The free-electron laser facilities driven by a superconducting radio-frequency (SRF) linac provide high-repetition-rate electron beam, which makes it feasible to feed multiple undulator lines at the same time. In this paper, we study a method of controlling the energy of multiple electron bunches by off-frequency detuning in the SRF linac. Based on the theoretical analysis, we present the available discrete frequency detunes and the optimal linac energy allocation solutions with given energy overhead and periodic energy pattern. The required off-frequency detune is not larger than half of the beam repetition rate, which can be realized with the frequency tuner in SRF cavities. We adopt the configuration of the high energy upgrade of the Linac Coherent Light Source II (LCLS-II-HE) as an example to discuss the possible schemes in practice to support two undulator lines simultaneously. We also discuss the energy jitter increase due to the off-crest acceleration, the tunable energy range with fixed total SRF linac energy capacity, the beam energy chirp and lattice design for multienergy beam transport.

CBETA, the Cornell BNL Energy-Recovery-Linac (ERL) Test Accelerator, is the first multiturn ERL with superconducting radio frequency (SRF) cavities cavities and will therefore be the first ERL whose current could be limited by the beam break-up (BBU) instability. To investigate the threshold current, we calculate HOMs in CBETA’s cavities, including their construction errors, and simulate the BBU threshold current with the established simulation code BMAD. For some construction errors, this current limit is not sufficiently large and means of increasing it are investigated. We find that some means that have been shown effective in single turn ERLs are not practical for multiturn ERLs. To make sure that simulations are trustworthy for CBETA, we revisit the BBU theory for multiturn configurations, and compare to simulation results. We also further explore the scaling law of the BBU threshold current for the case with symmetric ERLs, and a new scaling factor has been found. BBU suppression with lattice chromaticity has been investigated assuming bunches with a Gaussian energy spread. The ability to simulate BBU effect with multiple particles per bunch has been added into BMAD, and agreement with the derived theoretical formula is found. CBETA is currently under beam commissioning at Cornell University. Our simulations show that an optimized optics will push the BBU threshold current beyond the design current, for all realistic cavity production errors.

Temporally shaped electron bunches at ultrafast time scales are foreseen to support an array of applications including the development of small-footprint accelerator-based coherent light sources or as probes for, e.g., ultrafast electron-diffraction. We demonstrate a method where a transversely segmented electron bunch produced via photoemission from a transversely patterned laser distribution is transformed into an electron bunch with modulated temporal distribution. In essence, the presented transformation enables the mapping of the transverse laser distribution on a photocathode surface to the temporal coordinate and provides a proof-of-principle experiment of the method proposed in Reference [, , , and , Intense Superradiant X Rays from a Compact Source Using a Nanocathode Array and Emittance Exchange, Phys. Rev. Lett. 108, 263904 (2012)] as a path toward the realization of compact coherent x-ray sources, albeit at a larger timescale. The presented experiment is validated against numerical simulations and the versatility of the concept, e.g., to tune the current-distribution parameters, is showcased. Although our work focuses on the generation of electron bunches arranged as a temporal comb it is applicable to other temporal shapes.

We present the results from studies of soft x-ray seeding options for the LCLS–II x-ray free electron laser (FEL) at SLAC. The LCLS-II will use superconducting accelerator technology to produce x-ray pulses at up to 1 MHz repetition rate using 4 GeV electron beams. If properly seeded, these pulses will be nearly fully coherent, and highly stable in photon energy, bandwidth, and intensity, thus enabling unique experiments with intense high-resolution soft x-rays. Given the expected electron beam parameters from start to end simulations and predicted FEL performance, our studies reveal echo enabled harmonic generation (EEHG) and soft x-ray self-seeding (SXRSS) as promising and complementary seeding methods. We find that SXRSS has the advantage of simplicity and will deliver 5-35 times higher spectral brightness than EEHG in the 1–2 nm range, but lacks some of the potential for phase-stable multipulse and multicolor FEL operations enabled by external laser seeding with EEHG.

