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Landau damping represents the most efficient stabilization mechanism in hadron synchrotron accelerators to mitigate coherent beam instabilities. Recent studies allowed expanding the novel analytical criteria of loss of Landau damping (LLD) to the double harmonic RF system case above transition energy, providing an analytical estimate of the longitudinal stability. The threshold has a strong dependence on the voltage ratio between the harmonic and the main RF systems. Based on that, measurements of single bunch oscillations after a rigid-dipole perturbation have been performed in the CERN Proton Synchrotron (PS). Several configurations have been tested thanks to the multi-harmonic RF systems available in the PS. Higher-harmonic RF systems at 20 MHz and 40 MHz, both in phase (bunch shortening mode) and in counter-phase (bunch lengthening mode) with respect to the principal one at 10 MHz, have been measured.

The baseline design for the high-energy injector complex of a muon collider consists of a chain of pulsed synchrotrons spanning an energy range from 63 GeV to the target collision energy of 5 TeV. This chain incorporates both normal and hybrid synchrotrons, the latter featuring a combination of fixed-field superconducting magnets and pulsed normal-conducting magnets. Initial optics designs for the chain of synchrotrons have been completed, with optimization efforts focused on minimizing the aperture dimensions required for dipoles and quadrupoles.

Within the framework of the NIMMS (Next Ion Medical Machine Study) initiative at CERN, a comprehensive study is being performed for the Helium Light Ion Compact Synchrotron (HeLICS), a compact accelerator for hadron therapy. A key component of this facility is the radiofrequency (RF) cavity. Its proposed design is based on the wideband technology successfully implemented in the CERN PS Booster. It comprises four cells filled with Finemet material that enable the acceleration of protons and 4 He 2+ over a broad energy range. The cavity, designed to deliver a peak voltage of up to 2 kV within a frequency range from 0.88 to 10 MHz, features a compact design to meet the stringent requirements of the medical accelerator. It operates in double-harmonic mode, to effectively reduce longitudinal line density of the beam bunch and mitigate space-charge effects at low energy. The combination of compactness and operational flexibility positions this RF cavity as an optimal solution for compact synchrotrons, enabling more efficient, precise, and accessible hadron therapy for cancer treatment.

The heavy-ion physics programme at CERN relies on lead ion beams. In recent years, interest in conducting experiments with nuclei lighter than lead has grown significantly. Before new ion species can be considered operational for experiments, their feasibility for production and acceleration throughout the accelerator complex must be assessed. Several ion species have been tested in the past: argon and xenon were delivered for NA61/SHINE physics in 2015 and 2017, with xenon also reaching the LHC in 2017. More recent tests in the CERN accelerator complex include oxygen in 2023, in preparation for an LHC oxygen run in 2025; krypton, as a candidate for HL-LHC in Run 5 (2036-2041); and magnesium in 2024, requested by NA61/SHINE, an SPS North Area fixed target experiment. A boron test for the NA61/SHINE is planned during Long Shutdown 3 (2026-2029). This contribution reviews the performance of the ion complex with recent oxygen and magnesium beam tests and future plans for developing new ion species.

During the 2018 proton run, a new radio-frequency beam manipulation has been studied and successfully implemented at the CERN Proton Synchrotron (PS) for the first time. This technique is used to deplete a well-defined fraction of a continuous longitudinal beam distribution by creating a so-called barrier bucket. We propose a new application of the barrier bucket gymnastics in the multiturn extraction scheme used at CERN. These two exotic techniques are combined into a highly sophisticated procedure that dramatically reduces the beam losses at PS extraction, thus paving the way to high-intensity proton beams for future fixed-target experiments at the CERN Super Proton Synchrotron (SPS). In this paper, the expected performance of the PS and SPS is analyzed in detail to define a road map for making this novel extraction scheme operational.

The CERN Proton Synchrotron (PS) determines the basic bunch spacing for the Large Hadron Collider (LHC) by means of rf manipulations. Several rf systems in a frequency range from 2.8 MHz to 200 MHz are available for beam acceleration and manipulations. Each of the six bunches injected from the PS Booster is split in several steps into 12 bunches spaced by 25 ns, yielding a batch of 72 bunches at transfer to the Super Proton Synchrotron (SPS). In the framework of the LHC Injector Upgrade (LIU) project the bunch intensity must be doubled. However, with most of the planned upgrades already in place this intensity has not yet been achieved due to collective effects. One of them is uncontrolled longitudinal emittance blowup during the bunch splittings. In this contribution, measurements of the blow-up during the splitting process are presented and compared with particle simulations using the present PS impedance model. Beam-based measurements of the impedances of the rf cavities have been performed. They revealed that to reproduce the instability an additional impedance source is required in the PS impedance model.

A barrier bucket scheme is being considered to reduce losses during the Multi-Turn Extraction from the CERN Proton Synchrotron to the Super Proton Synchrotron for the fixed- target physics programme. For effective loss reduction, the extraction kicker has to be triggered during the gap at the time of the longitudinal barrier. Initial beam studies at injection energy and with low intensity beams allowed to fully qualify an existing wide-band cavity to generate one or multiple beam synchronous pulses per turn. Bunch-length stretching and shortening have been exercised with barriers moving in azimuth with respect to the beam. The encouraging results obtained at injection energy guided the implementation of a de-bunching manipulation at higher energy to move all bunches into a single barrier bucket. Beam measurements at a momentum of 14GeV/c, varying intensity and the width of the barrier, demonstrate that a quasi-constant longitudinal line density and an almost fully depleted gap can be achieved at highest intensities. The contribution summarises the results of the beam studies at high energy together with some observations related to the Multi-Turn Extraction.

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.

Coupling impedances and wakefields are fundamental quantities to characterize the electromagnetic interaction of a particle beam with the surrounding environment. In particular, collective effects, triggered by these self-induced fields, may play an important role in beam stability and machine performance. Within the framework of the LHC Injectors Upgrade project, since a significantly higher beam intensity is planned for the CERN Proton Synchrotron, wakefields are expected to increase their influence on the beam dynamics, and their evaluation is becoming important. In this paper we present the results of recent measurements of the longitudinal broadband coupling impedance by means of the incoherent quadrupole synchrotron frequency shift as a function of beam intensity. A detailed evaluation of the contribution of several machine installations to the total impedance budget is also presented and compared with the measurements.

With the progress made in 2015, the beams produced by the CERN Proton Synchrotron using multiturn extraction (MTE) have been delivered to the Super Proton Synchrotron (SPS) for the fixed-target physics run. Operation successfully started in the second half of September 2015 and continued until the end of the proton physics program by mid November. In this paper the overall performance and beam quality is discussed in detail considering the complete chain of accelerators, from the PS-Booster to the SPS. Moreover, a thorough comparison of the global performance of the MTE scheme against the previously used technique, the so-called continuous transfer (CT), is also carried out.