Twiss parameterization proposed by Courant and Snyder is a keystone of accelerator physics. Several authors have extended it later to the case of the fully coupled betatron motion and synchrobetatron motion of a coasting beam. A few proposals have been made as well how to construct a parameterization which is fully symmetric with respect to all three spatial degrees of freedom. The key point for each of them is to find a similarity transformation which turns the transport matrix into a block-diagonal form with $2\times 2$ cells. In the present work, this approach has been considered in detail. It is based on the idea initially proposed by Mais and Ripken for transport matrix eigenvalue calculation only. It shows how to introduce a symmetric Twiss-like parameterization and an emittance concept for an arbitrary symplectic $6\times 6$ matrix. The resulting parameterization can be reduced to the well-known Lebedev-Bogacz parameterization in case of $4\times 4$ matrix. Special attention has been paid to the intrinsic ambiguity existing in the Twiss parameterization of a coupled motion.

Vacuum breakdown in accelerator structures is a critical challenge that occurs under high electric fields. In environments subjected to hydrogen ion irradiation or high beam losses, such as in radio-frequency quadrupoles, residual hydrocarbons from the vacuum may result in carbon contamination of the metal surfaces from charged particle induced cracking. Under these conditions, it has been assessed that surface carbon contamination leads to a decrement of the surface electric field holding properties. This study extends the latest research by exploring the efficacy of oxygen plasma cleaning (OPC) on metal electrodes irradiated by low-energy hydrogen ion beam with the purpose of reducing surface carbon contamination. OPC treatment has been employed on different metals, namely, copper beryllium (CuBe), oxygen-free copper (Cu-OFE), and stainless steel (SS316LN). Treated electrodes have been tested for electric field performance in a dc pulsed system and results compared with nonirradiated electrodes and irradiated ones without OPC treatment. The study indicates a significant reduction in carbon contamination by OPC, enough to allow irradiated materials to achieve performances comparable with the electric field strength of raw surfaces. Moreover, it has been observed that stainless steel samples had some alteration on the surface chemistry that enhanced the material’s ability to sustain high electric fields while decreasing vacuum arcing events. Notably, OPC treated SS316LN electrodes surpassed the performance value of untreated ones, demonstrating the potential of plasma treatments in extending the operational performance of accelerator components.

In electron storage rings, it is possible to increase the bunch length by applying phase modulation to the radio-frequency accelerating field by choosing appropriate parameters for the modulation. Such a bunch lengthening effect improves beam parameters such as beam lifetime, which can help us achieve better beam stability. It is well known that the modulation frequency around the double synchrotron frequency is effective in lengthening the bunch. The dependence of bunch lengthening on modulation frequency, the so-called detuning property, has a peak around the double synchrotron frequency with a frequency width that depends on the modulation amplitude. Nonlinear effects due to phase modulation lead to a peak frequency shift in a negative direction from the double synchrotron frequency, accompanied by an asymmetric peak shape. Beam current also affects the properties of the detuning condition of such bunch lengthening. We investigated the detuning property using a theoretical model and systematic measurements at the electron storage ring Karlsruhe Research Accelerator, and we verified the qualitative agreement between the experiments and the theoretical model. The macroparticle simulations have confirmed the agreement.

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.

Developing multifrequency acceleration systems is crucial for optimizing beam dynamics in high-brightness particle beams, particularly for minimizing energy spread, manipulating bunch length, and facilitating beam bunching. This paper introduces a novel bimodal radio frequency (rf) cavity design that integrates both fundamental and harmonic modes within a single structure, offering enhanced spatial efficiency and improved operational flexibility for multifrequency rf systems. Unlike traditional designs, our cavity enables independent and simultaneous operation of each mode, along with effective suppression of higher-order modes (HOMs), which is critical for high-current beam stability. This breakthrough addresses significant challenges in bimodal cavity technology, such as intermode tuning coupling, rf-driving coupling, and effective HOM damping, providing essential solutions for high-current beam applications. Our work opens new research avenues in advanced rf cavity design, with significant implications for the future of high-brightness beam technologies, including advanced accelerator designs and improved beam quality.

This paper presents a radio frequency (rf) control system with attosecond resolution based on a carrier suppression interferometer operating a superconducting cavity at the Cryo Module Test Bench (CMTB). This novel application of the carrier suppression detector extends conventional heterodyne methods and improves the residual jitter of the regulated rf field in the cavity by more than one order of magnitude. The cavity operated at 1.3 GHz with a gradient of $8\mathrm{MV}/\mathrm{m}$ and a loaded quality factor of ${10}^7$. The setup achieved out-of-loop phase noise detection values of $\mathcal{L}=-180\mathrm{dBc}/\mathrm{Hz}$ at 10 kHz and $\mathcal{L}=-165\mathrm{dBc}/\mathrm{Hz}$ at 100 Hz with a time resolution of 189 as within an offset frequency range from 10 Hz to 1 MHz. The phase noise budget of subcomponents such as in-loop and out-of-loop detectors, high-power drive, microphonics, and the reference source is reported. The facility rf reference phase noise in the offset frequency range from 1 to 100 kHz is identified as the key noise contributor. Furthermore, the narrow-band cavity reduces the phase jitter experienced by the beam to just 116 as. The presented research combining conventional receivers with carrier suppression detectors in continuous wave operation is a key milestone toward attosecond resolution, in particular relevant for pump-probe experiments in free-electron laser facilities.

