Simulations of RF beam manipulations including intensity effects for CERN PSB and SPS upgrades

During Long Shutdown 2 (LS2, 2019-2021) all the injectors of the CERN LHC will undergo several upgrades to fulfill the requests of the LHC Injectors Upgrade (LIU) Project. Among them, an increase in luminosity of the LHC beam by a factor of ten and two respectively for proton and ion beams is expected. The upgrades of the CERN PSB, the first synchrotron in the LHC proton injection chain, will be significant. The injection and extraction beam energies will be increased respectively from 50 MeV to 160 MeV kinetic energy (via the new Linac4) and from 1.4 GeV to 2 GeV (using new magnet power supplies). The required beam intensities will be a factor of two higher for High-Luminosity LHC (HL-LHC) beams, and the currently used narrow-band ferrite RF systems will be replaced by broad-band Finemet® cavities. For ion beams instead, a fundamental upgrade will concern the CERN SPS, the LHC injector, where the Low Lever RF functionalities will be considerably enhanced to allow the interleaving of two batches in longitudinal phase space through momentum slip-stacking, aiming at halving the bunch spacing. In order to predict future longitudinal beam stability and optimize complex RF manipulations both for PSB and SPS, longitudinal macro-particle simulations have been performed. Concerning the PSB, an accurate impedance model and a careful estimation of the space charge effects were included in simulations. Beam and cavity-based feedbacks were also taken into account. Controlled longitudinal emittance blow-up, currently obtained through phase modulation with a dedicated higher harmonic RF system, was achieved in measurements and simulations for the first time injecting RF phase noise in the main harmonic cavity, showing some advantages in using this new method. As for the SPS, the slip-stacking dynamics with collective effects has been studied in details aiming at optimizing the numerous parameters present and satisfying the stringent constraints on losses and bunch length at extraction. Beam quality issues were analyzed together with possible remedies. All simulations have been performed with the macro-particle longitudinal beam dynamics CERN BLonD code, after particular efforts have been spent to implement several algorithms for non ultra-relativistic energy machines (like the PSB) and for slip-stacking dynamics in order to easily optimize the large parameter space available. Benchmarks between BLonD, other codes and analytical formulas have been performed to study different approaches for induced voltage calculation and give some guidelines on the pros and cons of each of them

High-precision RF voltage measurements using longitudinal phase-space tomography in CERN PSB and SPS

Precisely determining the gap voltage and phase in an RF cavity is essential for the calibration of the LLRF feedbacks. Following the conventional approach, measured RF power is converted into gap voltage, assuming a given shunt impedance. However, power and impedance evaluations can both have large uncertainties. Alternatively, the voltage can be obtained precisely with a technique based on longitudinal phase-space tomography. From a set of bunch profiles, tomography reconstructs the bunch distribution in the longitudinal phase-space. The quality of the reconstruction strongly depends on the RF voltage and therefore allows to derive its absolute value. In this paper we describe the tomography-based voltage measurements performed in the CERN PSB and SPS, where this method allowed to detect significant voltage errors for the main RF systems. After applying the correction factors in the LLRF, 1\% accuracies were reached. We report here also the remarkable results achieved by using this technique to calibrate the voltage of the SPS higher-harmonic cavities at 800 MHz, as well as their relative phases with respect to the 200 MHz cavities.Comment: Talk presented at LLRF Workshop 2023 (LLRF2023, arXiv: 2310.03199

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

Time varying RF phase noise for longitudinal emittance blow-up

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

Comparison of Different Methods to Calculate Induced Voltage in Longitudinal Beam Dynamics Codes

Collective effects in longitudinal beam dynamics simulations are essential for many studies since they can perturb the RF potential, giving rise to instabilities. The beam induced voltage can be computed in frequency or time domain using a slicing of the beam profile. This technique is adopted by many codes including CERN BLonD. The slicing acts as a frequency filter and cuts high frequency noise but also physical contributions if the resolution is not sufficient. Moreover, a linear interpolation usually defines the voltage for all the macro-particles, and this can be another source of unphysical effects. The MuSiC code describes interaction between the macro-particles with the wakes generated only by resonator impedances. The complications related to the slices are avoided, but the voltage can contain high frequency noise. In addition, since the computational time scales with the number of resonators and macro-particles, having a large number of them can be cumbersome. In this paper the features of the different approaches are described together with benchmarks between them and analytical formulas, considering both single and multi-turn wakes

Studies of Longitudinal Beam Stability in CERN PS Booster After Upgrade

The CERN PS Booster, comprised of four superposed rings, is the first synchrotron in the LHC proton injection chain. In 2021, after major upgrades, the injection and extraction beam energies, as well as the acceleration rate, will be increased. The required beam intensities should be a factor of two higher for nominal LHC and fixed-target beams, and the currently used narrow-band ferrite systems will be replaced by broad-band Finemet cavities in all four rings. Future beam stability was investigated using simulations with the Beam Longitudinal Dynamics (BLonD) code. The simulation results for existing situation were compared with beam measurements and gave a good agreement. An accurate impedance model, together with a careful estimation of the longitudinal space charge, was used in simulations of the future acceleration cycle in single and double RF, with phase and radial loops and controlled longitudinal emittance blow-up. Since the beam is not ultra-relativistic and fills the whole ring (h=1), the front and multi-turn back wakes were taken into account, as well as the RF feedbacks which reduce the effect of the Finemet impedance at the revolution frequency harmonics

Frequency-Dependent RF Voltage Calibration Using Longitudinal Tomography in the CERN PSB

Longitudinal phase-space tomography reconstructs the phase-space distribution from a set of bunch profiles and the accelerator parameters, which includes the RF voltage. The quality of the reconstruction depends on the accuracy to which these parameters are known. Therefore, it can be used for beam-based RF voltage calibration by analysing oscillations of a mismatched bunch. The actual RF voltage may be different from the programmed one due to uncertainties of the electrical gap voltage measurements and intensity effects. Tomography-based RF voltage calibration was systematically performed with low-intensity bunches in all four rings of the PS Booster (PSB) at injection and extraction energy. For each of the three RF cavities present in a given ring, the calibration was performed separately to extract the voltage errors while avoiding any influence of phase misalignments. The number of synchrotron oscillation periods available for the voltage calibration was constrained by the short duration of the PSB flat-bottom and top. Longitudinal beam dynamics simulations using the full PSB impedance model were performed to benchmark the results provided by the calibrations

Preparations for upgrading the RF systems of the PS Booster

The accelerators of the LHC injector chain need to be upgraded to provide the HL-LHC beams. The PS Booster, the first synchrotron in the LHC injection chain, uses three different RF systems (first, second and up to tenth harmonic) in each of its four rings. As part of the LHC Injector Upgrade the current ferrite RF systems will be replaced with broadband Finemet cavities, increasing the flexibility of the RF system. A Finemet test cavity has been installed in Ring 4 to investigate its effect on machine performance, especially beam stability, during extensive experimental studies. Due to large space charge impedance Landau damping is lost through most of the cycle in single harmonic operation, but is recovered when using the second harmonic and controlled longitudinal emittance blow-up. This paper compares beam parameters during acceleration with and without the Finemet test cavity. Comparisons were made using beam measurements and simulations with the BLonD code based on a full PS Booster impedance model. This work, together with simulations of future operation, have provided input for the decision to adopt a fully Finemet RF system