We present a noninterferometric method for measuring the transverse electron beam size at the European XFEL based on synchrotron radiation intensity autocorrelation. The technique enables cell-by-cell diagnostics along the SASE1 undulator using existing hardware: a commissioning monochromator and a spatial x-ray detector. We extend the results of [A. Trebushinin et al., companion paper, First observation of synchrotron radiation spikes for transverse electron beam size measurements at a free-electron laser, Phys. Rev. Lett. 135, 215001 (2025).] focusing on data analysis procedures and technical implementation. Our method allows for extraction of the beam size from noisy measured intensity distributions with a signal-to-noise ratio as low as 0.9 and is capable of distinguishing between the projected and slice sizes. To validate our approach, we introduced a mismatch in the magnetic lattice, inducing a controlled sinusoidal variation in the beam size along the undulator. The corresponding modulation was clearly reproduced in the electron beam size values extracted from the autocorrelation measurements. This method offers a practical solution for transverse electron beam size diagnostics in high-energy linacs, with direct application to the operation and tuning of free-electron laser facilities.

Tapering enhanced superradiance (TES) is a novel radiation scheme that significantly improves the energy conversion efficiency in free-electron lasers. The undulator tapering design and optimization are crucial to the success of this efficiency boost and are fairly complicated tasks. Here, we demonstrate how to optimize the linear tapering rate using analytical magnetic field maps derived from pure permanent magnet (PPM) equations. A TES undulator (waveguided tapered undulator) is designed to operate at 0.5 THz at the zero-slippage regime, ensuring phase synchronicity and group velocity match between the electron beam and the radiation field. The superradiance condition is fulfilled by compressing the electron bunch to emit coherently. The results reveal a significant enhancement in energy conversion efficiency for both ideal and realistic beams. The real beam simulations use the ORGAD FEL parameters from the Schlesinger Accelerator Center at Ariel University. This work shows the potential of the TES method to achieve higher radiation energies through careful undulator design and optimized tapering and provides a complete model for this purpose.

The low relative charge-to-mass ratio offset of 0.065% between fully ionized helium-4 and carbon-12 ions enables simultaneous acceleration in hadron therapy synchrotrons. At the same energy per mass, helium ions exhibit a stopping range approximately 3 times greater than carbon ions. They can therefore be exploited for online range verification downstream of the patient during carbon ion beam irradiation. One possibility for creating this mixed beam is accelerating the two ion species sequentially through the LINAC and subsequently “mixing” them at injection energy in the synchrotron with a double multiturn injection scheme. This work reports the first successful generation, acceleration, and extraction of a mixed helium and carbon ion beam using this double multiturn injection scheme, which was achieved at the MedAustron therapy accelerator in Austria. A description of the double multiturn injection scheme, particle tracking simulations, and details on the implementation at the MedAustron accelerator facility are presented and discussed. Finally, measurements of the mixed beam at delivery in the irradiation room using a radiochromic film and a low-gain avalanche diode detector are presented.

The nonlinear space-charge effect plays a significant role in high-intensity accelerators and has been extensively studied using multiparticle tracking methods. In this paper, we present a novel 2.5-dimensional symplectic space-charge solver specifically designed for long beam bunches. We begin by detailing its application to a transverse Gaussian density distribution under open boundary conditions in a straight system, where a semianalytical expression is derived. We then demonstrate the solver’s adaptation to arbitrary distributions in open space, as well as within rectangular and round conducting pipes. Finally, we discuss the extension of this solver to circular accelerator systems. This study shows that the fast 2.5-dimensional solver can be a good approximation to the fully three-dimensional solver for long bunches in large circular accelerators.

