Beam-beam interactions pose substantial challenges in the design and operation of circular colliders, significantly affecting their performance. In particular, the weak-strong simulation approach is pivotal for investigating single-particle dynamics during the collider design phase. This paper evaluates the limitations of existing models in weak-strong simulations, noting that while they accurately account for energy changes due to slingshot effects, they fail to incorporate longitudinal coordinate changes ($z$ variation). To address this gap, we introduce two novel transformations that enhance Hirata’s original framework by including both $z$ variation and slingshot effect-induced energy changes. Through rigorous mathematical analysis and extensive weak-strong simulation studies, we validate the efficacy of these enhancements in achieving a more precise simulation of beam-beam interactions. Our results reveal that although $z$ variation constitutes a higher-order effect and does not substantially affect the emittance growth rate within the specific design parameters of the Electron-Ion Collider, the refined model offers improved accuracy, particularly in scenarios involving the interaction between beam-beam effects and other random diffusion processes, as well as in simulations incorporating realistic lattice models.

We investigate the rf performance of several single-cell superconducting radio-frequency cavities subjected to low temperature heat treatment in nitrogen environment. The cavities were treated at temperature $120–165°\mathrm{C}$ for an extended period of time (24–48 h) either in high vacuum or in a low partial pressure of ultrapure nitrogen. The improvement in $Q_0$ with a $Q$ rise was observed when nitrogen gas was injected at $\sim 300°\mathrm{C}$ during the cavity cooldown from $800°\mathrm{C}$ and held at $165°\mathrm{C}$, without any degradation in accelerating gradient over the baseline performance. The treatment was applied to several elliptical cavities with frequency ranging from 0.75 to 3.0 GHz, showing an improved quality factor as a result of low temperature nitrogen treatments. The $Q$ rise feature is similar to that achieved by nitrogen alloying Nb cavities at higher temperature, followed by material removal by electropolishing. The surface modification was confirmed by the change in electronic mean free path and tuned with the temperature and duration of heat treatment. The decrease of the temperature-dependent surface resistance with increasing rf field, resulting in a $Q$ rise, becomes stronger with increasing frequency and decreasing temperature. The data suggest a crossover frequency of $\sim 0.95\mathrm{GHz}$ above that the $Q$ rise phenomenon occurs at 2 K. Some of these results can be explained qualitatively with an existing model of intrinsic field-dependence of the surface resistance with both equilibrium and nonequilibrium quasiparticle distribution functions. The change in the $Q$ slope below 0.95 GHz may result from masking contribution of trapped magnetic flux to the residual surface resistance.

Future ultralow emittance rings for $e^{-}/e^{+}$ colliders require extremely high beam brightness and can thus be limited by collective effects. In this paper, the interplay of effects such as synchrotron radiation, intrabeam scattering (IBS), and space charge in the vicinity of excited betatron resonances is assessed. In this respect, two algorithms were developed to simulate IBS and synchrotron radiation effects and integrated in the pyorbit tracking code, to be combined with its widely used space charge module. The impact of these effects on the achievable beam parameters of the Compact Linear Collider (CLIC) damping rings was studied, showing that synchrotron radiation damping mitigates the adverse effects of IBS and space charge induced resonance crossing. The studies include also a full dynamic simulation of the CLIC damping ring cycle starting from the injection beam parameters. It is demonstrated that a careful working point choice is necessary, in order to accommodate the transition from detuning induced by lattice nonlinearities to space-charge dominated detuning and thereby avoid excessive losses and emittance growth generated in the vicinity of strong resonances.

A high-energy electron-positron collider has been widely recognized by the particle physics community to be the next crucial step for detailed studies of the Higgs boson and other fundamental particles and processes. Several proposals for such colliders, either linear or circular, are currently under evaluation. Any such collider will be required to reach high lumimosities, in order to collect enough data at a reasonable time scale, while at the same time coping with high rates of background particles produced from beam-beam interactions during the collisions. In this paper, we analyze the luminosity and beam-beam interaction characteristics of the Cool Copper Collider (${\mathrm{C}}^3$) and perform a comparison with other linear collider proposals. We conclude that ${\mathrm{C}}^3$ can reach the same or higher collision rates as the other proposals, without having to cope with higher beam-induced background fluxes. Thus, ${\mathrm{C}}^3$ emerges as an attractive option for a future electron-positron collider, benefiting from the collective advancements in beam delivery and final focus system technologies developed by other linear collider initiatives.