With its extreme beam parameters, the FACET II facility enables the test of the down ramp injection scheme in the laboratory for the beam-driven plasma wakefield accelerator approach. In addition to the ideal cases studied in previous theoretical work, we investigate the effect of fluctuations in the down ramp plasma source profile on the emittance and current profile of the self-injected beam using 2D and 3D particle-in-cell simulations. We show that down ramps with a length of $\sim 10c/{\omega }_p$ can be reproducibly created by generating a shock in a supersonic flow. Simulations show that the emittance of the injected beam using such down ramps is $\sim 0.1\mu \mathrm{m}$. A gentler ramp can further reduce the slice emittance of the beam to $\sim 0.03\mu \mathrm{m}$. The emittance of the injected beam depends on the ramp length but is insensitive to the shape of the ramp. However, the current profile of the injected beam can be manipulated by changing the ramp shape. A simulation shows that, when a noncylindrical driver is used, the emittance of the injected beam differs in the two orthogonal transverse planes and is a few times larger than that of the cylindrical driver case. A full-scale simulation where we use a realistic density profile that includes the up ramp, the injecting down ramp, and the exiting down ramp is presented to show that the beam emittance is preserved during the acceleration and extraction of the beam.

A detailed study of the near-surface structure and composition of Nb, the material of choice for superconducting radio-frequency accelerator (SRF) cavities, is of great importance in order to understand the effects of different treatments applied during cavity production. By means of surface-sensitive techniques such as grazing incidence diffuse x-ray scattering, x-ray reflectivity, and x-ray photoelectron spectroscopy, single-crystalline Nb(100) samples were investigated in and ex situ during annealing in an ultrahigh vacuum as well as in nitrogen atmospheres with temperatures and pressures similar to the ones employed in real Nb cavity treatments. Annealing of Nb specimens up to $800°\mathrm{C}$ in a vacuum promotes a partial reduction of the natural surface oxides (${\mathrm{Nb}}_2{\mathrm{O}}_5$, ${\mathrm{NbO}}_2$, and NbO) into NbO. Upon cooling to $120°\mathrm{C}$, no evidence of nitrogen-rich layers was detected after nitrogen exposure times of up to 48 h. An oxygen enrichment below the Nb-oxide interface and posterior diffusion of oxygen species towards the Nb matrix, along with a partial reduction of the natural surface oxides, was observed upon a stepwise annealing up to $250°\mathrm{C}$. Nitrogen introduction to the system at $250°\mathrm{C}$ promotes neither N diffusion into the Nb matrix nor the formation of new surface layers. Upon further heating to $500°\mathrm{C}$ in a nitrogen atmosphere, the growth of a new subsurface ${\mathrm{Nb}}_x{\mathrm{N}}_y$ layer was detected. These results shed light on the composition of the near-surface region of Nb after low-temperature nitrogen treatments, which are reported to lead to a performance enhancement of SRF cavities.

A 56 MHz superconducting rf cavity was designed and installed in the Relativistic Heavy Ion Collider (RHIC). It is the first superconducting quarter wave resonator (QWR) operating in a high-energy storage ring. We discuss herein a design of the cavity and its key components and the cavity operation with $\mathrm{Au}+\mathrm{Au}$ collisions, and with asymmetrical $\mathrm{Au}+{}^3\mathrm{He}$ collisions. The cavity is a storage cavity, meaning that it becomes active only at the energy of the experiment, after the acceleration cycle is completed. Without beam, the cavity reached 1.93 MV and a $Q_0$ of $3.0\times {10}^8$ after helium conditioning. The cavity voltage was limited at 300 kV with beam operation due to heating in the Higher Order Mode (HOM) coupler. With the cavity operating at 300 kV, an improvement in luminosity was detected from direct measurements, and the bunch length has been reduced. The uniqueness of the QWR necessitated development of an innovative design of the higher order mode dampers with high-pass filters, and a distinctive fundamental mode damper that enables the cavity to be transparent to the beam during acceleration.