The SPring-8 Angstrom Compact free-electron LAser (SACLA) linear accelerator utilizes a dc gun with a thermionic cathode, known for delivering high beam quality, excellent operational stability, and low maintenance requirements. In the second part of our design study, we present a comprehensive beam dynamics analysis of the SACLA dc electron gun and outline a roadmap toward achieving submicrometer ($0.1\mathrm{\mu }\mathrm{m}$) beam emittance. We provide both analytical and numerical estimates of four key sources contributing to emittance growth: (i) image = charge effects on the cathode, (ii) nonlinear space-charge forces arising from imperfect beam edge geometry, (iii) aberrations in the accelerating field, and (iv) solenoid field aberrations due to longitudinal–transverse momentum exchange. The analysis yields a closed-form expression for the superposition of correlated emittance growth mechanisms, highlighting an “interference” term that amplifies the net emittance when space-charge and solenoid effects coexist. To address the challenge of emittance growth, we propose a compact hybrid magnet that ensures strong longitudinal confinement of the magnetic field. This confinement allows placement of the hybrid magnet in close proximity to the gun exit, thus mitigating emittance growth effectively, while having a negligible magnetic field on the cathode. The hybrid magnet design is achieved by symmetrically positioning permanent ring magnets on either side of a solenoid, enabling fine control over the field distribution and “squeezing in” it longitudinally. Our findings offer new insights applicable to low-voltage continuous-wave very high-frequency guns and superconducting radio-frequency electron guns.

Superconducting radio-frequency (SRF) cavities with high-loaded-Q are susceptible to ponderomotive instabilities arising from nonlinear electromechanical coupling. Under low-level rf feedback control, stability analysis is challenging and has, until now, lacked comprehensive experimental verification. In this work, we linearize the coupled cavity electromagnetic and mechanical equations about the operating point, deriving explicit small-signal stability criteria for both open- and closed-loop operation. A characteristic equation approach is used to map the oscillatory instability threshold in the detuning–gradient plane. Time-domain simulations confirm the predicted onset of self-excited oscillations at these thresholds. Furthermore, experiments on a 162.5 MHz SRF linac (CAFE2) show that the observed oscillation onset agrees with our analytical predictions within a small margin. By combining analytical modeling, numerical simulation, and direct experimentation, this study providescomprehensive validation of oscillatory ponderomotive instability theory under feedback control, offering practical guidance for the stable operation of high-gradient SRF accelerators.

In low and medium energy electron storage rings, intrabeam scattering (IBS) is a significant collective effect that can lead to an increase in equilibrium emittance, thereby diminishing the light source’s flux. Typically, the bunch length of the electron beam in storage rings is considered constant around the ring circumference. However, in the concept of steady-state microbunching storage rings, the bunch length can vary significantly around the ring in an effort to achieve high coherence in the longitudinal dimension. In this paper, we have extended the Bjorken and Mtingwa (B-M) model to accommodate this requirement, making it versatile enough to be used for arbitrary planar storage rings. Additionally, this paper addresses the simplification of equilibrium emittance calculations involving IBS through certain approximations, making it possible to directly calculate equilibrium emittance by a formula rather than conventional iteration method. This method reveals the physical relationship between equilibrium emittance and the IBS growth rates, and also allows for the IBS effect optimization of the ring lattice by directly using equilibrium emittance as the optimization target rather than the IBS growth rate.

Calculating the effects of coherent synchrotron radiation (CSR) is one of the most computationally expensive tasks in accelerator physics. Here, we use convolutional neural networks (CNNs), along with a latent conditional diffusion (LCD) model, trained on physics-based simulations to speed up calculations. Specifically, we produce the 3D CSR wakefields generated by electron bunches in circular orbit in the steady-state condition. Two datasets are used for training and testing the models: wakefields generated by three-dimensional Gaussian electron distributions and wakefields from a sum of up to 25 three-dimensional Gaussian distributions. The CNNs are able to accurately produce the 3D wakefields $\sim 250–1000$ times faster than the numerical calculations, while the LCD achieves a gain of a factor of $\sim 34$. We also test the extrapolation and out-of-distribution generalization ability of the models. They generalize well on distributions with larger spreads than what they were trained on but struggle with smaller spreads.

High-intensity positron sources are critical for next-generation electron-positron colliders, where positron beam quality and characteristics directly impact the luminosity. Accurate modeling and validated simulation tools for positron sources are essential to optimize their performance. However, modeling a positron source tends to be complex, as it involves multiple interdependent stages, from positron production and capture dynamics to beam transport through the injector linac to the collider ring. In this work, we present a start-to-end simulation tool developed for positron sources modeling. The model was benchmarked against existing simulation tools and validated through experimental measurements conducted at the SuperKEKB positron source. Key operational parameters were systematically scanned to evaluate the simulation model performance, including the primary electron impact position on the target, solenoid field strength around the capture linac, and rf phase settings. The primary figure-of-merit for all validation tests was the positron yield at the end of the SuperKEKB positron capture section. Our model reproduces the measured positron yield ($0.603\pm 0.003$) under nominal operating conditions, with the simulation result of 0.603 lying well within the 0.5% statistical uncertainty. Furthermore, the simulation results demonstrate a very good agreement with experimental data and other simulation tools, confirming the model’s reliability and establishing a framework for future positron source studies.

