Particle accelerators require constant tuning during operation to meet beam quality, total charge and particle energy requirements for use in a wide variety of physics, chemistry and biology experiments. Maximizing the performance of an accelerator facility often necessitates multiobjective optimization, where operators must balance trade-offs between multiple competing objectives simultaneously, often using limited, temporally expensive beam observations. Usually, accelerator optimization problems are solved off-line, prior to actual operation, with advanced beam line simulations and parallelized optimization methods (NSGA-II, swarm optimization). Unfortunately, it is not feasible to use these methods for online multiobjective optimization, since beam measurements can only be done in a serial fashion, and these optimization methods require a large number of measurements to converge to a useful solution. Here, we introduce a multiobjective Bayesian optimization scheme, which finds the full Pareto front of an accelerator optimization problem efficiently in a serialized manner and is thus a critical step towards practical online multiobjective optimization in accelerators. This method uses a set of Gaussian process surrogate models, along with a multiobjective acquisition function, to reduce the number of observations needed to converge by at least an order of magnitude over current methods. We demonstrate how this method can be modified to specifically solve optimization challenges posed by the tuning of accelerators. This includes the addition of optimization constraints, objective preferences and costs related to changing accelerator parameters.

We present measurements of slice energy spread at the injector section of the European X-Ray Free Electron Laser for an electron bunch with charge of 250 pC. Two methods considered in the paper are based on measurements at the dispersive section after a transverse deflecting structure (TDS). The first approach uses measurements at different beam energies. We show that with a proper scaling of the TDS voltage with the beam energy the rms error of the measurement is less than 0.3 keV for the energy spread of 6 keV. In the second approach we demonstrate that keeping the beam energy constant but adjusting only the optics we are able to simplify the measurement complexity and to reduce the rms error below 0.1 keV. The accuracy of the measurement is confirmed by numerical modeling including beam transport effects and collective beam dynamics of the electron beam. The slice energy spread measured at the European XFEL for the beam charge of 250 pC is nearly 3 times lower as the one reported recently at SwissFEL for the same cathode material and the beam charge of 200 pC.

Fine time-resolved analysis of matter—i.e., spectroscopy and photon scattering—in the linear response regime requires a fs-scale pulsed, high repetition rate, fully coherent x-ray source. A seeded free-electron laser (FEL) driven by a super-conducting linac, generating ${10}^8–{10}^{10}$ coherent photons at 2–5 keV with about 0.5 MHz of repetition rate, can address this need. The seeding scheme proposed is the echo-enabled harmonic generation, alimented by a FEL oscillator working at 13.6 nm with a cavity based on Mo-Si mirrors. The whole chain of the x-ray generation is here described by means of start-to-end simulations. Comparisons with the self-amplified spontaneous emission and a fresh-bunch harmonic cascade performed with similar electron beams show the validity of this scheme.

In this paper, we propose to manipulate a nonrelativistic electron beam during its emission and acceleration to create nanobunched electrons. Specifically, we simulate the acceleration of a structured electron beam emitted from a multiring photocathode in a photoinjector and show that, after acceleration, such a transversely structured beam can be transformed into a hollow beam with a longitudinal density modulation in the petahertz frequency range. Our theoretical study shows that, in the far-field zone, the coherent radiation of the bunched hollow beam approaches that of a similarly bunched solid beam in the paraxial limit.

Particle beam eigenemittances comprise the lowest set of rms-emittances that can be imposed to a beam through symplectic optical elements. For cases of practical relevance this paper introduces an approximation providing a very simple and powerful relation between transverse eigenemittance variation and the beam phase integral. This relation enormously facilitates modeling eigenemittance tailoring scenarios. It reveals that difference of eigenemittances is given by the beam phase integral or vorticity rather than by angular momentum. Within the approximation any beam is equivalent to two objects rotating at angular velocities $\pm \omega$. A description through circular beam modes has been done already in [A. Burov, S. Nagaitsev, and Y. Derbenev, Circular modes, beam adapters, and their applications in beam optics, Phys. Rev. E 66, 016503 (2002)]. The new relation presented here is a complementary and vivid approach to provide a physical picture of the nature of eigenemittances for cases of practical interest.

