Beam Longitudinal Dynamics Simulation Suite BLonD

The beam longitudinal dynamics code BLonD has been developed at CERN since 2014 and has become a central tool for longitudinal beam dynamics simulations. In this paper, we present this modular simulation suite and the various physics models that can be included and combined by the user. We detail the reference frame, the equations of motion, the BLonD-specific options for radio-frequency parameters such as phase noise, fixed-field acceleration, and feedback models for the CERN accelerators, as well as the modeling of collective effects and synchrotron radiation. We also present various methods of generating multi-bunch distributions matched to a given impedance model. BLonD is furthermore a well-tested and optimized simulation suite, which is demonstrated through examples, too

Possible Mitigations of Longitudinal Intensity Limitations for HL-LHC Beam in the CERN SPS

The Super Proton Synchrotron (SPS) at CERN is the injector of the Large Hadron Collider (LHC), the world's largest particle collider. The High-Luminosity LHC (HL-LHC) project is a major step forward in the improvement of the LHC performances and it requires a doubling of the nominal bunch intensity of the current LHC beam. In the SPS, multi-bunch instabilities and particle losses limit the beam intensity that can be accelerated to 450 GeV/c and transferred to the LHC. Without mitigation measures, the bunch intensity threshold for longitudinal instabilities is three times below the nominal intensity of the LHC beam. Moreover, the present limited RF power is not sufficient to accelerate beams with intensities well above nominal without substantial particle losses and a reduction of the RF voltage available for the beam at the flat top energy. The SPS will undergo significant upgrades but they may not be sufficient to ensure the stability of the HL-LHC beam. The objectives of this doctoral research are to study the longitudinal intensity limitations of the LHC proton beam in the SPS and to find possible mitigation measures to ensure the beam stability and quality at HL-LHC intensity. Beam measurements and particle simulations are used in conjunction with analytical estimations to study the multi-bunch instabilities during the cycle in the SPS. This work attempts to identify the main sources of instabilities and beam quality degradation. Possible scenarios of mitigation measures are investigated to explore the future beam parameters achievable after upgrades. The effects on beam stability of the foreseen RF upgrade, the double RF operation and the reduction of various longitudinal beam-coupling impedances are analysed in detail. The scenario of a lower-harmonic RF system in the SPS, for particle losses reduction, is also studied

Simulations of longitudinal beam stabilisation in the CERN SPS with BLonD

The Super Proton Synchrotron (SPS) at CERN, the Large Hadron Collider (LHC) injector, will be pushed to its limits for the production of the High Luminosity LHC proton beam while beam quality and stability in the longitudinal plane are influenced by many effects. Particle simulation codes are an essential tool to study the beam instabilities. BLonD, developed at CERN, is a 2D particle-tracking simulation code, modelling the longitudinal phase space motion of single and multi-bunch beams in multi-harmonic RF systems. Computation of collective effects due to the machine impedance and space charge is done on a multi-turn basis. Various beam and cavity control loops of the RF system are imple-mented (phase, frequency and synchro-loops, and one-turndelay feedback) as well as RF phase noise injection used forcontrolled emittance blow-up. The longitudinal beam stability simulations during long SPS acceleration cycle ($\sim$20 s)include a variety of effects (beam loading, particle losses, controlled blow-up, double RF system operation, low-level RF control, injected bunch distribution, etc.). Simulations for the large number of bunches in the nominal LHC batch (288) use the longitudinal SPS impedance model containing broad and narrow-band resonances between 50 MHz and 4 GHz. This paper presents a study of beam stabilisation in the double harmonic RF system of the SPS system with results substantiated, where possible, by beam measurements

Effect of the Extraction Kickers on the Beam Stability in the CERN SPS

Longitudinal beam instability in the CERN SPS is a major limitation in the ability to achieve the bunch intensities required for the goals of the High-Luminosity LHC project (HL-LHC). One of the major drivers in limiting the intensity of the machine is the broadband contribution to the beam-coupling impedance due to the kicker magnets. The extraction kickers (MKE) discussed in this paper are known to give a significant contribution to the overall longitudinal beam-coupling impedance. We present the results of bench measurements of the MKE's impedance to determine the accuracy of electromagnetic simulation models from which the impedance modelused for beam dynamics simulationsis constructed. In addition, we discuss the feasibility and implementation of beam measurements that can indicate the contribution of the MKE magnets to the longitudinal beam-coupling impedance of the SPS

