Recent work introduced a systematic method for designing so-called azimuthally modulated RF cavities that support transverse magnetic modes composed of user-desired multipoles, enabling precision control of the magnitude and orientation of multipolar components in RF cavity design. This paper extends this method to practical implementation by deriving the multipolar expansion of the longitudinal electric field in such RF cavities with beam pipes, as well as the momentum change of ultra-relativistic particles traversing these modes. The derived equations explicitly show the radial variation of the change in longitudinal and transverse momentum follows a polynomial rather than Bessel-function relationship. The expression for the longitudinal electric field is then compared to a field map obtained from the 3D electromagnetic simulation of an azimuthally modulated cavity designed to support a mode composed of monopole, dipole, and quadrupole components. Beam dynamics studies are presented to assess the derived expressions for the change in momentum, including the effects of relaxing the ultra-relativistic assumption. Finally, two example applications are presented: the first demonstrates the removal of unwanted transverse multipoles to create a multipole-free accelerating structure with a single-port coupler, whereas the second illustrates the synthesis of desired multipoles to create an RF cavity that transforms the transverse distribution of a beam from Gaussian to uniform.

The maximum achievable beam current in an energy recovery linac (ERL) is often constrained by beam breakup (BBU) instability. Our previous research highlighted that filling patterns have a substantial impact on BBU instabilities in multipass ERLs. In this study, we extend our investigation to the eight-cavity model of the Powerful ERL for Experiment (PERLE). We evaluate its requirements for damping cavity higher order modes (HOMs) and propose optimal filling patterns and bunch timing strategies. Our findings reveal a significant new insight: while filling patterns are crucial, the timing of bunches also plays a critical role in mitigating HOM beam loading and BBU instability. This previously underestimated factor is essential for effective BBU control. We estimated the PERLE threshold current using both analytical and numerical models, incorporating the designed PERLE HOM dampers. During manufacturing, HOM frequencies are expected to vary slightly. Our study found no significant difference in BBU suppression for relative rms frequency jitters of 0.001, 0.002, and 0.005 for the same HOM. Introducing a jitter of 0.001 into our models, we found that the dampers effectively suppressed BBU instability, achieving a threshold current an order of magnitude higher than the design requirement. Our results offer new insights into ERL BBU beam dynamics and have important implications for the design of future ERLs.

The vertical plane transverse emittance of accelerated electron bunches at the AWAKE experiment at CERN has been determined, using three different methods of data analysis. This is a proof-of-principle measurement using the existing AWAKE electron spectrometer to validate the measurement technique. Large values of the geometric emittance, compared to that of the injection beam, are observed (∼0.5 compared with ∼0.08), which is in line with expectations of emittance growth arising from plasma density ramps and large injection beam bunch size. Future iterations of AWAKE are anticipated to operate in conditions where emittance growth is better controlled, and the effects of the imaging systems of the existing and future spectrometer designs on the ability to measure the emittance are discussed. Good performance of the instrument down to geometric emittances of approximately 1e-4 is required, which may be possible with improved electron optics and imaging.

In this paper, a fast cell to cell tracking algorithm (FC2CT) is developed, that determines the change in 6D phase space of a particle beam through rf accelerating cavities operated in both Standing and Traveling Wave modes. The performance is compared to well trusted tracking codes - ASTRA and RF-Track - for proton beams with relativistic beta = 0.5. The FC2CT algorithm produces a complete analytical method to determine the change in particle momentum, with the constant particle velocity approximation over the integration region. Additional developments for FC2CT are discussed, such as altering the integration length. FC2CT can be used as a fast method class in common tracking codes to perform fast simulations through rf cavities.

Powerful ERL for experiments (PERLE) is a novel energy recovery linac (ERL) test facility [1], designed to validate choices for a 50 GeV ERL foreseen in the design of the Large Hadron Electron Collider and the Future Circular Collider and to host dedicated nuclear and particle physics experiments. Its main goal is to demonstrate the high current, continuous wave, multipass operation with superconducting cavities at 802 MHz. With very high beam power (10 MW), PERLE offers an opportunity for controllable study of every beam dynamic effect of interest in the next generation of ERLs and becomes a "stepping stone" between the present state-of-the-art 1 MW ERLs and the future 100 MW scale applications.

Higher order mode (HOM) damping is a crucial issue for the next generation of high-current energy recovery linacs (ERLs). Beam-induced HOMs can store sufficient energy in the superconducting RF (SRF) cavities, giving rise to beam instabilities and increasing the heat load at cryogenic temperatures. To limit these effects, using HOM couplers on the cutoff tubes of SRF cavities becomes crucial to absorb beam-induced wakefields consisting of all cavity eigenmodes. The study presented here focuses on a 5-cell 801.58 MHz elliptical SRF cavity designed for the multi-turn energy recovery linac PERLE (Powerful Energy Recovery Linac for Experiments). Several coaxial coupler designs are analyzed and optimized to enhance the damping of monopole and dipole HOMs of the 5-cell cavity. The broadband performance of HOM damping is also confirmed by the time-domain wakefield and the frequency-domain simulations. In addition, the thermal behavior of the HOM couplers is investigated. A comparison between various HOM-damping schemes is carried out to guarantee an efficient HOM power extraction from the cavity.