An implementation of surface-impedance boundary conditions in finite-difference time-domain electromagnetic field solvers was described by Oh and Schutt-Aine. This algorithm allows for modeling of the effects of objects with finite conductivity which lie along grid-conformal surfaces. Here we describe the extension of the algorithm to allow for modeling of arbitrarily shaped objects. This is accomplished by combining the model of Oh and Schutt-Aine with the locally conformal method for modeling of perfectly conducting objects developed by Dey and Mittra. The resulting hybrid algorithm yields a second-order accurate implicit field solution, in which the standard orthogonal grid is deformed only locally at the conductor-vacuum interface, which is modeled by partially filled grid cells. Field solutions inside the conductor are not sought and the approximate boundary condition is used to set the nonzero tangential electric fields along interfaces. This method obviates the need to resolve skin depths on the grid. We briefly review the Oh and Schutt-Aine algorithm and describe its implementation in the Dey-Mittra partial-cell treatment. The use of the model is then demonstrated by performing several test problems involving objects with finite conductivity in both relatively simple and more complex geometries.

In general, optimizing chromaticity and transverse feedback parameters is important in suppressing beam instabilities for stable operation in high-intensity proton machines. Meanwhile, space charge effects impact the intrabunch motion of the proton bunch within a large chromaticity region in the machines, such as the main ring (MR) in the Japan Proton Accelerator Research Complex (J-PARC). To address this issue, the decoherence and recoherence of the transverse motion of the particles comprising the proton bunch are investigated. The analysis reveals that the space charge effects have a significant influence on the recoherence period through the chromaticity. Nevertheless, the relationship between the maximum frequency in the bunch and the chromaticity is not affected by the space charge effects. These findings are demonstrated with particle tracking simulations, including the direct and indirect space charge effects, and the impedance source of the J-PARC MR. Furthermore, we illustrate the influence of the indirect space charge effect on particle motion by examining the excitation patterns of radial and head-tail modes.

The high-energy linac of the Future Circular Collider electron-positron (FCC-ee) injector complex requires high-performance rf accelerating structures to efficiently accelerate beams up to 20 GeV while ensuring operational stability. This study presents an analytical approach to the rf design of traveling-wave structures, incorporating a pulse compression system to enhance power efficiency and meet the demanding FCC-ee specifications. By utilizing lookup tables and analytical models, we systematically explored a broad parameter space to determine the fundamental mode at 2.8 GHz and analyze higher-order mode (HOM) characteristics. The structure’s geometry, particularly the iris parameters, was optimized to maximize effective shunt impedance, minimize peak surface fields, and implement HOM detuning for wakefield suppression. Furthermore, a comparative analysis against existing high-gradient S-band linacs was performed, demonstrating the competitive performance and advantages of the proposed design in terms of gradient, efficiency, and wakefield control. Additionally, we investigated the bunch-to-bunch energy spread minimization including the impact of transient beam loading, with a focus on top-up operation, where bunch charges vary dynamically among four bunches. To accommodate these variations, we introduce the concept of the “golden” rf pulse, an optimized input rf waveform that averages the solutions for fully loaded and unloaded conditions. While this method does not eliminate energy deviations entirely, it provides a practical compromise, reducing energy spread across all possible charge distributions. Finally, comprehensive thermal and mechanical simulations were performed to evaluate the structural integrity and operational performance of the HE-linac under 100 Hz repetition frequency, ensuring long-term reliability.

Laser wakefield accelerators produce ultrashort, highly relativistic electron and x-ray pulses in plasma over millimeter distances. Crucial for investigations and applications of these pulses is a reproducible and controlled output beam pointing. Even with a perfectly stable laser, pulse-front tilt in the driving laser pulse has been shown to cause both the laser pulse and the electron beam to deviate differently from the optical axis after the plasma. We show that this steering also extends to the generated x-rays, but in such a way that they perfectly follow the electron beam. The electron beam or x-ray beam pointing can thus be noninvasively inferred from the other, even when pulse-front-tilt steering is present. This enables active stabilization of either beam, without significant impact on key beam parameters such as energy, charge, and divergence.