Effect of the Various Impedances on Longitudinal Beam Stability in the CERN SPS

The High Luminosity (HL)-LHC project at CERN aims at a luminosity increase by a factor ten and one of the necessary ingredients is doubling the bunch intensity to 2.4x10¹¹ ppb for beams with 25 ns bunch spacing. Many improvements are already foreseen in the frame of the LHC Injector Upgrade (LIU) project, but probably this intensity would still not be reachable in the SPS due to longitudinal instabilities. Recently a lot of effort went into finding the impedance sources of the instabilities. Particle simulations based on the latest SPS impedance model are now able to reproduce the measured instability thresholds and were used to determine the most critical impedance sources by removing them one by one from the model. It was found that impedance of vacuum flanges and of the already damped 630 MHz HOM of the main RF system gave for 72 bunches the comparable intensity thresholds. Possible intensity gains are defined for realistic impedance modifications and for various beam configurations (number of bunches, longitudinal emittances) and RF programs (single and double RF). The results of this study are used as a guideline for planning of a new campaign of the SPS impedance reduction

Lower-Harmonic RF System in the CERN SPS

Significant beam losses increasing with intensity are observed at capture and along the SPS flat bottom for the LHC-type proton beam. The intensity should be doubled for HL-LHC and high losses may be a major performance limitation. Bunches extracted from the PS, the SPS injector, are produced in a 40 MHz RF system applying a bunch rotation at the end of the cycle and therefore cannot be perfectly matched to the 200 MHz SPS RF bucket. The possibility of using a lower harmonic additional RF capture system in the SPS was already proposed after the LEP era in preparation for transfer of the LHC beam but the bunch rotation was the preferred solution, since the induced voltage in the SPS 200 MHz RF system would be too large to ensure stability in a low harmonic system without mitigation measures. However, the use of the upgraded one-turn feedback and the 200 MHz RF system as a Landau cavity could help to improve stability. The feasibility of this scenario to reduce capture losses in the SPS is analysed and presented in this paper. The choice of an optimum RF frequency and voltage is also discussed. The transfer to the main 200 MHz is simulated using a realistic bunch distribution

Improvement of the Longitudinal Beam Transfer from PS to SPS at CERN

The beam transfer from the Proton Synchrotron (PS) to the Super Proton Synchrotron (SPS) at CERN is a critical process for the production of beams for the Large Hadron Collider (LHC). A bunch-to-bucket transfer is performed with the main drawback that the rf frequency in the SPS (200 MHz) is five times higher than the one in the PS (40 MHz). The PS bunches are therefore shortened non-adiabatically before extraction by applying a fast rf voltage increase (bunch rotation) to fit them into the short rf buckets in the SPS. However, particles with large amplitude of synchrotron oscillations in the PS longitudinal phase space are not properly captured in the SPS. They contribute to losses at the injection plateau and at the start of acceleration in the SPS. In this contribution, we present measurements and simulations performed to identify the source of the uncaptured particles. The tails of the particle distribution were characterized by applying longitudinal shaving during acceleration. Furthermore, the rotated bunch distribution was improved by linearizing the rf voltage using a higher-harmonic rf cavity

Studies of Capture and Flat-Bottom Losses in the SPS

One of the strong limitations for reaching higher beam intensities in the SPS, the injector of the LHC at CERN, are particle losses at flat bottom that increase with beam intensity. In this paper, different sources of these losses are investigated for two available SPS optics, using both measurements and simulations. Part of the losses originate from the PS-to-SPS bunch-to-bucket transfer, because the PS bunches are rotated in longitudinal phase space before injection and do not completely fit into the SPS RF bucket. The injection losses due to different injected bunch distributions were analyzed. Furthermore, at high intensities the transient beam loading in the SPS has a strong impact, which is (partially) compensated by the LLRF system. The effect of the present and future upgraded one-turn delay feedback system and phase loop on flat-bottom losses was studied using the longitudinal tracking code BLonD. Finally, the total particle losses are also affected by limitations in the SPS momentum aperture, visible for higher RF capture voltages in optics with lower transition energy and higher dispersion

Capture and flat-bottom losses in the CERN SPS

Particle losses on the flat bottom of the SPS, the last accelerator in the injector chain of the LHC at CERN, are a strong limitation for reaching the high intensities required by the high-luminosity upgrade of the LHC. Two contributions to these losses are investigated in this paper. The first losses occur during the PS-to-SPS bunch-to-bucket transfer, since the bunch rotation in the PS creates halo particles and the bunch does not completely fit into the SPS RF-bucket. The effect of longitudinal shaving in the PS on the beam transmission was recently tested. At high intensities, further capture losses are caused by beam loading in the main travelling wave RF system of the SPS, which is partially compensated by the LLRF system, in particular by the one-turn delay feedback. While the feedforward system reduces the capture losses, it also increases the losses along the flat bottom due to the RF noise