Light sources worldwide have experienced rapid growth in the last decades, pushing toward higher brightness with lower emittance to meet growing demands from the user community. The quest for higher brightness motivates the development of low-emittance ring lattices. At this point, all fourth-generation storage ring light sources employ variations of the multibend achromat (MBA) lattice. In this paper, we discuss an extension of this approach, known as complex bend achromat lattice in relation to the future NSLS-II upgrade. A detailed approach for the lattice design will be described and the developed lattice will be presented. The advantages of using our complex bend approach are evident in reaching a natural emittance as low as 23 pm at a beam energy of 3 GeV, providing a straight section of 8.4 m for long insertion devices, and acquiring a ratio of about 50% of free space with respect to the ring circumference. The design includes the use of permanent magnets largely reducing the need for power supplies. Our new approach provides an extension to the MBA concept for the next-generation light source lattice design.

The passive superconducting harmonic cavity (PSHC) scheme is adopted by several existing and future synchrotron light source storage rings, as it has a relatively smaller $R/Q$ and a relatively larger quality factor ($Q$), which can effectively reduce the beam-loading effect and suppress the mode-one instability. By using a minimum search algorithm to solve the mode-zero Robinson instability equation of uniformly filled rigid bunches, we have revealed that the fundamental mode of PSHC with a large loaded $Q$ possibly triggers the $D$-mode Robinson instability [T. He et al., Mode-zero Robinson instability in the presence of passive superconducting harmonic cavities, Phys. Rev. Accel. Beams 26, 064403 (2023)]. This instability is a mode-zero coupled bunch instability, with an oscillation frequency close to the PSHC detuning ($D$-mode). Uniquely, it is anti-damped by the radiation damping effect. In this paper, we derive analytical formulas for the frequency and growth rate of the $D$-mode Robinson instability by taking several appropriate approximations. These formulas provide crucial insights for analyzing and understanding the $D$-mode Robinson instability.

The measurement of betatron tunes is important in the studies of beam dynamics in circular accelerators. Here, we report a new method to extract the fractional tune values using revolution times of single ions stored for a few hundred turns in a heavy-ion storage ring utilizing a single time-of-flight detector. The experiment was done at the experimental Cooler Storage Ring (CSRe) in Lanzhou. The unbunched cocktail secondary beam was injected into the ring and allowed to coast without further excitation. Since the average number of simultaneously stored ions inside the 128.8 m-circumference ring was merely $\sim 20$, the obtained tune values are considered to be incoherent. Given that the revolution time of an individual ion is related to its momentum, the chromaticity of the ring could be addressed. Moreover, the data indicate a possible beam mismatch in vertical direction $\widehat{y}$ at the injection into CSRe. The new method is developed for ultralow beam intensities and is thus a sensitive approach to tune measurements. Thanks to its simplicity, the method can straightforwardly be employed at other circular accelerators by applying the same detection approach.

In this paper, a self-consistent transverse beam dynamics framework is demonstrated that incorporates acceleration into the transverse beam dynamics studies for a proton linac machine. Two focusing schemes are developed and discussed: the FODO-like scheme and the minimum aperture scheme. The FODO-like scheme is a simple scheme, requiring only one quadrupole per cavity. The scheme is analytically solved to minimize the beam size at the cavity entrance/exit and ensures a constant beam size along the lattice, with respect to adiabatic damping due to longitudinally accelerating rf cavities. The minimum aperture scheme describes the regime that matches the beam ellipse to the acceptance ellipse of a cavity, allowing for the smallest possible aperture, for a given cavity length. A simple approximation of an rf cavity map is determined to allow changes in particle energy along a lattice, and acceleration is assumed only in the longitudinal direction.

