Radio-frequency cavities used in modern particle accelerators operate in ${\mathrm{TM}}_{m10}$-like modes composed of a single, dominant multipole of order $m$; $m=0$ modes are used for the longitudinal acceleration of a particle beam and $m\ne 0$ modes for controlling transverse beam dynamics. The practical design of the latter, however, can be complex and require extensive analysis through the iteration of both approximate mathematical models and computationally expensive simulations to optimize the performance of the structure. In this paper we present a new, systematic method for designing azimuthally modulated rf cavities that support modes composed of any number and magnitude of user-specified transverse multipoles, either with or without a longitudinally accelerating component. Two case studies are presented of rf cavity designs that support modes composed of a longitudinally accelerating field in addition to a single transverse multipole, and designs that support modes composed of two transverse multipoles. We discuss generalizing the discoveries and conclusions from the two case studies to designing cavities that support modes composed of any number of multipoles. The theoretical work is verified with analysis of 3D simulations and experimental measurements are presented of a cavity operating in a 3 GHz mode that simultaneously longitudinally accelerates and transversely focuses a beam.

Several proposals to measure a possible small electric dipole moment (EDM) of charged particles aligned with the spin and the well-known magnetic dipole moment (MDM) are based on the concept to circulate bunches with an initial polarization in the horizontal plane and to observe the buildup of a vertical spin component caused by the EDM. Most proposals aim at operating the ring with “frozen spin,” such that, with an MDM only, the spin remains aligned with the trajectory. The signature of a finite EDM is the buildup of a vertical spin component. Machine imperfections may lead as well to a vertical spin buildup, which can be misinterpreted as an EDM and thus limit the sensitivity of the experiment. For that reason, a good understanding of spin dynamics is mandatory to estimate and limit such systematic errors in the measurement. In this paper, a coordinate system attached to the trajectory is introduced to expand the spin. This is of particular interest for fully electric EDM rings operated at the “magic energy” to satisfy the frozen spin condition. The procedure is used for a straightforward analysis of geometric phase and other second order effects, which limit the possible sensitivity, i.e., the smallest EDM which can be detected in presence of systematic effects.

The aim of this study is to make the parameter space of zero-current phase advance greater than 90° available to the high-intensity linear accelerator (linac) design and operation, which has been excluded to avoid the envelope instabilities and particle resonances. The earlier study of Cheon et al. [Nucl. Instrum. Methods Phys. Res., Sect. A 1013, 165647 (2021)] reported that the spinning of ion beams can mitigate the fourth-order particle resonance and the associated envelope instability in high-intensity linacs. In the present work, we further investigate the effects of beam spinning on the fourth-order particle resonance in the case of 3D bunched beams with fast acceleration. We also explore the space-charge-driven resonance in the longitudinal plane and confirm that the fourth-order particle resonance can be manifested when the longitudinal zero-current phase advance ${\sigma }_{z0}$ is larger than 90° and the depressed phase advance ${\sigma }_z$ is less than 90°, similar to the transverse case. The beam spinning effects are examined in both transverse and longitudinal planes during beam acceleration through periodic solenoid and quadrupole-doublet focusing channels.

A two-dimensional boundary element method for calculating the impedance of infinitely long cryogenic vacuum chambers of general cross section is presented. The formulation is based on combining Kirchhoff’s boundary integral representation of an electromagnetic field with the surface impedance boundary condition for the anomalous skin effect, which can occur in metals at cryogenic temperature. As a result, the electromagnetic field in the chamber is expressed as a superposition of the direct and indirect space charge fields and resistive-wall wakefield. This feature allows us to compute the corresponding three impedance contributions separately. This method does not assume a specific transverse charge density such as uniform and Gaussian distributions as well as the ultrarelativistic approximation. A technique for computing the impedances and the form factors in the method is also described. The presented method is applied to circular, rectangular, elliptical, and racetrack-type vacuum chambers. The geometric effect of the cryogenic vacuum chamber cross section on the resistive-wall impedance is shown. The effect of beam velocity is demonstrated for the racetrack-type cryogenic vacuum chamber.