Symplectic simulation of space-charge effects is crucial for the design and operation of high-intensity particle accelerators. Traditional methods for simulating these effects are often computationally expensive, resulting in significant overhead. In this work, we introduce a generative model based on a U-Net architecture within a generative adversarial network framework to efficiently simulate space-charge effects. The model is trained to predict the transverse multiparticle space-charge Hamiltonian, which can be physically computed using a gridless spectral method. The one-step symplectic transverse transfer map for the particles is then obtained by differentiating the predicted Hamiltonian. Benchmarking results demonstrate that this generative model achieves an order of magnitude higher computational efficiency compared to the spectral method, providing a highly efficient alternative for simulating space-charge effects with a large number of particles. By maintaining symplecticity, the model effectively preserves the phase-space structure and mitigates nonphysical errors in long-term simulations. This model has been integrated into jutrack, a novel autodifferentiable accelerator modeling code developed in the julia programming language.

We present a method to construct high-order polynomial approximate invariants (AI) for nonintegrable Hamiltonian dynamical systems and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps expressed as square matrices, AIs can be constructed order by order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

Particle accelerators have played a pivotal role in scientific research, medical applications, and industrial processes. However, conventional radio-frequency accelerators face limitations due to their large size, high cost, and dependence on external microwave sources. This paper presents a novel linear accelerator design that integrates a high-power microwave source directly into the accelerator structure, eliminating the need for external drivers and enabling a more compact, cost-effective, and simplified system. The proposed design employs an X-band backward wave oscillator driven by a 50 keV hollow continuous electron beam. The generated microwave power is coupled into a central X-band standing-wave acceleration structure via a radial coupler. Simulations demonstrate that a witness beam passing through this structure can be accelerated from 50 keV to over 4 MeV across 10 acceleration cells. This work serves as a foundational study on integrated accelerator concepts, offering a pathway toward more efficient, scalable, and versatile particle acceleration systems.

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.

Recent studies have actively explored the feasibility of a novel storage ring light source based on the steady-state microbunching (SSMB) mechanism. Many interesting investigations have been limited to single-particle or pure-optics effects. In SSMB storage rings, laser modulators, consisting of an undulator and a copropagating laser beam, are utilized to manipulate the longitudinal bunch length at the radiator position. When the electron bunch traverses the modulator undulator, it emits coherent undulator radiation around the resonant wavelength with respect to the modulation laser wavelength. To increase the intensity of the modulation laser, an enhancement cavity can be used. Within the enhancement cavity, the modulation laser field is confined in a closed path, allowing the intracavity power to be accumulated and enhanced. Within this cavity, not only is there an accumulated modulation laser from external injection, but also coherent undulator radiations—both of which influence the dynamics of the electron beam on subsequent turns. In this paper, we develop a simple model to analyze the electron beam dynamics in laser modulator cavities, including the effects of finite loss due to mirrors in the cavity and the externally injected laser power required to compensate for this energy dissipation, as well as the dynamical effects of coherent undulator radiation accumulated in the cavity over multiple turns. This model also allows the estimatation of the radiation characteristics in the radiator of the SSMB storage ring. Our method combines the beamline transfer matrices with a low-gain free-electron-laser oscillator model. The advantage of this approach lies in its ability to provide quick estimates for the aforementioned dynamical effects. We then discuss the feasibility of three recently proposed scenarios, namely, the amplifier SSMB, the frequency-beating SSMB, and the harmonic SSMB, in the presence of the aforementioned dynamical effects. The analysis indicates that all three scenarios remain feasible under the current preliminary design parameters.

Beams of radioactive heavy ions allow researchers to study rare and unstable atomic nuclei, shedding light on the internal structure of exotic nuclei and on how chemical elements are formed in stars. However, the extraction and transport of radioactive beams rely on time consuming expert-driven tuning methods, where hundreds of parameters are manually optimized. Here, we introduce a system that employs artificial intelligence (AI), specifically utilizing Bayesian optimization, to assist in the transport process of radioactive beams. We apply our methodology to real-life scenarios showing advantages when compared with standard tuning methods. This AI-assisted approach can be extended to other radioactive beam facilities around the world to improve operational efficiency and enhance scientific output.

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.

Angular streaking experiments enable for experimentation in the attosecond regions. However, the deployed time-of-flight (TOF) detectors are susceptible to noise and failure. These shortcomings make the outputs of the TOF detectors hard to understand for humans and further processing, such as, for example, the extraction of beam properties. In this article, we present an approach to remove high noise levels and reconstruct up to three failed TOF detectors from an arrangement of 16 TOF detectors. Due to its fast evaluation time, the presented method is applicable online during a running experiment. It is trained with simulation data, and we show the results of denoising and reconstruction of our method on real-world experiment data.

