The accurate knowledge of the beam coupling impedance in particle accelerators is important in order to address potential impedance-driven instabilities and for planning machine upgrades. While simple models exist for various components (e.g., beam pipes, step transitions, and collimators), they are often insufficient to correctly describe the overall machine impedance with the necessary precision. Numerical 3D simulations, such as those performed with CST wakefield and eigenmode solvers, are typically used to improve the impedance model accuracy accounting for the accelerator device's detailed geometry. Nevertheless, for structures exhibiting low ohmic losses in low energy machines, where the beam velocity is not yet ultrarelativistic, existing 3D codes face computational challenges. Specifically, wakefield simulation times can become excessively long, and the eigenmode resonator model is not physically valid for nonultrarelativistic cases. To overcome these limitations, the mode matching technique, previously applied exclusively to canonical geometries, has been extended to arbitrary 3D particle accelerator structures by numerically computing the eigenmodes within their volume. With appropriate field manipulation at the beam pipe interfaces, the impedance of resonant structures can be accurately calculated without being affected by ohmic losses or particle velocity. Additionally, being combined with CST eigenmode simulations, this method takes advantage of the underlying tetrahedral mesh, providing a more accurate representation of device geometry compared to the hexahedral mesh used in wakefield simulations. In this work, we present the theory, development, and results of this generalized method, with a particular focus on the longitudinal impedance computation for a buncher of the High Brightness Beams Test Facility, where the effects of low wall losses and low beam velocity play a significant role.

In view of the High-Luminosity upgrade of the Large Hadron Collider (HL-LHC) at CERN, different materials were investigated for the upgrade of the LHC collimation system. A key objective was to determine how the jaws of the new collimators could be manufactured to meet the demanding requirements of HL- LHC, such as thermo-mechanical robustness and stability, beam coupling impedance, Ultra-High Vacuum (UHV), etc. During the Long-Shutdown 2 (LS2), five primary and ten secondary low-impedance collimators were already produced using novel materials. For LS3, in addition to more secondary collimators, the production and installation of other types of devices, including tertiaries and physics-debris collimators, is planned. This paper details the final mate-rial choices and rationale for each collimator family.

The Low Energy Ion Ring (LEIR) at CERN is the first synchrotron in the Large Hadron Collider ions injector chain. The performance of LEIR is mainly determined by the number of charges extracted from the machine and transferred to the downstream chain of accelerators. Ions are delivered by the linear accelerator Linac 3. In the intensity accumulation phase, the machine operates with coasting beams: each injected beam is cooled, reducing its transverse dimensions and momentum spread, and brought into a stacking momentum position to allow subsequent injections. In this context, the evolution of the beam parameters for an injected beam under the effects of electron cooling, impedance, intrabeam scattering (IBS), and space charge is of interest in order to optimize the machine working point with respect to the accumulated intensity and to contribute to the understanding of the interplay of the different collective effects. This work describes the advancement in modeling coasting beam dynamics for LEIR accounting for the interplay of electron cooling, impedance, IBS, and space charge. Each effect is presented and progressively included to compute the simulated equilibrium longitudinal Schottky spectrum, which is found in good agreement with the measured one.

The High Luminosity (HL-LHC) project aims to increase the integrated luminosity of CERN's Large Hadron Collider (LHC) by an order of magnitude compared to its initial design. This requires a large increase in bunch intensity and beam brightness compared to the first three LHC runs, and hence poses serious collective-effects challenges, related in particular to electron cloud, instabilities from beam-coupling impedance, and beam-beam effects. Here, we present the associated constraints and the mitigation measures proposed to achieve the baseline performance of the upgraded LHC machine. We also discuss the interplay of these mitigation measures with other aspects of the accelerator, such as optics, physical and dynamic apertures, the collimation system, and crab cavities. Additional potential sources of intensity limitations are also briefly discussed.