A novel method is developed to take into account realistic boundary conditions in intense nonlinear beam dynamics. The algorithm consists of three main ingredients: the boundary element method that provides a solution for the discretized reformulation of the Poisson equation as boundary integrals; a novel fast multipole method developed for accurate and efficient computation of Coulomb potentials and forces; and differential algebraic methods, which form the numerical structures that enable and hold together the different components. The fast multipole method, without any modifications, also accelerates the solution of intertwining linear systems of equations for further efficiency enhancements. The resulting algorithm scales linearly with the number of particles $N$, as $m\log m$ with the number of boundary elements $m$, and, therefore, establishes an accurate and efficient method for intense beam dynamics simulations in arbitrary enclosures. Its performance is illustrated with three different cases and structures of practical interest.

Momentum bandwidth is an important characteristic for final focus systems (FFS) of future high-energy colliders. A large momentum bandwidth is a notable feature of the novel local-chromaticity-correction FFS, being demonstrated at the KEK Accelerator Test Facility 2 (ATF2), owing to the locality of chromaticity correction. In this article, analytical estimations and simulations of momentum bandwidth for various optics of ATF2 are presented. Possible deviations of the momentum bandwidth due to realistic machine imperfections are studied. Experimental measurements at ATF2 following successful tuning of small vertical beam size at the interaction point (IP) are also described, which agree well with numerical predictions and further verify the robustness of the local chromaticity correction scheme.

Beam-driven collinear wakefield accelerators (CWAs) that operate by using slow-wave structures or plasmas hold great promise toward reducing the size of contemporary accelerators. Sustainable acceleration of charged particles to high energies in the CWA relies on using field-generating relativistic electron bunches with a highly asymmetric current profile and a large energy chirp. A new approach to obtaining such bunches has been proposed and illustrated with the accelerator design supported by particle tracking simulations. It has been shown that the required particle distribution in the longitudinal phase space can be obtained without collimators, giving CWAs an opportunity for employment in applications requiring a high repetition rate of operation.

The use of a periodic electron beam bunch train to resonantly excite plasma wakefields in the quasinonlinear (QNL) regime has distinct advantages over employing a single, higher charge bunch. Resonant QNL excitation can produce plasma electron blowout using a small charge per pulse if the beam emittance beams are very low. The local density perturbation in such a case is extremely nonlinear, achieving total rarefaction, yet the resonant response of the plasma electrons at the plasma frequency is preserved. The needed electron beam pulse train with interbunch spacing equal to the plasma period can be produced via inverse free-electron laser bunching. As such, in achieving resonance with a laser wavelength of a few microns, a high plasma density is employed, with the attendant possibility of obtaining extremely large wakefield amplitudes, near $1\mathrm{TV}/\mathrm{m}$ for FACET-II parameters. In this article, we use particle-in-cell (PIC) simulations to study the plasma response, the beam evolution including density modulation, and the instabilities encountered when using a bunched-beam scheme to resonantly excite waves in a dense plasma.

The resonant interaction of a bunched particle beam with short-range wakefields is the cause of head-tail instability, which is a major limitation for single-bunch beam intensity in circular accelerators. There are several processes that suppress this type of instability, such as fast chromatic damping and Landau damping due to machine nonlinearity. Beam-based feedback systems (transverse dampers) provide active suppression of the beam oscillations. The combined effect of the transverse dampers and chromaticity is discussed in this article. A brief overview of theoretical and experimental studies of the head-tail instability and its mitigation is presented. Results of experimental studies of the transverse mode coupling carried out at National Synchrotron Light Source-II are compared with the theoretical model.

