The beam-beam interaction is one of the most critical factors determining the luminosity performance of colliders. As a circular collider utilizing the crab-waist scheme, multiple factors, such as beam-beam, crab waist, impedances, etc., interact to determine the luminosity of SuperKEKB. The interplay of these factors makes it challenging to predict luminosity via simulations. This paper presents recent advances in understanding the luminosity performance of SuperKEKB from beam-beam simulations and experiments. The key aspects affecting the luminosity of SuperKEKB, as well as the areas where further research is needed, are highlighted.

Undulator tapering based on a prebunched electron beam and a strong seed laser has been demonstrated as a promising method to greatly enhance free-electron laser (FEL) efficiency and suppress sideband instability. Different from the former works that introduce an ideal bunching or a seed laser or a self-seeding mechanism, in this paper, we propose to enhance FEL efficiency by optimizing the tapering strategy with a prebunched electron beam from echo-enabled harmonic generation (EEHG). The simulation results demonstrate that the efficiency enhancement can be effectively maintained in a quite long undulator, in which the whole FEL efficiency is improved by more than 2 orders and a clear center spectrum inherited from EEHG can be preserved. Benefitting from a stable initial phase space with an appropriate tapering strategy, the nature of stabilities can be well preserved at both time and frequency domain. Through jumping the resonant phase, an effective sideband suppression can be realized and the stability of output power is improved. In this scheme, the inhomogeneous shot noise and microbunching instability also have an important impact on efficiency enhancement and output stability. It shows a different instability feature from the first stage to the following tapered undulator in comparison to the self-seeding tapered scheme.

Regulating the arrival time of electron bunches is a crucial step to improve the temporal resolution of accelerator-based pump-probe experiments. In this regard, an electron beam regulation method called beam-based feedback, has been shown to work well for stabilizing longitudinal beam properties on pulsed accelerator machines. Essentially, the method resembles a typical design of a proportional regulator, where the plant is represented by an electron beam response matrix, and where the inversion of such matrix produces the regulator. In recent years, however, linear accelerators that operate in a continuous-wave mode have received increasing attention. One of the key features of such machines is the improved statistics of measured data, which enables a high-resolution spectral analysis of the noise acting on the electron beam. This new insight allows us to reinterpret the electron beam regulation as a disturbance rejection goal, where the disturbance is based on measured frequency data. In this work, we show that the proportional beam-based feedback method has a principal performance limitation that becomes apparent by analyzing continuous-wave data. To improve this situation, we propose a regulator design that incorporates a dynamical disturbance model formulated in the context of the so-called ${\mathcal{H}}_2$ mixed-sensitivity problem. The designed regulator demonstrated excellent agreement between the model and measurements carried out at the continuous-wave linear accelerator ELBE and showed a potential to improve the proportional regulator approach.

Short-pulse two-beam acceleration (TBA) is a promising advanced accelerator concept that may meet the luminosity and cost requirements of future large-scale linear colliders. Accelerating structures with high group velocity (on the order of 0.1c) are required in this scheme to reduce the filling time so as to efficiently accelerate the main beam with multiple bunches. In conventional accelerating structures such as metallic disk-loaded and dielectric-loaded, high group velocity usually implies low shunt impedance, which limits the rf-to-main-beam efficiency and causes a bottleneck in the overall wall-plug-to-main-beam efficiency. A dielectric disk accelerator (DDA) is a hybrid structure, which has geometry similar to metallic disk-loaded accelerators, but replaces the metal disks with dielectric disks to form the cells. Such a configuration could achieve simultaneous high group velocity and high shunt impedance, making a DDA a very attractive candidate for the short-pulse TBA approach by significantly improving power efficiency. In this manuscript, we present the start-to-end development of two $X$-band single-cell DDA prototypes, including the rf and mechanical design, fabrication, cold test, high power beam test, and post-test inspection. Of the two, a clamped structure performed better, achieving $102\mathrm{MV}/\mathrm{m}$ accelerating gradient from 320-MW input power.

A higher harmonic cavity (HHC) is popularly employed in synchrotron light storage rings to enhance the machine performance, which requires its fundamental mode resonant frequency to be tuned above the radio-frequency harmonic. However, this detuning is likely to cause Robinson instability. In this paper, we focus on a mode-zero Robinson instability driven by the fundamental mode of a passive superconducting harmonic cavity (PSHC). This instability oscillates slightly below the detuning frequency of PSHC and was recently observed in tracking simulations or experiments for several synchrotron light sources, but the underlying mechanisms have not been well understood. To investigate this instability, we modify the conventional Robinson instability equation with the inclusion of the damping effect. By solving directly this modified equation combined with performing macroparticle tracking simulation, it is found that this instability is largely dependent on the momentum compaction factor, the $Q$ value and detuning of PSHC, and even the radiation damping time. Most importantly, this instability can be significantly enhanced by a higher $Q$ of PSHC and a lower radiation damping time, which is completely contrary to the conventional Robinson instability.

