Automatic differentiation is a powerful tool for computing derivatives of simulation results with respect to given parameters. In this Letter, we have applied this tool to investigate the instability of a dynamical system governed by 21 ordinary differential equations. This second-order instability (named envelope instability) is driven by space-charge effects and has a significant impact on the operational regimes of particle accelerators. Our study delves into the three-dimensional envelope instability, incorporating both transverse and longitudinal coupling. Conventionally, analyzing this complex system would necessitate solving 441 ordinary differential equations, which is computationally intractable. However, by employing automatic differentiation, we were able to track only 21 equations. This approach allowed us to uncover an additional instability stopband, which arises from space-charge-induced coupling and has not been reported in previous studies. This research highlights the significant advantages of automatic differentiation in analyzing complicated dynamical systems involving a large number of ordinary differential equations.

In the framework of the LHC injectors upgrade project, the CERN proton synchrotron underwent hardware changes during the long shutdown 2. These changes required an update of the CERN proton synchrotron impedance model and an assessment of their impact on beam quality. In the following, the updated CERN proton synchrotron impedance model is presented and then validated with beam-based measurements, comparing impedance-induced tune shifts and instability growth rates with simulations performed with a macroparticle tracking code, pyheadtail, which includes the effects of beam-coupling impedance, betatron motion, nonlinear synchrotron motion, and space charge. The interplay between first- and second-order chromaticity, space-charge forces, and their effect on beam observables is thus studied in detail. Their respective impacts have been assessed and benchmarked with measurements to validate the PS transverse impedance model.

Studies of plasma processing for reduction of field emission in quarter-wave resonator (QWR) cryomodules are underway at the Facility for Rare Isotope Beams (FRIB), where a total of 104 QWRs are presently in operation. Driving the plasma with a higher-order mode allows for less mismatch at the fundamental power coupler and higher plasma density. The first plasma processing trial for FRIB QWRs in a cryomodule was conducted in January 2024. In-bunker cold tests of the cryomodule showed a significant reduction in field emission x-rays after plasma processing.

Highly overmoded and periodically loaded structures, such as the iris-line waveguide, offer an attractive solution for the efficient transportation of diffraction-prone THz pulses over long distances (hundreds of meters). This paper presents the full-scatter field theory that allows us to analytically derive all the spectral (modal) coefficients at the discontinuities of the iris line. The spectral analysis uses vector fields, superseding scalar field descriptions, to account for diffraction loss, polarization effects, and ohmic loss on practical conductive surfaces. An advanced application of Lorentz’s reciprocity theory, using a generalized guided-field configuration, is developed to reduce the complexity of the mode-matching problem over nonuniform sections. The used technique is quite general and applies to a wide class of structures, as it only assumes a paraxial incidence (i.e., a parabolic wave equation) along the axis of the structure. It removes the traditional assumption of very thin screens, allowing for the study of thicker screens in the high-frequency limit, while formulating the problem efficiently by scattering matrices whose coefficients are found analytically. The theory agrees with and expands previously established techniques, including Vainstein’s asymptotic limit and the forward-scatter approximation. The used formulation also facilitates accurate visualization of the transient regime at the entrance of the structure and how it evolves to reach steady state.

Radio frequency (rf) photoguns are widely used in modern particle accelerator facilities, particularly in free electron lasers (FELs), as they provide very low-emittance, high-brightness electron bunches. Presently, the rf technology mostly used for photoguns is the S-band ($\sim 3$ GHz), with typical cathode peak fields of 80–120 MV/m and maximum repetition rates of $\sim 100$ Hz. According to beam dynamics studies, the higher the peak electric fields on the cathode, the better the quality of the beam emerging from the gun. In this respect, S-band rf guns represent the state-of-the-art, both in terms of reachable cathode peak fields and repetition rates. An innovative C-band rf gun, operating at 5.712 GHz and aiming at reaching cathode peak fields larger than 160 MV/m, with repetition rates exceeding 400 Hz, has been designed, realized, and high-power tested. Its device consists of a 2.5-cell standing wave (SW) cavity with a four-port mode launcher whose overcoupled design allows it to operate with short rf pulses (300 ns). Its realization has been based on the new brazing-free technology developed and successfully tested at the Frascati Laboratories of the National Institute of Nuclear Physics (INFN-LNF, Italy). In the paper, we illustrate the design and realization performed by INFN-LNF, and its high-power rf test, which was conducted at the C-band test facility at the Paul Scherrer Institute (Switzerland).

