to the transverse plane and limit the transverse emittance growth. Moreover, we have discovered that the beam can exhibit sawtooth instability at high energy and that broadband impedance is one of the key factors in suppressing transverse coupled-bunch instability.

We use Bayesian optimization in combination with three-dimensional particle-in-cell simulations to determine the optimal laser and plasma parameters that, for a given laser pulse energy, maximize the cut-off energy of an electron beam produced by laser wakefield accelerators. We assume a Gaussian laser driver with matched spot size and amplitude and investigate both self-guiding in a uniform-density plasma and guiding in a preformed plasma channel with matched radius. To interpret the simulation results quantitatively, we derive novel analytical expressions for the maximum electron energy and the corresponding acceleration distance, accounting for the effects of laser diffraction and energy depletion. Based on the results obtained, we discuss the potential scalability of the optimal input (plasma density, pulse duration, amplitude, spot size, and channel radius) and output (electron energy, electron charge, acceleration length, and acceleration efficiency) parameters to laser systems of arbitrary energy.

High-power proton linear accelerators have important applications in both scientific research and industry. However, the operation of such accelerators with megawatt-level beam power is expensive and limits the broad availability of these facilities. In this Letter, we propose a novel energy recovery proton linear accelerator in which the final GeV-level proton beam is reinjected into the linear accelerator from the accelerator exit and is decelerated in the same accelerator down to about 2 MeV, close to the initial beam energy. This substantially reduces the power consumption of the proton linear accelerator and also avoids the need for a high-power beam dump. We demonstrate this concept through self-consistent simulations and show that the beam-beam effect between the forward-accelerating beam and the backward-decelerating beam would not be a limiting factor for the proposed concept. A potential application of this concept to an electron-ion collider based on energy recovery electron and ion accelerators is discussed.

We show that an anomalous pinch can occur in ultrarelativistic electron-electron or positron-positron beam interaction, caused by the combined interplay of collective beam motion (disruption) and strong-field quantum electrodynamics (SF-QED). The locally created electron-positron pairs, from SF-QED effects, screen the self-fields of the beams and can invert the polarity of the Lorentz force, resulting in a pinch of the beams. A theoretical model predicts the pinch condition and is confirmed by first-principles three-dimensional particle-in-cell simulations. This anomalous pinch causes density compression, increases the collision luminosity, and amplifies the local magnetic fields and the quantum parameter of the beam particles by several orders of magnitude.

Laser-plasma accelerators present a promising alternative to conventional accelerators. To fully exploit the extreme amplitudes of the plasma fields and produce high-quality beams, precise control over electron injection into the accelerating structure is required, along with effective laser pulse guiding to extend the acceleration length. Recent studies have demonstrated efficient guiding and acceleration using hydrodynamic optically field-ionized plasma channels. This guiding technique has also been combined with controlled electron injection to produce high-quality electron beams at the GeV level using a 50 TW laser. The present work extends these results to higher laser power, demonstrating the generation of quasimonoenergetic electron beams with peak energies exceeding 2 GeV, for a PW-class laser.