Transverse feedback systems are essential for stable operation of all hadron accelerators with high intensity beams. An important component of such a system is a powerful digital signal processing unit. Current digital technology enables the implementation of advanced algorithms to process signals and analyze key parameters of both the accelerator and its feedback systems. In the paper, we present a new digital filter, which is suitable for the construction of a single pickup feedback with a larger tune acceptance and higher gain than can be achieved by the traditionally used Hilbert phase-shifter technique. We propose a method to extract key parameters required for optimal feedback operation, such as the closed-loop phase and delay, as well as accelerator parameters like bunch-by-bunch damping time and machine tune. This is achieved solely through active manipulation of the beam by the transverse feedback system and its analysis of acquired data. Accurate knowledge of these parameters is essential for ensuring beam stability and the reliable operation of the accelerator. Easy access to them is important for automated TFB setting up, performance monitoring, or efficient troubleshooting.

Coherent synchrotron radiation (CSR) has long been recognized as a significant source of longitudinal impedance driving microwave instability in electron storage rings. In the pursuit of higher luminosity, next-generation circular $e^{+}{e}^{-}$ colliders operating in the few-GeV energy range, such as B-factories and Tau-Charm factories, are being designed with low-emittance beams and high beam currents. Damping wigglers are commonly introduced to reduce damping times and control beam emittance. In this study, we systematically investigate the impact of coherent wiggler radiation (CWR), a specific form of CSR generated within wigglers, on beam stability in Tau-Charm factories. We revisit the threshold conditions for CWR-induced microwave instability and evaluate its effects under realistic lattice configurations of collider rings. Furthermore, we examine theoretical models of longitudinal CWR impedance and identify improved formulations that better capture its influence. As an illustrative example, the developed CWR impedance models are applied to simulate beam stability in the Super Tau-Charm Facility currently under design in China.

The use of very high-energy electron (VHEE) beams for radiotherapy has been actively studied for over two decades due to their advantageous dose distribution, deep penetration depth, and great potential of ultrahigh dose-rate irradiation. Recently, laser-plasma wakefield accelerator (LWFA) has emerged as a promising method for the compact generation of VHEE beams, due to its substantially higher accelerating gradients compared to traditional radio-frequency accelerators. However, how to compactly deliver the LWFA-based VHEE beams of relatively large energy spread and create a maximum dose deeply inside the body remains very challenging. In this article, we present a simple dose delivery scheme utilizing only two dipole magnets for LWFA-based VHEE treatment. By adjusting the magnet strengths, the electron beams can be guided along different angular trajectories toward a precise position as deep as 20 cm within a water phantom, creating a maximum dose over the target region and significantly reducing the entrance dose. Supported by Monte Carlo simulations, such a beam delivery approach is demonstrated to be insensitive to the beam energy spread and meanwhile capable of controlling precisely the dose-peak position in both lateral and longitudinal directions. As such, a uniform dose peak can be generated by the weighted sum of VHEE beams that reach different dose-peak depths. These results demonstrate that LWFA-based VHEE beams can be compactly delivered into a deep-seated tumor region in a controllable manner, thus advancing the development of the VHEE radiotherapy toward the practical clinical applications in the near future.

Magnets in the accelerator interaction region (IR) present significant challenges because of high field requirements and limited available space. Conical-shaped magnets offer advantages in these environments by allowing closer placement to the interaction point while maintaining clearance from synchrotron radiation. Interestingly, numerical studies have shown that conical canted-cosine-theta (CCT) designs produce a constant field distribution along the axial direction in the IR quadrupoles for the Electron-Ion Collider (EIC) at Brookhaven National Laboratory. However, the field harmonics generated by conical CCT windings are not yet fully understood. This paper presents an analytical approach to describe the magnetic field produced by a conical surface current and proposes a method for designing conical CCT magnets for accelerator applications. First, we begin with a surface current sheet having a general cosine-theta distribution in spherical coordinates and solve the vector potential using the Green’s function. The magnetic fields generated by the conical current sheet are expressed using associated Legendre polynomials. These results are then related to circular field harmonics and integral field harmonics for designing a coil that produces a pure multipole field. Next, a single layer of the conical CCT winding path is produced based on the cosine-theta current distribution. Finally, the magnetic field quality of dipole and quadrupole conical CCT coils with multiple layers is verified using the Biot-Savart law.