CompactLight is a Design Study funded by the European Union under the Horizon 2020 research and innovation funding programme, with Grant Agreement No. 777431. CompactLight was conducted by an International Collaboration of 23 international laboratories and academic institutions, three private companies, and five third parties. The project, which started in January 2018 with a duration of 48 months, aimed to design an innovative, compact, and cost-effective hard X-ray FEL facility complemented by a soft X-ray source to pave the road for future compact accelerator-based facilities. The result is an accelerator that can be operated at up to 1 kHz pulse repetition rate, beyond today’s state of the art, using the latest concepts for high brightness electron photoinjectors, very high gradient accelerating structures in X-band, and novel short-period undulators. In this report, we summarize the main deliverable of the project: the CompactLight Conceptual Design Report, which overviews the current status of the design and addresses the main technological challenges.

Self-modulation is a beam–plasma instability that is useful to drive large-amplitude wakefields with bunches much longer than the plasma skin depth. We present experimental results showing that, when increasing the ratio between the initial transverse size of the bunch and the plasma skin depth, the instability occurs later along the bunch, or not at all, over a fixed plasma length because the amplitude of the initial wakefields decreases. We show cases for which self-modulation does not develop, and we introduce a simple model discussing the conditions for which it would not occur after any plasma length. Changing bunch size and plasma electron density also changes the growth rate of the instability. We discuss the impact of these results on the design of a particle accelerator based on the self-modulation instability seeded by a relativistic ionization front, such as the future upgrade of the Advanced WAKefield Experiment.

The CompactLight design for a next-generation x-ray free-electron laser utilizes a C-band injector.This requires that the harmonic system used to linearize the beam's phase space must operate at X-band rf or higher.We investigate the optimum frequency for the harmonic system in the range of frequencies from 12 to 48 GHz.We describe the reasoning behind selecting 36 GHz (Ka-band) as our working harmonic frequency.The full linearizer system design including the power source, pulse compressor, and linearizing structure, along with options, is considered and presented.These designs are compared in terms of rf and beam dynamics performance.Two potential MW-level rf sources are discussed; a multibeam klystron and a gyro-klystron, while a klystron-based upconverter with an X-band driver is briefly discussed as an alternative path if even higher peak powers are needed.To further increase peak power, novel options for pulse compressors at Ka-band are discussed.Traveling and standing wave solutions for the structure are presented.

There has been a renewed interest in applying multiobjective (MO) optimization methods to a number of problems in the physical sciences, including to rf structure design. The results of these optimizations generate large datasets, which makes visualizing the data and selecting individual solutions difficult. Using the generated results, Pareto fronts can be found giving the trade-off between different objectives, allowing one to utilize this key information in design decisions. Although various visualization techniques exist, it can be difficult to know which technique is appropriate and how to apply them successfully to the problem at hand. First, we present the setup and execution of MO optimizations of one standing wave and one traveling wave accelerating cavity, including constraint handling and an algorithm comparison. In order to understand the generated Pareto frontiers, we discuss several visualization techniques, applying them to the problem, and give the benefits and drawbacks of each. We found that the best techniques involve clustering the resulting data first to narrow down the possible choices and then using multidimensional visualization methods such as parallel coordinate plots and decision maps to view the clustered results and select individual solutions. Finally, we give some examples of the application of these methods and the cavities selected based on arbitrary design requirements.

In this work, we apply multi-objective optimization methods to single-cell cavity models generated using non-uniform rational basis splines (NURBS). This modeling method uses control points and a NURBS to generate the cavity geometry, which allows for greater flexibility in the shape, leading to improved performance. Using this approach and multiobjective genetic algorithms (MOGAs) we find the Pareto frontiers for the typical key quantities of interest (QoI) including peak fields, shunt impedance and the modified Poynting vector. Visualizing these results becomes increasingly more difficult as the number of objectives increases, therefore, in order to understand these frontiers, we provide several techniques for analyzing, visualizing and using multidimensional Pareto fronts specifically for RF cavity design.