Permeable mirrors are typically used for coupling photons out of laser cavities. A similar approach was proposed for output coupling photons from the cavities of x-ray free-electron laser (XFEL) oscillators. One of the Bragg-reflecting crystal mirrors is thin, just a few extinction length, and is used as a permeable mirror with reduced reflectivity. However, this method is very often limited to extractions of only a few tenths of the intracavity power. Other cavity-based XFELs, such as the high-gain regenerative amplifier XFEL, require much higher outcoupling efficiency. Here, alternative schemes are proposed and analyzed for coupling x-ray photons out of XFEL cavities using intracavity Bragg-reflecting x-ray-transparent diamond crystal beam splitters, with all cavity crystal mirrors being thick and featuring high reflectivity. The intracavity beam splitters are efficient and flexible in terms of the amount of the power they are capable of coupling out of the cavity, an amount that can be varied promptly from zero to close to 100%. The stability and performance of the cavity are now separated from the outcoupling and can be developed and optimized individually. The schemes can be readily extended to multibeam outcoupling. Other types of beam splitters are discussed as well.

Complementary to the physics research at the LHC, several fixed-target facilities receive beams from the LHC injector complex. To serve the fixed-target physics programme at the super proton synchrotron, high-intensity proton beams from the proton synchrotron are extracted using the multiturn extraction technique based on trapping parts of the beam in stable resonance islands. Considering the number of protons requested by future experimental fixed-target facilities, such as the proposed search for hidden particles experiment, the currently delivered beam intensities are insufficient. Experimental studies were conducted to optimize the multiturn extraction technique, pushing its capabilities in the domain of high-intensity proton beams, and their results are presented in this paper. The success of these studies led to the decision to discontinue the former continuous transfer and remove the related hardware from the accelerator. Therefore, the multiturn extraction becomes standard operational practice for delivering proton beams for the fixed-target physics programme at the CERN super proton synchrotron.

Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to reliably extrapolate the results of numerical simulations well beyond what is currently possible in terms of CPU time. In earlier work, a proposal for a model based on Nekhoroshev theorem and Kolmogorov–Arnold–Moser theory was made. This model has been studied in detail and proved successful in describing the evolution of the dynamic aperture in numerical simulations, however a number of shortcomings had been identified and new models are proposed in this paper, which solve the observed issues. The new models have been benchmarked against numerical simulations for a simple system, the 4D Hénon map, as well as a realistic, non-linear representation of the beam dynamics in the LHC at 6.5 TeV providing in both cases excellent results.

The study of magnetized electron beam has become a high priority for its use in ion beam cooling as part of electron ion colliders and the potential of easily forming flat beams for various applications. In this paper, a purpose-specific diagnostic is described with the intention of studying transverse magnetized beam properties. The device is a modification to the classic pepper-pot, used in this context to measure the uncorrelated components of transverse emittance in addition to the typical effective emittance. The limitations of traditional methods are discussed, and simulated demonstrations of the new technique shown.

Many state-of-the-art applications for linear accelerators, such as free-electron lasers (FELs) and plasma-wakefield accelerators (PWFAs), require small normalized emittances, and PWFAs in particular are very sensitive to transverse slice offsets along the beam. Dispersive systems, such as bunch compressors, can cause different chromatic aberrations, one of which yields transverse slice offsets. In this paper, we show a design approach to double-achromat bunch compressors which greatly reduces different chromatic aberrations and mitigates coherent synchrotron radiation effects.

Space-charge effects play an important role in high intensity accelerators. These effects can be studied self-consistently by solving the Poisson equation with the dynamically evolved charge density distribution subject to appropriate boundary conditions. In this paper, two computationally efficient methods are proposed to solve the Poisson equation inside an elliptical perfectly conducting pipe. One method uses a spectral method and the other uses a spectral finite difference method. The former method has a high accuracy and the latter one has a computational complexity of $O(N\log (N))$, where $N$ is the total number of unknowns. These methods implemented in a beam dynamics tracking code enable the fast simulation of space-charge effects in an accelerator with an elliptical conducting pipe.