We conduct a detailed measurement and analysis of a hadron beam in five-dimensional phase space at the Spallation Neutron Source Beam Test Facility. The measurement’s resolution and dynamic range are sufficient to image sharp, high-dimensional features in low-density regions of phase space. To facilitate the complex task of feature identification in the five-dimensional phase space, we develop several analysis and visualization techniques, including nonplanar slicing. We use these techniques to examine the transverse dependence of longitudinal hollowing and longitudinal dependence of transverse hollowing in the distribution. This analysis strengthens the claim that low-dimensional projections do not adequately characterize high-dimensional phase space distributions in low-energy hadron accelerators.

We present analytical and numerical studies of short-range wakefields in an L-shaped corrugated structure. This structure has variable streaking polarization and the quadrupole wakefield component is suppressed when the beam moves with equal distances to both plates. These features provide promising capability in multidimensional beam phase space diagnostic and fresh-slice applications. We first give zeroth-order analytical expressions of the longitudinal and the transverse wake functions using the conformal mapping method. Then we combine these results with the first-order approximate formulas of a single-plate structure to obtain more accurate analytical approximations of the wake functions of the L-shaped structure. In order to confirm the accuracy of the analytical model, we have developed a numerical method based on integral equations in the frequency domain for arbitrarily shaped waveguides with surface impedance boundary conditions.

Plasma waves can be used to create efficient and small-sized electron accelerators. Despite the already demonstrated success in reaching GeV-scale energy gain in the motion of electrons, laser-induced wakefields still suffer from the transverse spreading and the loss of synchronization with the accelerating particles. In this work, to tackle these problems, we propose using a two-wavelength structured laser beam with a designed angular dispersion and adjustable group velocity in free space to efficiently excite a nondiverging plasma wave. This approach allows one to generate an electron bunch with low transverse spread and reach high average acceleration gradients.

We revisit free-electron laser (FEL) equations in the presence of a planar undulator to investigate effects on longitudinal FEL dynamics upon seeding by a harmonic. For this study, we adopt slowly varying phase approximation, collective variables, and Klimontovich description of particle beams to explore the effects of harmonic seeding on low-gain saturation, low-gain amplification, and exponential growth for on-axis radiation emission. We also investigate the effects of frequency detuning and nonzero energy spread on power gain and growth rate for low-gain and high-gain FELs, respectively.

In the aspect of longitudinal beam bunching, the bunching strength can be controlled by the rf cavity phase and voltage. However, these machine parameters are different from those that interact with the beam itself. In order to gain control of the beam-cavity interaction, cavity calibration must be performed. Furthermore, it relies on fitting the beam energy gain versus cavity phase to a calibration function. Under the conventional assumption of relativistic beam conditions, the calibration function is a first harmonic sinusoidal function (a sinusoidal function with a period of $2\pi$). However, this expression is insufficient for a high-voltage bunching cavity. Due to beam acceleration inside the cavity, an energy bias and a second harmonic function should be included to modify the conventional calibration function, even for a relativistic electron beam. In this paper, we will derive this modification and provide a comparison to both the Coherent Electron Cooling Experiment and the impact-t simulation, respectively.

The crab-waist scheme becomes the baseline for future circular $e^{+}{e}^{-}$ colliders, where a large Piwinski angle is a must. It has been first found that a strong coherent head-tail instability in the vertical direction may be induced by the interplay of beam-beam interaction and ring impedance below the conventional transverse mode-coupling instability threshold. The collision would be stable only considering pure beam-beam interaction. That is to say, the new instability is a combined effect of beam-beam interaction and ring impedance. The instability can limit the performance of future colliders based on the crab-waist scheme. Mode analysis has been done to help understand the physics. Mitigation schemes are also presented and verified by analysis and simulation.

We report the high-gradient acceleration of electrons driven by a subnanosecond pulse of Ka-band Cherenkov superradiance (SR). The experiments are carried out in a combined “generator-accelerator” scheme, powered by two electron beams from a coaxial explosive-emission graphite cathode. The outer tubular beam ($\approx 300\mathrm{keV}$; $\approx 2.3\mathrm{kA}$) propagates along the periodic slow-wave structure (SWS) and generates a backward moving gigawatt-level SR pulse, which pumps a low-Q “pill-box” resonator located at the SWS input. The inner paraxial test beam ($\approx 250\mathrm{keV}$; $\approx 150\mathrm{A}$) passes through a hole in the resonator wall and is accelerated in extreme SR fields exceeding $500\mathrm{MV}/\mathrm{m}$. The energy of accelerated electrons is estimated by measuring the test beam current after it passes through aluminum filters (foils) that absorb low-energy electrons. It is shown that the test beam contains fractions with a maximum energy of 1.25 MeV, which, taking into account the pill-box length of 4 mm, corresponds to the extremely high averaged accelerating gradient of $250\mathrm{MV}/\mathrm{m}$.