In particle accelerators, the beam quality can be strongly affected by the interaction with self-induced electromagnetic fields excited by the beam in the passage through the elements of the accelerator. The beam coupling impedance quantifies this interaction and allows predicting the stability of the dynamics of high intensity, high brilliance beams. The coupling impedance can be evaluated with finite element methods or using analytical approaches, such as field matching or mode matching. In this paper we present an application of the mode matching technique for an azimuthally uniform structure of finite length: a cylindrical cavity loaded with a toroidal slab of lossy dielectric, connected with cylindrical beam pipes. In order to take into account the finite length of the structure, with respect to the infinite length approximation, we decompose the fields in the cavity into a set of orthonormal modes. We obtain a complete set of equations using the magnetic field matching and the nonuniform convergence of the electric field on the cavity boundaries. We present benchmarks done with CST Particle Studio simulations and existing analytical formulas and codes, pointing out the effect of different material conductivities, finite length, and nonultrarelativistic particle beam velocity.

The High Luminosity (HL) upgrade of the Large Hadron Collider (LHC) will increase the peak luminosity at the experiments by more than a factor of 5 with respect to the LHC design value. To achieve this goal, among the upgrade of several beam and machine parameters, the beam intensity will nearly double with respect to the operational LHC value, and the transverse beam emittance will decrease by 50% compared to the LHC design value. Past operational experience showed that coherent beam instabilities may occur for low, positive values of chromaticity, and a higher tune spread than predicted from simulations is required from the dedicated octupole magnets to provide enough Landau damping. With the HL-LHC brighter beams, stability margins will become tighter, and coherent instabilities become stronger if no dedicated mitigation measures are taken. An impedance reduction plan is therefore taking place targeting the collimation system, and the main contributor to the transverse beam coupling impedance at the flattop energy. New collimators with lower resistivity materials will replace the current LHC ones. In this work, we assess the benefits of this impedance reduction with respect to the transverse mode coupling instability threshold. This study quantifies the discrepancy between measured and predicted beam stability thresholds at low chromaticity. It also probes the expected gain of the impedance reduction plan of HL-LHC.

Beam Intercepting Devices (BIDs) are essential protection elements for the operation of the Large Hadron Collider (LHC) complex. The LHC internal beam dump (LHC Target Dump Injection or LHC TDI) is the main protection BID of the LHC injection system; its main function is to protect LHC equipment in the event of a malfunction of the injection kicker magnets during beam transfer from the SPS to the LHC. Several issues with the TDI were encountered during LHC operation, most of them due to outgassing from its core components induced by electron cloud effects, which led to limitations of the injector intensity and hence had an impact on LHC availability. The absorbing cores of the TDIs, and of beam intercepting devices in general, need to deal with high thermo-mechanical loads induced by the high intensity particle beams. In addition, devices such as the TDI — where the absorbing materials are installed close to the beam, are important contributors to the accelerator impedance budget. To reduce impedance, the absorbing materials that make up the core must be typically coated with high electrical conductivity metals. Beam impact testing of the coated absorbers is a crucial element of development work to ensure their correct operation. In the work covered by this paper, the behaviour of several metal-coated absorber materials was investigated when exposed to high intensity and high energy proton beams in the HiRadMat facility at CERN. Different coating configurations based on copper and molybdenum, and absorbing materials such as isostatic graphite, Carbon Fibre Composite (CfC) and Silicon Carbide reinforced with Silicon Carbide fibres (SiC-SiC), were tested in the facility to assess the TDI's performance and to extract information for other BIDs using these materials. In addition to beam impact tests and an extensive Post Irradiation Examination (PIE) campaign to assess the performance of the coatings and the structural integrity of the substrates, extensive numerical simulations were carried out.

Received 7 November 2022DOI:https://doi.org/10.1103/PhysRevAccelBeams.25.129901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeam impedanceBeam instabilitiesAccelerators & Beams

During the Long Shutdown 2 (LS2) at CERN, several upgrades were performed to beam intercepting devices in the framework of the HL-LHC Project. Upgraded equipment included two internal injection beam dumps (TDIS) intended for LHC machine protection located at the injection points from the SPS to the LHC. These two units have been assembled, tested and then installed around LHC Point 2 and Point 8 and are currently ready to get commis-sioned with beam. They are 5.8 m-long, three-module-seg-mented vacuum tanks, with large aperture to accommodate the injected and circulating beams and equipped with absorbing materials. These comprise graphite and higher-Z alloys that are embedded in sub-assemblies reinforced with back-stiffeners made of molybdenum alloy containing Ti and Zr (TZM).