Since its inauguration in 1976, the Super Proton Synchrotron (SPS) at CERN relies on a traveling wave system for particle acceleration instead of making use of standing wave cavities that are more common in circular accelerators. These traveling wave structures (TWSs) are essentially periodically loaded waveguides operated at a fundamental frequency of about 200 MHz. In the frame of the LHC injector upgrade project, the SPS accelerating system is presently improved to better cope with the increased beam intensity required for the future High Luminosity LHC era. The available accelerating voltage provided by the TWSs by means of radio-frequency (rf) generators is a fundamental and valuable input for machine operation and particle tracking codes used to simulate beam phenomena in the SPS. Measurement of the voltage with well known nonresonant and on-axis perturbation methods is however infeasible due to the extreme mechanical length of the SPS structures. It is shown that a good estimate of the rf voltage can be obtained from off-axis measurement samples in each accelerating gap in addition to the in- and output reflection coefficients of the structures. The rf voltage for the LHC proton beam delivered by the system configuration that was installed during the first and second exploitation run of the LHC is measured by this method, not including the beam loading. The impact on the fundamental accelerating mode and the rf voltage of additional higher order mode (HOM) couplers, which are also required for the upgrade of the acceleration system, is assessed by the proposed method as well.

Transverse oscillation is an important issue in beam dynamics of cyclotrons and can be described by the Mathieu equation. We review the standard form of the Mathieu equation, $\frac{d^{2}u}{d{\theta }^2}+(\delta +ϵ·\cos 2\theta )u=0$, and propose a modification of the method of multiple scales (i.e., a perturbation method) so that the asymptotic analytical solutions of the Mathieu equation can be computed in the stable and unstable regions for both $\delta \ge 0$ and $\delta <0$. This method was applied to the nonlinear transverse oscillation equations for a cyclotron. Analytical solutions for transverse oscillation in the stable and unstable regions (i.e., vicinity of the resonances) were obtained, and the accuracy of these analytical solutions was confirmed by their close agreement with the direct numerical integration. Useful results such as the analytical solution of the transverse oscillation frequency, increasing rate of the amplitude in unstable regions, and the resonance width were also derived; the stable condition and driving terms of the resonances can be obtained from the analytical solutions.

Combined function magnets with dipole and quadrupole components were designed and built for the Extremely Brilliant Source. These magnets are low power consumption single sided off-axis quadrupoles. The field of the magnets was optimized for particles with a curved trajectory and within an elliptical good field region. A specific moving stretched wire magnetic measurement method was developed for measuring the magnetic length of the magnets, the radius of curvature of the poles and the field multipoles. The effect of the curvature of the magnets on the field multipoles was investigated.

We present the design of a free-electron laser (FEL) doubler suitable for the simultaneous operation of two FEL lines, in either self-amplified spontaneous emission or externally seeded configuration. The doubler relies on the physical selection of two longitudinal portions (beamlets) of a single electron bunch at a low energy and on their spatial separation at high energy. Since the two beamlets are naturally synchronized, FEL pump–FEL probe experiments are enabled when the two photon pulses are sent to the same experimental station. The proposed solution offers improved flexibility of operation compared with existing or designed two-pulse, two-color FEL schemes, as it allows independent control and continuous tunability of the color, timing, intensity, and angle of incidence of the radiation pulses at the user end station. Detailed numerical simulations and experimental results demonstrate its feasibility at the Free Electron laser Radiation for Multidisciplinary Investigations (FERMI) FEL facility.

We present a new accelerator toolbox (AT)-based toolkit for simulating the commissioning of light-source storage rings. The toolkit provides a framework for supporting high-level scripts to represent with realism the various procedures (e.g., orbit and optics correction, beam-based alignment, etc.) encountered during commissioning and is designed to mirror as closely as possible the reality as seen from the control room. Emphasis is placed on the inclusion of a comprehensive set of error sources and faithful modeling of beam diagnostics. The toolkit capabilities are demonstrated in an application to the recent design and commissioning studies of the Advanced Light Source Upgrade (ALS-U) Accumulator Ring, a short-time successful commissioning of which will be critical to the overall ALS-U project success.