Laser-driven ion beams offer significant advantages over radio-frequency accelerated beams, making them particularly promising for biomedical applications. Key features include their ultrashort pulse duration, on the order of picoseconds, and high peak fluxes ranging from ${10}^{11}$ to ${10}^{13}$ particles per shot. These characteristics enable the delivery of ultrahigh dose rates, potentially reaching the FLASH therapy regime. The future implementation of laser-driven ion beams in clinical settings relies on the development of advanced focusing and beam transport systems capable of precisely controlling parameters such as energy range, beam focus, and dose distribution to meet stringent therapeutic requirements. However, the integration of ultrashort laser-driven ion beams into medical treatments presents challenges, particularly due to their broad energy spectrum and high angular divergence. We present 3D simulation-based studies investigating the focusing effects of different high-current solenoid configurations on laser-plasma-accelerated proton beams. To identify the optimal focusing solution, we designed, analyzed, and compared high-current solenoids of varying dimensions and shapes, both as stand-alone magnetic elements and as part of two-solenoid focusing systems. Our analysis focuses on magnetic fields between 6 and 9 T, generated by the high-current solenoids. The study considers a proton beam with an energy range from a few MeV to 20 MeV and an initial divergence of 21°. Results are evaluated in terms of collection efficiency, beam focusing position, and beam profile. The optimized beamline configuration was then used to assess the dose distribution in a cylindrical water target with a volume of $78{\text{mm}}^3$ by calculating the absorbed dose and dose delivery rates, demonstrating the potential of laser-plasma-accelerated proton beams for radiotherapy applications.

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.

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 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.

Symplecticity of transfer maps is important for reliable evaluation of space-charge dominated beams in accelerators. Unfortunately, most simulation codes that include collective effects, such as space charge, do not use canonical phase-space variables and therefore are not symplectic in the presence of electromagnetic fields. In this paper, we present a numerical method to extract local linear symplectic transfer maps using particle tracking simulation code impact-t for space-charge dominated beams. We demonstrate this method for the photoinjector (113 MHz SRF gun) section of the Coherent electron Cooling (CeC) Proof of Principle (POP) experiment.

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.

SACLA is the world’s most compact hard x-ray free-electron laser and has been successfully and reliably operated for over a decade. To meet increasing user demands, an upgrade of the SACLA linear accelerator is planned in order to achieve a kHz-level repetition rate and enhanced beam brightness. A key component of this upgrade is a new injector, based on the existing pulsed dc gun with a thermionic cathode, which has demonstrated high beam quality, excellent stability, and simple maintenance. In this work, we present an in-depth beam dynamics study of a highly promising new SACLA injector architecture. Multistage velocity bunching, combined with one stage of magnetic compression and careful control of emittance growth, allows for up to 3 orders of magnitude of bunch compression while keeping the emittance growth at the submicron level. Our optimization approach utilizes a genetic algorithm coupled to 3D space-charge-dominated beam tracking to refine beam performance and identify optimal injector parameters. Thus, we demonstrate that the proposed injector can deliver electron beams with bunch durations and emittances comparable to those produced by the state-of-the-art $C$-band injector based on an rf photocathode gun [A. Giribono et al., Phys. Rev. Accel. Beams 26, 083402 (2023)]. Additionally, our extensive beam dynamics analysis of the dc electron gun (see part 2) provides valuable insights applicable to low-voltage continuous-wave very high frequency guns and superconducting radio-frequency guns.