The objective of the High Luminosity Large Hadron Collider (HL-LHC) upgrade is to attain an instantaneous luminosity that is 5 times greater than the design value of the LHC. This requires nearly 2 times higher beam intensity compared to the operational LHC value during Run 2 (2015–2018). Higher bunch intensity makes the beam more prone to coherent instabilities. To keep beam stability under control and preserve beam quality, it is therefore necessary to reduce the machine beam coupling impedance. The collimation system of the LHC is presently responsible for a significant portion of the total machine impedance budget. In this context, during the LHC long-shutdown 2 (LS2), the LHC machine has been upgraded with newly engineered low-impedance collimators whose absorbing jaws are made of molybdenum-graphite (MoGr) compared to the previously used carbon fiber composite (CFC). Secondary collimators are also coated with molybdenum (Mo) to further boost conductivity. In order to validate the benefits of the impedance reduction targeted at the collimators and to identify possible nonconformities, we performed a series of tune shift measurements on the newly installed primary and secondary collimators with LHC beams and quantified the agreement with predictions. As expected, the results show a significant reduction in the collimators’ impedance contribution. Additionally, the remaining discrepancy between measurements and predictions is investigated with 3D numerical simulations by using the Wakefield Solver of Computer Simulation Technology.

The performance and stability of radio-frequency quadrupoles (RFQs) depend critically on the structural integrity of their electrodes (vanes or rods), which are subjected to high-intensity ion beam exposure during accelerator operation. This study investigates the sputtering induced vane erosion on the European Spallation Source (ESS) RFQ, a critical component of the ESS linear accelerator. Particle tracking simulations for the determination of RFQ beam loss profiles were coupled to sdtrimsp software (static-dynamic transport of ions in matter sequential-parallel processing) modeling to estimate the sputtering yield distribution and the resulting erosion rates under nominal operating conditions. Methodology validation and benchmarking was performed using quartz crystal microbalance (QCM) measurements employing proton (2, 6 keV) and argon (${\mathrm{Ar}}^{+}$ 2 keV, ${\mathrm{Ar}}^{6+}$ 36 keV) ion beams with incident angles of 0°–70°. The QCM experiments were used to benchmark sdtrimsp software simulation parameters for the calculation of sputtering yields and total electrode erosion rates across the energy and angular ranges relevant to the ESS RFQ. The results and conclusions are extended to RFQs employed for heavy-ion acceleration providing insights into long-term stability and performance degradation. The results indicate that heavy-ion irradiation leads to significantly higher sputtering yields and erosion rates compared to protons. It is estimated that the increased erosion rates result in critical frequency perturbations in RFQ cavities especially in high current or cw configurations that need to be effectively compensated.

In recent years, ultrahigh dose rate (FLASH) radiotherapy has become a novel cancer treatment technique because of its similar tumor-killing efficacy as conventional particle therapy while significantly protecting normal tissues. However, due to the limitation of the number of particles, achieving FLASH condition in a compact heavy-ion synchrotron requires a short spill time of tens of milliseconds, which is challenging for the conventional rf-KO method. To tackle this challenge, we introduce autoresonance into the third-order resonant extraction for the first time, offering an alternative to the conventional approach of merely increasing the excitation amplitude. Resulting from a strong detuning effect, a frequency sweeping excitation with small amplitude can drive the entire beam into the autoresonant state, thus enabling rapid beam extraction within a single sweeping period. Compared with the conventional method, this innovative method requires only the addition of an octupole magnet. At the same time, conventional slow extraction rf-KO employs a repetitive multicycle frequency sweeping excitation, a specific particle resonates when the sweeping frequency aligns with its tune. In contrast to the autoresonance rf-KO, which engages the entire beam in resonance simultaneously. In this research, the autoresonance threshold of a particle in the presence of sextupole and octupole magnetic fields is analyzed, and the single particle simulation shows good agreement with the theoretical formula. Furthermore, the autoresonance-based rapid extraction process is simulated and studied, showing the possibility of millisecond scale beam extraction.