Radiation therapy is currently the most utilized technique for the treatment of tumors by means of ionizing radiation, such as electrons, protons and x/gamma rays, depending on the type, size and depth of the cancer mass. Radiation therapy has in general fulfilled the main requirement of targeting thus damaging the malignant cells and sparing the healthy tissues as best as possible. In this scenario, electron linear accelerators have been operated as viable tools for the delivery of both high-energetic electrons and x-ray beams, which are obtained via the bremsstrahlung process of the electrons hitting on a high-Z material. Recently, it has been experimentally demonstrated that ultrahigh dose-rate bursts of electrons and x-ray beams increase the differential response between healthy and tumor tissues. This beneficial response is referred to as the FLASH effect. For this purpose, we have developed the first dedicated compact $S$-band linear accelerator for FLASH radiotherapy. This linac is optimized for a nominal energy of 7 MeV and a pulsed electron beam current of 100 mA and above. The accelerator is mounted on a remote-controlled system for preclinical research studies in the FLASH regime. We will show the rf and beam dynamics design of the $S$-band linac as well as the commissioning and high-power rf tests. Furthermore, the results of the dosimetric measurements will be illustrated.

Next-generation plasma-based accelerators can push electron beams to GeV energies within centimeter distances. The plasma, excited by a driver pulse, is indeed able to sustain huge electric fields that can efficiently accelerate a trailing witness bunch, which was experimentally demonstrated on multiple occasions. Thus, the main focus of the current research is being shifted towards achieving a high quality of the beam after the plasma acceleration. In this paper we present a beam-driven plasma wakefield acceleration experiment, where initially preformed high-quality witness beam was accelerated inside the plasma and characterized. In this experiment the witness beam quality after the acceleration was maintained on high level, with 0.2% final energy spread and $3.8\mu \mathrm{m}$ resulting normalized transverse emittance after the acceleration. In this article, for the first time to our knowledge, the emittance of the plasma wakefield accelerated beam was directly measured.

For the purposes of this paper, we define self-consistent beams as those which give rise to linear internal electric fields and maintain this property under any linear transport. Their analytic tractability provides valuable insights into space-charge effects, and they would possess a number of ideal properties if realized in practice. Although the Kapchinsky and Vladimirsky distribution is the most famous example, a larger class of self-consistent beams exists. Here, we focus on a particular case which we call the Danilov distribution. The beam is characterized by an elliptical shape, uniform charge density, and linear relationships between the particle positions and momenta in the transverse plane. The dynamical beam behavior is more complicated than that of the Kapchinsky and Vladimirsky distribution due to space-charge-driven linear coupling between the two transverse dimensions. There is current interest in generating the Danilov distribution experimentally; however, the beam dynamics have not yet been studied in detail. In this paper, we present an iterative method to calculate the matched envelope of the Danilov distribution in both coupled and uncoupled lattices using an existing parametrization of coupled motion. We demonstrate the method by calculating matched envelopes and studying the resulting beam properties for a few simple lattices, thus laying the groundwork for future calculations to optimize the injection of a self-consistent beam in a more complicated focusing system.

A large-scale proton or ${\mathrm{H}}^{-}$ accelerator often requires a jump in radio frequency, typically in the beam velocity range of $\beta =0.4–0.6$. The MYRRHA linac has two frequency jumps: one at $\beta \cong 0.2$ and another one in the typical beam velocity range at $\beta =0.56$. Using the MYRRHA linac as an example, this study investigates two new solutions, whereby the frequency jump in the range of $\beta =0.4–0.6$ is eliminated. A single frequency jump at $\beta \cong 0.2$ can shorten the whole linac considerably and reduce the construction and operation costs. The proposed frequency jump sections will use 704.4 MHz radio-frequency quadrupole and cross-bar $H$-type drift tube linear accelerators. To ensure a safe and reliable cw operation at such very high frequency for these kinds of accelerating structures, careful design studies with respect to beam dynamics and rf structures including water-cooling channels have been performed. The results demonstrated the feasibility of both solutions.

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 dataset of the Fermilab Muon $g-2$ Experiment. Two corrections to the measured muon precession frequency ${\omega }_a^m$ are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary, because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed $RC$ time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to ${\omega }_a^m$ is $0.50\pm 0.09\mathrm{ppm}$; the uncertainty is small compared to the 0.43 ppm statistical precision of ${\omega }_a^m$.