In this paper, we discuss different approaches for the estimation of transverse bunch characteristics, namely, tune and chromaticity, using Schottky-based diagnostics. In particular, we show how, depending on the signal quality and the availability of other instruments or information sources, we can choose appropriate strategies combining both spectrum fitting procedures and explicit parameter calculations. In addition, we revisit and formally derive the expression that relates the chromaticity with the width of the Schottky spectral sidebands, discussing the rigorous meaning of this width and in which conditions it can be applied. Results obtained using the proposed approaches are compared with the standard techniques for different fills in the LHC.

The Hadron Experimental Facility at the Japan Proton Accelerator Research Complex is used for various nuclear and elementary particle physics experiments that use secondary particle beams. The secondary-particle production target is a key element for the generation of particles such as kaons and pions. To increase beam power, a new target was developed and installed. The target, which is made of gold and indirectly cooled with water, was designed so that the maximum stresses do not exceed the allowable stresses determined based on the pressure vessel standard. 95 kW is considered to be the maximum power of the primary proton beam for a 5.2-s beam duration. The new target was stably operated up to a power of 65 kW. In addition, beam position estimation based on multipoint temperature measurements of the target was demonstrated.

The production of high spectral brilliance radiation from electron beam sources depends critically on the electron beam qualities. One must obtain very high electron beam brightness, implying simultaneous high peak current and low emittance. These attributes are enabled through the use of very high field acceleration in a radio-frequency (rf) photoinjector source. Despite the high fields currently utilized, there is a limit on the achievable peak current in high brightness operation, in the range of tens of Ampere. This limitation can be overcome by the use of a hybrid standing wave/traveling wave structure; the standing wave portion provides acceleration at a high field from the photocathode, while the traveling wave part yields strong velocity bunching. This approach is explored here in a C-band scenario, at field strengths ($>100\mathrm{MV}/\mathrm{m}$) at the current state-of-the-art. It is found that one may arrive at an electron beam with many hundreds of Amperes with well-sub-micron normalized emittance. This extremely compact injector system also possesses attractive simplification of the rf distribution system by eliminating the need for an rf circulator. We explore the use of this device in a compact 400 MeV-class source, driving both inverse Compton scattering and free-electron laser radiation sources with unique, attractive properties.

Because of the inherent value of high-energy particle beams for the study of quantum electrodynamics effects, it is of great importance to accurately model the physics in numerical simulations. Numerical effects may alter the dynamics of a simulation and may change the physics of energy losses on account of the radiation reaction (RR) force. In this work, the numerical Cherenkov effect in combination with the RR force are analyzed in the vacuum propagation of an ultrarelativistic electron bunch. It is revisited that the use of the standard Yee solver in the present setup triggers the numerical Cherenkov instability. With the instability at hand, the simulation results of the Yee solver are compared to data obtained by the $X$-dispersionless Maxwell solver, also known as the rhombi-in-plane (RIP) solver. There, the numerical instability is suppressed by several orders of magnitude. Afterward, the impact of radiation reaction on the dynamics is studied for both cases. It is shown that the combination of the Yee solver and the RR force enhances the error significantly and the electron bunch loses about 90% of its energy as a result. These huge energy losses can be observed only if both the Lorentz force and the RR force are enabled in the code. In contrast, the RIP Maxwell solver is not plagued by these issues and accurately calculates the dynamics of the electron bunch.

Accurate numerical modeling of normal-conducting accelerator magnets requires a reliable characterization of the iron saturation and hysteresis as well as a precise knowledge of the magnet geometry as built. Computations of the field quality are not easily achieving the accuracy required by the accelerator operation, particularly for eddy-current effects in fast-ramping magnets. This paper proposes a (measurement) data-driven model for the nonlinear magnetization of normal-conducting magnets. The model adopts a volume integral formulation compatible with eddy-current simulations. A two-step updating procedure is applied. The first step is the fitting of material parameters directly in the magnet model. The second step is the updating of the magnetization by measurements of the integral field harmonics. The result is a full-order updated model that can be employed in static or dynamic simulations. Finally, the procedure is validated on an iron-dominated, normal-conducting magnet.