The High Luminosity Large Hadron Collider (HL-LHC) project will upgrade the LHC machine to allow operation with increased luminosity for the experiments. In order to achieve this goal, different operational parameters of the machine need to be pushed beyond the present design values, including the stored beam energy. One of the main challenges related to the achievement of the upgraded performance is the beam collimation system and its contribution to the overall machine impedance budget. In this perspective, new low impedance collimators have been designed, fabricated, and installed in the LHC. In this study, we will present their detailed electromagnetic (EM) characterization by means of radio frequency (RF) measurements and EM simulations.

The crystal-based primary collimators installed in the Large Hadron Collider (LHC) at CERN use the channelling process in bent crystals to steer halo particles efficiently onto downstream collimators. This scheme, called crystal collimation, is also considered for applications of fixed-target implementations in the context of the Physics Beyond Collider at the LHC. Crystal collimation uses 4 mm-long silicon crystals that need to be approached very close to the high-intensity circulating beams, posing obvious concerns for machine impedance. A complex mechanical assembly was developed for this purpose. The setup includes also a system to control with sub-grad accuracy the angular orientation of the crystal, which is done with a high-precision interferometric system. In order to prevent possible beam-induced instabilities and/or damage of the device components from excessive RF-heating, the electromagnetic (EM) characterization of this device is essential prior to its usage with high-intensity beams. In this article, the longitudinal impedance of the crystal primary collimator is studied extensively and estimations of power loss inside the device are provided for the different beam types planned at the LHC and at its High-Luminosity upgrade (HL-LHC). Electromagnetic simulations are performed on a realistic model that includes all the relevant components. The model is described in detail and computational challenges coming from its complexity are discussed. Care is taken to characterize the materials of each relevant sub-component. In particular, the lossy properties of silicon, whose complex permittivity is also evaluated through RF rectangular-cavity perturbation measurements, are taken into account. Numerical results are then compared with dedicated RF measurements performed on a prototype built for the LHC.

The mode coupling instability for coasting beams has been discussed in a previous paper using macroparticle tracking simulations from the pyHeadTail code and a simple analytical formula which was proposed as an extension of the ansatz used for the single-particle formalism. In this paper, we propose a self-consistent derivation of this formula based on the linearized Vlasov equation. The proposed mode coupling instability for coasting beams was never predicted or discussed in the past and we believe that the reason is twofold. First, to derive it analytically from the linearized Vlasov equation, one should not make the usual approximation sin(φ) ' (e)/(2j), where φ is the transverse betatron phase, but really consider the two terms of sin(φ) = (e − e−jφ)/(2j) as the second term is the one responsible for the mode coupling in coasting beams. It should be stressed here that mode coupling is found already with driving impedance only. Note that the previous approximation is also usually made for bunched beams and this case should therefore also be carefully reviewed in the future. Second, by including the detuning impedance, the coupling is much stronger and this is what we found also in pyHeadTail simulations.

Landau damping is an essential mechanism for ensuring collective beam stability in particle accelerators. Precise knowledge of the strength of Landau damping is key to making accurate predictions on beam stability for state-of-the-art high-energy colliders. In this Letter, we demonstrate an experimental procedure that would allow quantifying the strength of Landau damping and the limits of beam stability using an active transverse feedback as a controllable source of beam coupling impedance. In a proof-of-principle test performed at the Large Hadron Collider, stability diagrams for a range of Landau octupole strengths have been measured. In the future, the procedure could become an accurate way of measuring stability diagrams throughout the machine cycle.

The presented document if the Letter of Intent for the Gamma Factory Proof-of-Principle Experiment.