The development of long, tunable structures is critical to increasing energy gain in laser-driven dielectric accelerators (DLAs). Here we combine pulse-front-tilt illumination with slab-geometry structures assembled by precisely aligning off-the-shelf 4 mm long transmission gratings to achieve up to 200 keV energy modulation for 6 MeV injected electrons. The effective interaction length is longer than 1 mm, limited by the dephasing of the accelerated particles in the structure. The piezo-based independent mounting system for the gratings allows tuning of the gap and field distribution inside the structure.

The low-energy muon (LEM) beamline at the Paul Scherrer Institute currently stands as the world’s only facility providing a continuous beam of low-energy muons with keV energies for conducting muon spin rotation experiments on a nanometer depth scale in heterostructures and near a sample’s surface. As such, optimizing the beam quality to reach its full potential is of paramount importance. One of the ongoing efforts is dedicated to improving the already applied technique of single muon tagging through the detection of secondary electrons emerging from an ultrathin carbon foil. In this work, we present the results from installing a thinner foil with a nominal thickness of $0.5\mathrm{\mu }\mathrm{g}{\mathrm{cm}}^{-2}$ and compare its performance to that of the previously installed foil with a nominal thickness of $2.0\mathrm{\mu }\mathrm{g}{\mathrm{cm}}^{-2}$. Our findings indicate improved beam quality, characterized by smaller beam spots, reduced energy loss and straggling of the muons, and enhanced tagging efficiency. Additionally, we introduce a method utilizing blue laser irradiation for cleaning the carbon foil, further improving and maintaining its characteristics.

The European Synchrotron Radiation Facility Extremely Brilliant Source (ESRF-EBS) is the first fourth generation 6 GeV storage ring (SR) light source making use of the hybrid multibend achromat lattice, reaching a natural horizontal emittance of 140 pm rad. Further, reducing the horizontal emittance would provide a more brilliant and a higher quality photon source for the EBS users. One way of achieving this is to operate the SR off-energy. The first approach reduces the electron beam energy by $-1\%$, which gives a 121 pm rad natural horizontal emittance. To fulfill operation requirements, the full ring had to be rematched, including both the quadrupoles and the sextupoles in the linear optics correction. The off-energy settings are then tested in the SR in terms of lifetime, injection efficiency, and operability.

Cherenkov optical beam loss monitors (oBLMs) based on optical fibers are a revolutionary achievement among the monitoring systems in particle accelerators. Due to the nature of the Cherenkov phenomenon and the intrinsic characteristics of optical fibers, the photon production and fiber light transmission need to be studied to deduce the total amount of Cherenkov photons detected by the photosensors attached at the end of the system. Simulations of the Cherenkov oBLM detector system have been implemented using the fluka software with postprocessing considering the light attenuation and capture factors in the optical fiber. In addition, the study includes the longitudinal beam loss localization of the controlled beam losses produced along the CERN Linear Electron Accelerator for Research (CLEAR) test facility line. In this paper, the Cherenkov photon detection by an oBLM installed in the CLEAR facility is simulated, analyzed, and compared with experimental data.

Machine learning has emerged as a powerful solution to the modern challenges in accelerator physics. However, the limited availability of beam time, the computational cost of simulations, and the high dimensionality of optimization problems pose significant challenges in generating the required data for training state-of-the-art machine learning models. In this work, we introduce cheetah, a pytorch-based high-speed differentiable linear beam dynamics code. cheetah enables the fast collection of large datasets by reducing computation times by multiple orders of magnitude and facilitates efficient gradient-based optimization for accelerator tuning and system identification. This positions cheetah as a user-friendly, readily extensible tool that integrates seamlessly with widely adopted machine learning tools. We showcase the utility of cheetah through five examples, including reinforcement learning training, gradient-based beamline tuning, gradient-based system identification, physics-informed Bayesian optimization priors, and modular neural network surrogate modeling of space charge effects. The use of such a high-speed differentiable simulation code will simplify the development of machine learning-based methods for particle accelerators and fast-track their integration into everyday operations of accelerator facilities.