We examine the effect of higher-harmonic passive cavities (HHCs) on the beam response to rf noise. Upon invoking certain assumptions to make the problem tractable, we employ Vlasov methods to show that when the dipole approximation applies the HHCs have a generally limited impact. Beam loading in the main cavity is included in the analysis. We illustrate our results and the limitations of our model in application to the Lawrence Berkeley National Laboratory ALS (Advanced Light Source) and the future ALS Upgrade (ALS-U) offering validation against macroparticle simulations.

We derive evolution equations for the first and second moments of an initially mismatched, coupled, and displaced arbitrary Gaussian phase-space distribution under the influence of decoherence due to amplitude-dependent tune shift. Moreover, we find expressions for the asymptotic values of the beam matrix and the emittance and use them to evaluate error tolerances for injection.

We calculate equilibrium emittances and damping times due to the emission of synchrotron radiation for coupled storage ring lattices by evaluating the projections of the commonly used synchrotron radiation integrals onto the normal modes of the coupled motion. Orbit distortion is included by calculating off-axis contributions to the radiation integrals. We provide explicit formulas for fast forward calculation, which have been implemented into the interactive lattice design code opa.

With the development of high-performance photon sources which have extremely low emittance, autotuning magnet girders have drawn more and more attention, especially for diffraction-limited storage rings and free-electron lasers. The biggest challenge is to simultaneously obtain high stability and high flexibility. In this paper, an autotuning magnet-girder prototype has been designed and developed. Topological optimization, multipoint supports, and locking systems have been applied for magnet-girder design to improve the stability. The modal analysis accords with the vibration test well. The natural frequency of the magnet-girder assembly is deduced as high as 45.6 Hz, which demonstrates good stability. Ball-cam movers have been chosen as adjustment mechanisms, and a closed-loop control scheme has been used to pursue high accuracy. The kinematic resolution is better than $1\mu \mathrm{m}$, and the accuracy is better than $1\mu \mathrm{m}$ within the adjusting range of $\pm 5\mathrm{mm}$. Besides, it can eliminate most of the calibration, which can save much manpower and time. The tests demonstrate that the magnet girder can be used for beam-based girder alignment with high stability and high accuracy.

We show that under certain conditions a longitudinal mismatch between an electron and a hadron beam in a coherent electron cooling (CeC) scheme creates a circular attractor in the longitudinal phase space of the cooled hadrons. Formation of an attractor completely stops the cooling and results in anticooling (“heating”) causing small synchrotron amplitudes to grow to the attractor’s radius, rather than being damped. We present a theory of this effect, compare the analytical results with simulations and derive tolerances to possible sources of the longitudinal mismatch. We further show that under certain conditions a “weak” attractor, affecting hadrons with large synchrotron amplitudes, can appear in the hadrons’ longitudinal phase space and explain that formation of such an attractor does not require the presence of any mismatches.

The heavy heat load on optical components from the normal planar undulator has become a serious problem in the synchrotron radiation light source, especially for generating the low-energy photon in a high-energy storage ring and/or a diffraction-limited storage ring. The asymmetric magnet pole undulators have different period lengths between the upper and lower magnet poles. Taking the advantage of the asymmetric magnet pole undulators in building various magnetic fields, this paper proposes a new class of undulators to obtain the specific magnetic fields which can scatter the electron velocity away from the undulator axis. It consists of four magnet arrays and has a similar structure compared to the DELTA/APPLE-X undulator; however, each couple of magnet arrays has a different period length with the period ratio of $n_1:n_2$. Taking the one-to-two and two-to-three period ratios as examples, a novel Figure 8 undulator and a novel Knot undulator are demonstrated. The polarization state can be flexibly switched from the linear polarization to the circular polarization by tuning the phase shifts of magnetic fields, with the on-axis heat load greatly suppressed. The heat-load suppressions of linear polarization at two predetermined orthogonal directions are almost the same and fully effective. Analysis and simulations of undulator designs with the corresponding radiation characteristics are reported.