Although accelerator technology has matured sufficiently, state-of-the-art x-ray linacs for radiotherapy and cargo-scanning capture merely 30%-50% of the electrons from a thermionic cathode, requiring a higher cathode current and leaving uncaptured electrons to cause problems such as back bombardment on the cathode leading to a shortening of cathode life. Any solution to increase capture should be effective, simple, reliable, compact, and low cost in order to be adopted by the industry. To address this, we present the design of a 6 MeV high capture efficiency S-band electron linac that captures 90% of the initial dc beam. This linac does not require any extra parts that would increase the cost as the high efficiency is achieved via a low-field amplitude in the first bunching cell to decrease the number of back-streaming electrons, to velocity bunch the electron beam, and recapture back-streaming electrons. Under the low field amplitude, any electrons launched at decelerating phases travel backward with low speeds, thus most of them can catch the next rf cycle, and get reaccelerated/recaptured. As the electron speed is low, the cell length is also shorter than existing linacs. Such a short field is achieved by the use of asymmetric cells with differential coupling to the side-coupled cells. Our novel design has implications for all commercial high current thermionic gun linacs for increasing beam current and increasing cathode lifetime.

The Large Hadron electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High Luminosity--Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron-proton and proton-proton operation. This report represents an update of the Conceptual Design Report (CDR) of the LHeC, published in 2012. It comprises new results on parton structure of the proton and heavier nuclei, QCD dynamics, electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics in extending the accessible kinematic range in lepton-nucleus scattering by several orders of magnitude. Due to enhanced luminosity, large energy and the cleanliness of the hadronic final states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, the report represents a detailed updated design of the energy recovery electron linac (ERL) including new lattice, magnet, superconducting radio frequency technology and further components. Challenges of energy recovery are described and the lower energy, high current, 3-turn ERL facility, PERLE at Orsay, is presented which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution and calibration goals which arise from the Higgs and parton density function physics programmes. The paper also presents novel results on the Future Circular Collider in electron-hadron mode, FCC-eh, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies.

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported [F. Braunmller, T. Nechaeva et al. (AWAKE Collaboration), Phys. Rev. Lett. 125, 264801 (2020)]: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement.

We present the initial design studies and specifications for an accelerator and conveyor system to irradiate collagen samples, modifying properties such as the putrescibility and mechanical behaviours in a paradigm shift from existing, widely used technology. We show the integrated design requirements for a magnetic rastering scheme to move the beam position in order to ensure a uniform dose distribution over the full surface of the hide and discuss its dependence on factors such as the size of the hide, the beam current and conveyor speed. We also present initial energy deposition studies using beam particle interaction simulation program G4beamline, in order to determine the numerical beam parameters and angle of incidence needed to ensure a uniform depth-dose distribution throughout the hide thickness.

Beam breakup instability is a potential issue for all particle accelerators and is often the limiting factor for the maximum beam current that can be achieved. This is particularly relevant for energy recovery linacs (ERLs)with multiple passes where a relatively small amount of charge can result in a large beam current. Recent studies have shown that the choice of filling pattern and recirculation scheme for a multipass energy recovery linac can drastically affect the interactions between the beam and rf system. In this paper, we further explore this topic to study how filling patterns affect the beam breakup instability and how this can allow us to optimize the design in order to minimize this effect. We present a theoretical model of the beam-rf interaction as well as numerical modeling and show that the threshold current can vary by a factor of 5, and potentially, even more, depending on the machine design parameters. Therefore a judicious choice of filling pattern can greatly increase the onset of beam breakup, expanding the utility of future ERLs.

Staged acceleration, driven by terahertz (THz) frequency radiation pulses in a lattice with alternating orientation dielectric-lined waveguides and intervening matching optics, is shown to mitigate transverse emittance and energy spread growth, opening a route to multistage THz linacs. Decomposition of the longitudinal THz field into the multipolar components reveals a quadrupole field component with strong radial dependence. As such, it induces a transverse energy correlation in the beam during acceleration due to the large variation in the electric field with radius and azimuthal position of the electrons. An alternating orientation of stages separated by a matching section provides a compensation of transverse energy spread correlation induced in the beam during its interaction with the THz field. Furthermore, the monopolar component of the accelerating LSM11 mode was found to be constant with respect to transverse position, entailing zero monopolar transverse voltage and preventing emittance growth, unlike conventional radiofrequency structures. We demonstrate in a rectangular dielectric-lined waveguide structure that, when used for the acceleration of relativistic electrons, the slice transverse emittance is conserved and the growth in the slice energy spread is reduced by 70%-80% simultaneously over a system of two stages, each providing an interaction length of 4 mm and an energy gain of up to 2 MeV.

A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

Recirculating energy recovery linacs are a promising technology for delivering high power particle beams (similar to GW) while only requiring low power (similar to kW) rf sources. This is achieved by decelerating the used bunches and using the energy they deposit in the accelerating structures to accelerate new bunches. We present studies of the impact of the bunch packet filling pattern on the performance of the accelerating rf system. We perform rf beam loading simulations under various noise levels and beam loading phases with different injection schemes. We also present a mathematical description of the rf system during the beam loading, which can identify optimal beam filling patterns under different conditions. The results of these studies have major implications for design constraints for future energy recovery linacs, by providing a quantitative metric for different machine designs and topologies.