Beam injection is one of the most crucial issues for next-generation light sources such as diffraction-limited storage rings. We propose a novel transparent off-axis beam injection scheme for low-emittance storage rings of future light sources. The scheme aims to achieve efficient beam injection into a narrow dynamic aperture with small injection amplitude, while minimizing perturbation to the stored beam with transparent beam injection. An in-vacuum thin eddy-current septum magnet is one of the key components of the scheme to achieve the small injection amplitude. A prototype of the magnet with an accommodating ultrahigh vacuum (UHV) chamber was designed and fabricated. Magnet performance of the prototype demonstrated that an injection amplitude as small as 3 mm is feasible, fulfilling the tight constraint of injection amplitude in off-axis beam injection for next-generation light sources. The prototype achieved a UHV pressure of better than $1\times {10}^{-7}\mathrm{Pa}$, ensuring the vacuum performance required for stable operation in storage rings.

The LHC beam dumps are responsible for the safe absorption of the Large Hadron Collider (LHC) particle beams. In 2018, the two 6.4-tonne beam dumps that had been in operation since the LHC’s startup in 2008 were removed and replaced with upgraded versions. Endoscopic inspections of these beam dumps and experimental high-intensity proton-beam irradiation of material samples raised concerns about the structural integrity of the carbon-based materials in their cores. It was therefore decided to undertake an accelerated project of dismantling and postirradiation examination of the removed dumps as part of a wider program of work to ensure the safe operation of the LHC beam dumps in the coming years. This paper describes the decommissioning process for the two beam dumps carried out at CERN between 2021 and 2023, covering the preparatory studies, practical challenges encountered, and solutions implemented. It details the establishment of an operational framework, including the preparation of the working environment, the development of a method for cutting the irradiated 12-mm-thick duplex stainless-steel vessel, and the cut sequencing. Additionally, the paper presents the findings derived from the postirradiation examination of the different carbon-based core materials subjected to deposited energy densities up to $1.5\mathrm{kJ}/\mathrm{g}$. The extruded graphite plates within the vessel exhibited a cracking pattern, which was likely due to the dynamic response of the device upon beam impact, and their retaining rings were found to be displaced. Despite minor signs of surface deterioration, the expanded graphite sheets were intact, and the isostatic graphite blocks showed no evidence of material degradation. These findings were consistent across both beam dumps. Finally, this manuscript discusses the implications of these results for the safe operation of the beam dumps during LHC Run 3 (2022–2026) and for the design and construction of Run 3 operational spares.

We propose a modified maximum-entropy (MENT) algorithm for six-dimensional phase space tomography. The algorithm uses particle sampling and low-dimensional density estimation to approximate large sets of high-dimensional integrals in the original MENT formulation. We implement this approach using Markov Chain Monte Carlo (MCMC) sampling techniques and demonstrate convergence of six-dimensional MENT on both synthetic and measured data.

At the 3-GeV rapid cycling synchrotron (RCS) of the Japan Proton Accelerator Research Complex, we have minimized the beam loss at high-intensity beam operation up to the designed beam power of 1 MW. This was accomplished through systematic numerical simulations and experimental studies conducted over 2 years from 2020 and 2022. We first focused on mitigating uncontrolled beam losses originating from the foil scattering of the circulating beam, which results in high residual radiation levels, particularly in the injection area. These uncontrolled beam losses were well mitigated by reducing the stripper foil size and optimizing the injection beam size. Subsequently, we attempted to minimize the space charge effects and the associated beam losses at 1 MW by implementing several measures, such as refining both longitudinal and transverse injection paintings, correcting betatron resonances, and optimizing betatron tunes at injection. Consequently, we reduced beam losses throughout the RCS, including the collimator area, by 80% as compared to those observed at 1-MW trial operation in 2020. The residual beam loss at 1 MW is now estimated to be well below ${10}^{-3}$, which is primarily attributed to residual foil scattering-induced beam losses. Notably, beam losses in areas other than the collimator section are uncontrolled and required to be well minimized to ensure stable operation and regular accelerator maintenance. We have considerably reduced the machine activation, achieving a 1-order-of-magnitude decrease at the collimator compared to that in 2020. This improvement has enabled the RCS to maintain more than 98% availability for user operation recently. The simulation and measurement results, demonstrating good agreement, provide a detailed understanding of the beam loss mechanism at each step and guide the implementation of effective optimizations.