We present an ultracompact plasma-based method to measure spatial and temporal concurrence of intense electron and laser beams nonintrusively at their interaction point. The electron beam couples with a laser-generated seed plasma in dependence of spatiotemporal overlap, which triggers additional plasma production and manifests as enhanced plasma afterglow. This optical observable is exploited to measure beam concurrence with $\sim 4\mu \mathrm{m}$ spatial and $\sim 26.7\mathrm{fs}$ temporal accuracy, supported by auxiliary diagnostics. The afterglow interaction fingerprint is highly sensitive and enables ultraversatile femtosecond-micrometer beam metrology.

We report the generation of up to 565 MW, 2.7 ns (FWHM) pulses at 11.7 GHz from a metamaterial structure in test at the Argonne Wakefield Accelerator. The highest power was generated by a train of eight 65 MeV electron bunches spaced at 1.3 GHz with a total charge of 355 nC. The metamaterial structure consists of 100 copper unit cells each consisting of a wagon-wheel plate and a spacer plate with a total structure length of 0.2 m. The 565 MW pulse generates a wakefield with a peak on-axis gradient of $135\mathrm{MV}/\mathrm{m}$ that could be used to accelerate a trailing main bunch. An estimated surface electric field of over $1\mathrm{GV}/\mathrm{m}$ is generated on the metamaterial plates at the peak power level but no evidence of breakdown was observed during testing. Tests with single electron bunches and with trains of bunches of up to 100 nC produced output power levels in excellent agreement with simulations. At higher total bunch charge, offsets of the bunches from the axis resulted in beam interception and reduced output power. Simulations indicate that a perfectly aligned bunch train would generate more than 1 GW of power from the structure.

We propose a method to simultaneously determine the magnetic centers of multiple quadrupoles in a transport line or a storage ring. The method finds the magnet centers by correcting the induced orbit shift due to a change of the quadrupole gradient strengths, with the goal of eliminating or minimizing such orbit shifts. The correction of the induced orbit shift is done by steering the orbit toward the quadrupole centers with correctors, using the response matrix of the induced orbit shift with respect to the correctors. The quadrupoles are selected with orbit corrector magnets and beam position monitors in between to ensure that orbit correction at the quadrupole locations can be achieved. The response matrix can be measured or calculated. Simulations with a section of the Linac Coherent Light Source II and the Stanford Positron Electron Asymmetric Ring (SPEAR3) storage ring are done to demonstrate the feasibility and performance of the method. It is also experimentally tested on SPEAR3. The method can be extended for beam-based alignment measurement of nonlinear magnets.

The SIS100 synchrotron as a part of the new Facility for Antiproton and Ion Research (FAIR) accelerator facility at GSI should be operated at the “space charge limit” for light- and heavy-ion beams. Beam losses due to space-charge-induced resonance crossing should not exceed a few percent during a full cycle. The recent advances in the performance of particle tracking tools with self-consistent solvers for the 3D space charge forces now allow us to reliably identify low-loss areas in tune space, considering the full SIS100 accumulation plateau of one second (160 000 turns) duration. A realistic magnet error model, extracted from precise bench measurements of the SIS100 main dipole and quadrupole magnets, is included in the simulations. Previously, such beam dynamics simulations required non-self-consistent space charge models. By comparing to the self-consistent simulations results, we are now able to demonstrate that the predictions from such faster space charge models can be used to identify low-loss regions with sufficient accuracy. The findings are applied by identifying a low-loss working point region in SIS100 for the design FAIR beam parameters. The bunch intensity at the space charge limit is determined. Several countermeasures to space charge are proposed to enlarge the low-loss area and to further increase the space charge limit.