We show how to construct an accelerator lattice cell that minimizes all intrinsic spin resonances. We then apply this approach to various toy electron and proton accelerators, considering, AGS-booster, AGS-like and CEPC/FCC-ee, and FCC-hh-like rings.

Magnetic field errors pose a limitation in the performance of synchrotrons, as they excite nonsystematic resonances, reduce dynamic aperture, and may result in beam loss. Their effect can be compensated by assuming knowledge of their location and strength. Established identification procedures are based on orbit response matrices or resonance driving terms. While they sequentially build a field error model for subsequent accelerator sections, a method detecting field errors in parallel could save valuable beam time. We introduce deep Lie map networks, which enable the construction of an accelerator model including multipole components for the magnetic field errors by linking charged particle dynamics with machine learning methodology in a data-driven approach. Based on simulated beam position monitor readings for the example case of SIS18 at GSI, we demonstrate inference of location and strengths of gradient and sextupole errors for all accelerator sections in parallel. The obtained refined accelerator model may support setup of corrector magnets in operation to allow more precise control over tunes, chromaticities, and resonance compensation.

Multibend magnetic bunch compressors are commonly used to produce beams with high peak current in modern accelerators that call for high-brightness beams. If not well controlled, the coherent synchrotron radiation (CSR) in the dipoles of magnetic bunch compressors can severely affect the produced beam qualities, e.g., leading to emittance dilution. In contrast to the case without bunch compression, suppression of the CSR-induced emittance growth with bunch compression can be more challenging mainly due to the difficulties of analyzing the net CSR effect that involves a varying bunch length. In this paper, with the aid of the CSR point-kick model, theoretical CSR cancelation conditions of a double-bend achromat (DBA) with bunch compression are obtained. Such conditions point to an asymmetric DBA design, having dipoles of different bending angles or different radii or both and satisfying a certain transfer matrix relation. Taking a DBA with dipoles of different bending angles as an example, it is demonstrated that the CSR-induced emittance growth can be significantly suppressed if the proposed conditions are satisfied. As a numerical demonstration of application, we implement multiple DBA cells basically satisfying the proposed conditions in a 180° arc compressor, showing promising performance in suppressing the CSR-induced emittance growth. This study suggests a new appealing way to design practical arc compressors and is promising to serve as a starting point for the design and optimization of CSR-immune arc transfer lines in energy recovery linacs and other modern recirculation accelerators.

Acceleration of polarized electron (positron) beams in a booster synchrotron may suffer from depolarization due to crossings of many spin depolarization resonances and this could limit its applications. We have studied the structure of spin depolarization resonances of a 100-km-scale booster lattice of the Circular Electron Positron Collider (CEPC). The lattice has eight arc regions with hundreds of FODO cells, interleaved with straight sections, leading to a high periodicity. Our analysis shows the contributions to the strength of intrinsic and imperfection spin resonances add up coherently near the superstrong resonances beyond 120 GeV but mostly cancel out and result in generally weak resonance strengths at lower beam energies. Detailed simulations confirm that beam polarization can be mostly maintained in the fast acceleration to 45.6 and 80 GeV but that severe depolarization may occur at even higher energies. This study suggests the possibility of acceleration of polarized electron (positron) beams to ultrahigh beam energies without the help of Siberian snakes and supports injecting highly polarized beams into the collider rings as an attractive solution for resonant depolarization measurements and longitudinally polarized colliding beam experiments for future 100-km-scale circular $e^{+}{e}^{-}$ colliders.

We improved a previously proposed method of using closed-orbit modulation for linear optics and coupling correction. Instead of fitting individual closed orbits, the improved method decomposes the orbit oscillation data into two orthogonal modes and fits the amplitudes of the modes at all beam position monitors. While the original method is limited to process around tens to a hundred orbits, the improved method can process thousands of orbits, which are easily available when alternating-current waveforms are applied to the two modulating correctors. The method has been experimentally demonstrated on the National Synchrotron Light Source (NSLS)-II storage ring.

Microscopic, or short-wavelength, instabilities are known for a drastic reduction of the beam quality and strong amplification of the noise in a beam. Space charge and coherent synchrotron radiation are known to be the leading causes of such instabilities. In this paper, we present a rigorous 3D theory of such instabilities driven by the space-charge forces. We define the condition when our theory is applicable to an arbitrary accelerator system with 3D coupling. Finally, we derive a linear integral equation describing such instability and identify conditions when it can be reduced to an ordinary second-order differential equation.