The High-Luminosity LHC Project aims to increase the integrated luminosity that will be collected by the Large Hadron Collider for the needs of the high energy physics frontier by the end of its Run 3 by more than a factor ten. This will require doubling the beam intensity, and in order to ensure coherent stability until the brighter beams are put in collision, the transverse impedance of the machine has to be reduced. As the major portion of the ring impedance is generated by its collimation system, several low resistivity jaw materials have been considered to lower the collimator impedance and a special collimator has been built and installed in the machine to study their effect. In order to assess the performance of each material we performed a series of tune shift measurements with LHC beams. The results show a significant reduction of the resistive wall tune shift with novel materials, in good agreement with the impedance model and the bench impedance and resistivity measurements. The largest improvement is obtained with a molybdenum coating of a molybdenum-graphite jaw. This coating, applied to the most critical collimators, is estimated to lower the machine impedance by up to 30% and the stabilizing Landau octupole threshold by up to 240 A after accounting for uncertainties of the model and other destabilising effects. A half of the overall improvement can be obtained by coating the jaws of a subset of 4 out of 11 collimators identified as the highest contributors to machine impedance. This subset of low-impedance collimators is being installed during the Long Shutdown 2 in 2019-2020.

Unmatched terminations of single elements were recently identified to be responsible for beam instabilities in the CERN PSB and LEIR machines. Impedance models are needed to estimate the impedance of similar devices and to assess potential intensity limitations. A circuital model that includes the effect of coupling to cables on the beam coupling impedance will be discussed. Moreover, examples of low impedance design with special emphasis on the mitigation of the impedance of ferrite kickers (e.g. longitudinal serigraphy) will be presented and guidelines for optimized impedance design will be provided. Finally, the potential of metamaterials for impedance mitigation will be discussed.

This report summarises the results of MD1875 about impedance measurements of single LHC secondary collimators in IR7. The activity was carried out during MD block 5 of 2016, on 28 October. The impedance of each collimator was measured from the tune shift induced by cycling its gap. As done in previous measurements of the same kind, the tune was reconstructed from the damped oscillations of the beam when coherently kicked with the MKQA, in order to have a clearer signal. The same methodology was applied to crystals, measured during this MD activity for the first time since the LHC start-up. Due to the high level of losses while kicking and the consequent cut of tails, tune signals are not clean; therefore, measurements do not agree with expectations by a factor 2–3.

The LHC at CERN is equipped with a sophisticated collimation system, aimed at protecting superconducting magnets against quenches in case of losses from the circulating beams. The collimation system is one of the major contributors to the machine impedance at top energy. A relevant hardware upgrade of the system will take place in the context of the High Luminosity LHC (HL-LHC) project; one of the main objectives is to make stabilisation of the brighter HL-LHC beams reachable within the capabilities of the Landau octupoles. In fact, a relevant fraction of the carbon–based collimators will be exchanged with new ones, the jaws of which are made of materials more optimised in terms of impedance; hence, the footprint of the collimation system will be significantly reduced. The present contribution gives an overview of the baseline low-impedance upgrade of the LHC collimation system as foreseen by the HL-LHC project and the expected impact on impedance. Additional options that could further improve the footprint of the collimation system on the machine impedance are briefly summarised.

The Gamma Factory project offers the possibility of creating novel re- search tools by producing relativistic beams of highly ionised atoms in CERN’s accelerator complex and exciting their atomic degrees of freedom by lasers to produce strongly collimated high-energy photon beams. Inten- sity of such beams would exceed by several orders of magnitude the ones offered by the presently operating light sources, in the particularly interest- ing energy domain from about 100 keV to above 400 MeV. In this energy regime, the high-intensity photon beams can be used to produce secondary beams of polarised electrons, polarised positrons, polarised muons, neu- trinos, neutrons and radioactive ions. New research opportunities in many domains of physics, from particle physics through nuclear physics to atomic physics, can be opened by the Gamma Factory scientific programme based on the above primary and secondary beams. Except for basic research, it offers also a possibility for various application studies, e.g. in medical physics and nuclear power.