The most significant advances in accelerator-based light sources (i.e., x-ray free electron lasers) are driven by the production of a kiloampere-level peak current. As a prerequisite to achieve the desired high peak current, multistage symmetric C-chicane compressors are widely utilized due to their simple geometry and effectiveness. However, during the bunch compression process, coherent synchrotron radiation (CSR) effects may lead to transverse emittance dilution, eventually hindering progress toward achieving a higher peak current. Therefore, suppressing or even canceling the CSR effects in chicane compressors is essential. In this paper, we consider a general model of a four-bend chicane and conduct an explicit point-kick analysis of the coherent synchrotron radiation (CSR) effects, based on which we derive the conditions for completely canceling the steady-state CSR (ss-CSR) kicks using analytical formulas. These results yield two novel ss-CSR-immune chicanes that feature nonsymmetric C-shape and S-shape layouts, respectively. We also demonstrate their excellent emittance preservation capabilities with particle tracking simulations. By utilizing the proposed chicanes instead of the widely used C-chicane, the CSR-induced emittance growth can be reduced by about 1 order of magnitude in an almost identical bunch compression scenario.

This paper presents the concept and design of a novel accelerator magnet consisting of two concentric rings of permanent magnets arranged in a Halbach layout. By replacing one component, the device can be converted to any transverse multipole configuration. By the individual rotation of the two rings, both the strength and the direction of the field pattern can be continuously tuned in a wide range, including the special case of polarity reversal. The tuning range can be changed by a parametric change of the design. The device is split into two halves and can be easily opened to allow for its installation and removal around an existing beampipe. The performance of a quadrupole demonstrator prototype is presented, including measurement results of field quality, integrated gradient and hysteresis, and discussion of sensitivity to the remanent magnetization of the permanent magnets.

The Diamond-II storage ring upgrade will provide users with 1–2 orders of magnitude increase in brightness over the existing Diamond facility, as well as double the number of straight sections to allow for the installation of additional beamlines. A key performance requirement for the upgrade will be to provide a quasitransparent top-up injection scheme. The ring was originally designed to use a single-bunch aperture sharing injection scheme, in which short stripline kickers are used to kick the injected bunch into the storage ring’s dynamic aperture, while the kick remains weak enough to avoid displacing the existing stored bunch outside the acceptance. This scheme has been modified to implement a kick-and-cancel method to place the stored bunch back on axis and leave only the injected bunch to oscillate. The kicker power supplies are thus required to provide a double pulse with a few-microsecond pulse spacing. This new method is expected to significantly improve the transparency of the injection process and reduce the recovery time for the targeted bunch, along with minimizing the transverse wakefield effects and any interactions with the transverse multibunch feedback and harmonic cavity.

The room temperature continuous wave (cw) very-high-frequency (VHF) gun is one of the candidates for the electron gun of the high-repetition-rate free-electron lasers (FELs). The VHF gun operates with a cathode gradient of $\sim 20\mathrm{MV}/\mathrm{m}$ and an accelerating voltage of $\sim 750\text{kV}$. The gun dark current emission leads to beam loss along the FEL machine, therefore, it is a critical parameter for the performance of the cw gun. In this paper, we present a systematic study of the dark current reduction of the VHF gun, including cathode region optimizations, dark current tracking simulations, and measurements. Over-inserted cathode plugs were tested in two VHF guns of different acceleration gap sizes, and both demonstrated significant dark current reduction ratios of more than two orders of magnitude.