In typical studies of collective effects in a storage ring, an important assumption is that the longitudinal bunch length remains constant over one turn, which is referred to as the adiabatic approximation. This approximation is reasonable for conventional storage rings. However, for extremely short bunch length storage rings, such as steady-state microbunching storage ring, the global phase slippage is very small, and the local or partial phase slippage can significantly influence the longitudinal dynamics of the bunch. Consequently, the bunch length can vary greatly around the ring, and the adiabatic approximation no longer holds. In this work, we investigate the microwave instability caused by the coherent synchrotron radiation, which represents one of the dominant collective effects in short bunch storage rings, beyond the adiabatic approximation. We present a general formula for the instability threshold considering the variation of longitudinal optics around the ring and offer valuable guidance for the design of extremely short bunch storage rings. Our results show that depending on the distribution of the partial phase slippage, the instability threshold of a real lattice can be increased by a factor of 2 or even more compared to the classical prediction.

High-intensity proton accelerators are utilized for neutron, neutrino, and hadron sources. Increasing the beam intensity is important for science that utilizes these particles. However, as beam intensity increases in these proton accelerators, beam instability has emerged as a limiting factor. Coupled-bunch instability, resulting from impedance with frequency components near or below the revolution frequency, stemming from the electrical resistance of beam chambers, ceramic chambers in rapid cycling synchrotrons, and kicker magnets, poses a significant challenge in these proton accelerators. The oscillation frequency of beams observed during operation with chromaticity is considerably higher than the impedance frequency. Space charge forces exhibit significant strength, with a tune shift exceeding 0.1 as an absolute value. In single-bunch behavior, space charge forces dominate, influencing the oscillation modes of instability. It is inevitable that the effect will extend to coupled-bunch modes. This paper provides a theoretical discussion on the coupled-bunch instability of beams subjected to intense space charge forces.

High efficiency is essential for plasma-wakefield accelerators to be a cost-effective alternative in high-power applications, such as a linear collider. However, in a plasma-wakefield accelerator, the beam-breakup instability can be seeded by a transverse offset between the driver and trailing bunch. This instability, which rapidly increases the oscillation amplitude of the trailing bunch, grows with higher power-transfer efficiency from the driver to the trailing bunch [V. Lebedev et al., Phys. Rev. Accel. Beams 20, 121301 (2017)]. In this paper, we use particle-in-cell simulations to investigate the efficiency–instability relation that constrains the driver-to-trailing-bunch power-transfer efficiency in beam-driven plasma accelerators. We test the relation using a grid of simulations across all parameters that affect the beam-breakup instability, assuming a uniform accelerating field (optimal beam loading) and no ion motion. We find that the previously proposed efficiency–instability relation represents a lower limit on the strength of the instability for a given efficiency. For each normalized wake radius, only a certain accelerating field reaches this lowest value of the transverse instability; deviating from this point can increase the growth rate by several orders of magnitude. Finally, we highlight how the oscillation-amplitude growth of the trailing bunch can be reduced or damped with an initial uncorrelated energy spread and the presence of ion motion.

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 analysis of plasma wakefield acceleration experimental measurements, particularly in the characterization of photons emitted through the betatron radiation mechanism, requires the development of accurate numerical models. These computational models are crucial for supporting modern instrumentation designed to measure the single-shot, double-differential angular-energy radiation spectra resulting from interactions between beams and plasmas. Motivated by the needs of such applications, this paper presents detailed numerical models of betatron radiation generated in beam-plasma acceleration experiments. These models are based on the integration of the Liénard-Wiechert (LW) potentials, applied to computed particle trajectories. The particle trajectories are generated using three distinct methods: first, by tracking particles through idealized fields in the blowout regime of PWFA; second, by obtaining trajectories using the fast quasistatic particle-in-cell (PIC) code quickpic; and third, obtaining trajectories from the fully self-consistent PIC code osiris. To ensure the accuracy and reliability of these models, the paper includes various benchmark tests using analytical expressions, as well as employing the PIC code epoch, which takes an alternative approach by using a Monte Carlo quantum electrodynamics (QED)-based radiation model. Additionally, the paper presents simulations of the expected experimental betatron radiation spectra, taking into account parameters relevant to PWFA and plasma photocathode experiments at the SLAC FACET-II facility.

Transverse stabilization of the beam is crucial for optimizing the performance of a particle accelerator, regardless of its application. The most common method for minimizing transverse beam jitter is the Balakin-Novokhatsky-Smirnov (BNS) damping technique. Although this method has been successfully implemented worldwide, it has limitations since a significant fraction of the accelerating structures are operated off crest. In this work, we propose an alternative approach to induce the required energy spread, utilizing the natural curvature of the accelerating rf field in combination with a relatively long bunch and a longitudinal wakefield. This approach achieves strong damping of the transverse beam oscillations, similar to BNS damping, while simultaneously optimizing beam quality and maximizing acceleration efficiency. We have applied this method to the design of the Future Circular Collider injector linacs, designed to reach a beam energy of up to 20 GeV. However, this method is general and can be applied in principle to any accelerator.