Plasma wakefield acceleration provides ultrahigh acceleration gradients of tens of GeV/m, providing a novel path toward efficient, compact, TeV-scale linear colliders, and high brightness free electron lasers. Critical to the success of these applications is demonstrating simultaneously high gradient acceleration, high energy transfer efficiency, and preservation of emittance, charge, and energy spread. Experiments at the FACET-II National User Facility at SLAC National Accelerator Laboratory aim to achieve all of these milestones in a single-stage plasma wakefield accelerator, providing a 10 GeV energy gain in a $<1\mathrm{m}$ plasma with high energy transfer efficiency. Such a demonstration depends critically on diagnostics able to measure emittance with mm mrad accuracy, energy spectra to determine both percent level energy spread, and broadband energy gain and loss, incoming longitudinal phase space, and matching dynamics. This paper discusses the experimental setup at FACET-II, including the incoming beam parameters from the FACET-II linac, plasma sources, and diagnostics developed to meet this challenge. Initial progress on the generation of beam ionized wakes in meter-scale hydrogen gas is discussed as well as commissioning of the plasma sources and diagnostics.

The measurement of phase space has always been an important topic in the field of accelerator physics, playing an indispensable role in understanding the beam dynamics. The phase space distribution of the injected beam is crucial for optimizing the multiturn accumulation injection process in synchrotrons. However, directly and accurately measuring the phase space distribution is a challenging task. In this study, we propose an innovative tomographic algorithm based on the measurement data of the accumulated beam profile obtained from the wall current monitor (WCM) in a synchrotron, to reconstruct the longitudinal phase space of the injected beam. Simulations were conducted for various initial distribution scenarios, and the results showed that this algorithm can achieve a difference of about 4% in the rms momentum spread between the initial and reconstructed phase space distribution of the injected beam. This algorithm has been applied to the China Spallation Neutron Source and successfully measured the momentum spread of the injected beam. Machine studies considering the phase error of the injected beam showed a high consistency between the reconstructed beam profiles and the measurement results from the WCM on Rapid Cycling Synchrotron. The research results demonstrate that this algorithm can be an effective approach for measuring the momentum distribution of the injected beam in a synchrotron. Furthermore, this method also has the potential to be extended to reconstruct the transverse phase space of the injected beam.

The novel experimental system “S-POD” (Simulator of Particle Orbit Dynamics) is employed to explore the stability of short hadron bunches in high-intensity linacs. In a previous study with the S-POD [M. Goto et al., Phys. Rev. Accel. Beams 25, 054201 (2022)], a static potential was used to focus the bunch in the longitudinal direction. We here make a step forward to include the possibility of pure synchrotron resonance, introducing periodic modulation to the longitudinal potential well. The modulation period was taken a half of the transverse alternating-gradient focusing period, which reflects the most typical lattice condition of a drift-tube linac. Detailed stability maps are constructed to reveal dangerous parameter regions where serious beam loss may occur due to resonance. We reconfirm the existence of various betatron and synchrobetatron resonance stop bands whose widths and locations change in tune space depending on the bunch intensity. It turns out that the periodicity of the longitudinal focusing potential brings about no pronounced effect on the resonance feature; the result is very similar to what we obtained in the previous study with a static longitudinal potential. As long as the lattice periodicity mentioned above is maintained, no serious noncoupling synchrotron resonance appears even with a high synchrotron phase advance above 90° per unit alternating-gradient cell. Severe envelope instability may, however, be excited in the longitudinal direction if the axial focusing force includes error components that affect the original lattice periodicity. The experimental observations can be explained with the stop-band diagram free from the concept of incoherent tune spread.

In electron guns, generating high-intensity beams comes with the cost of increasing the number of secondary ions produced by the residual gas ionization which can be a limiting factor in the cathode lifetime. However, it is often overlooked that the longitudinal potential generated by the beam can be the main factor influencing secondary ions to drift back toward the source and limit the maximum beam intensity. Using 3D simulations, this paper shows how the flux of trapped ions depends on the beam parameters. The results provide a practical framework that can be used as a guide in the design of the electron gun focal point to mitigate the ion back bombardment.