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 CERN FCC-ee top-up booster synchrotron will accelerate electrons and positrons from an injection energy of 20 GeV up to an extraction energy between 45.6 GeV and 182.5 GeV depending on the operation mode. These accelerated beams will be used for the initial filling of the high-luminosity FCC-ee collider and for keeping the beam current constant over time using continuous top-up injection. Due to the high-intensities of the circulating beams, collective effects may represent a limitation in the top-up booster. In this work we present a first evaluation of the impedance model and the effects on beam dynamics. Methods to mitigate possible instabilities will be also discussed.

RF phase noise was shown to be effective for controlled longitudinal emittance blow-up in the Proton Synchrotron Booster (PSB) at CERN during beam tests in 2017, with further developments in 2018. At CERN, RF phase noise is used operationally in the Super Proton Synchrotron (SPS) and Large Hadron Collider (LHC). In this paper we show that it is suitable for operation with a variety of beam types in the PSB. In the PSB the synchrotron frequency changes by approximately a factor 4 during the 500 ms acceleration ramp, requiring large changes in the frequency band of the noise. During 2018, a new method of calculating the noise parameters has been demonstrated, which gives upper and lower bounds to the noise frequency band that are smoothly varying through the ramp. The new calculation method has been applied to operational beams accelerated in both single and double RF harmonics, the final results are presented here.

The injectors have delivered different beam types for luminosity production in the LHC during the 2017 run. Besides the nominal beam with 25 ns spacing and 72 bunches at PS extraction, the batch-compression-merging-splitting (BCMS) beam with multiples of 48 bunches at extraction from the SPS has been produced. The reduced number of bunches per batch from the PS is compensated by almost twice as smaller transverse emittance. The vacuum related issues in the LHC (16L2 cell) could be mitigated by switching to the so-called 8b4e beam, where mini-batches of 8 bunches are followed by 4 empty bunch positions in between. Thanks to the flexibility of the injectors, a higher brightness version of the 8b4e has been prepared to quickly react to the needs of the LHC. In this paper, an overview of the beams from the injector complex is given, describing how the beams are produced and summarizing their characteristics, achieved performance and specific limitations. In view of the operation in 2018, the expected beam parameters are presented, as well as a reminder of possible alternative beam types from the injectors. BEAM PRODUCTION SCHEMES All the accelerators in the LHC injector chain contribute to the definition of the beam parameters. The transverse emittance is initially defined at injection in the PS Booster (PSB) and increases linearly with the bunch intensity (brightness curve [1]). The beam pattern is then defined in PS, where rf manipulations are performed to split, merge and compress the beam. The versatility of the rf systems in the PS allows to produce various beam patterns and the rf manipulations used during the 2017 run are shown in Fig. 1. At extraction from the PS, the bunch spacing is 25 ns with the longitudinal emittance adjusted to εL = 0.35 eVs per bunch as a compromise for low capture losses and beam stability in the SPS. The nominal bunch intensity at PS extraction is Nb = 1.3 × 1011 protons per bunch (p/b). Finally, 1 to 4 batches are extracted from the PS to the SPS to maximize the number of bunches per injection into the LHC. An important limitation for beam brightness occurs at the transfer from the PSB to the PS. The longitudinal emittance extracted from the PSB should bemaximized to reduce space charge effects on the PS flat bottom [2]. However, the maximum bunch length for extraction from the PSB to the PS is limited by the rise time of the recombination kickers [3]. In addition, too large momentum spread leads to transverse emittance blow-up due to a known, and unavoidable with ∗ alexandre.lasheen@cern.ch h = 9 .. 1 4 m 7 1 4 2 1 h = 9 .. 1 4 .. 2 1 h = 7 → 2 1 25 ns BCMS 8b4e BC 8b4e standard h = 7 1 4 2 1 Standard h = 2 1 → 4 2 → 8 4

Controlled longitudinal emittance blow-up (from 1 eVs to 1.4 eVs) for LHC beams in the CERN PS Booster is currently achievied using sinusoidal phase modulation of a dedicated high-harmonic RF system. In 2021, after the LHC injectors upgrade, 3 eVs should be extracted to the PS. Even if the current method may satisfy the new requirements, it relies on lowpower level RF improvements. In this paper another method of blow-up was considered, that is the injection of band-limited phase noise in the main RF system (h=1), never tried in PSB but already used in CERN SPS and LHC, under different conditions (longer cycles). This technique, which lowers the peak line density and therefore the impact of intensity effects in the PSB and the PS, can also be complementary to the present method. The longitudinal space charge, dominant in the PSB, causes significant synchrotron frequency shifts with intensity, and its effect should be taken into account. Another complication arises from the interaction of the phase loop with the injected noise, since both act on the RF phase. All these elements were studied in simulations of the PSB cycle with the BLonD code, and the required blow-up was achieved.

Beam instabilities cover a wide range of effects in particle accelerators and they have been the subjects of intense research for several decades. As the machines performance was pushed new mechanisms were revealed and nowadays the challenge consists in studying the interplays between all these intricate phenomena, as it is very often not possible to treat the different effects separately. The aim of this paper is to review the main mechanisms, discussing in particular the recent developments of beam instability theories and simulations.

The CERN PS Booster is the first synchrotron in the LHC proton injection chain, it currently accelerates particles from 50 MeV to 1.4 GeV kinetic energy. Several upgrades foreseen by the LHC Injectors Upgrade Program will allow the beam to be accelerated from 160 MeV to 2 GeV after Long Shutdown 2 in 2021. The present RF systems will be replaced by a new one, based on Finemet technology. These and other improvements will help to increase the LHC luminosity by a factor of ten. In order to study beam stability in the longitudinal plane simulations have been performed with the CERN BLonD code, using an accurate longitudinal impedance model and a reliable estimation of the longitudinal space charge. Particular attention has been dedicated to the three main features that currently let the beam go stably through the ramp: Double RF operation in bunchlengthening mode to reduce the transverse space charge tune spread, exploitation of feedback loops to damp dipole oscillations, and controlled longitudinal emittance blow-up. RF phase noise injection has been considered to study if it could complement or substitute the currently used method based on sinusoidal phase modulation.