The strong space charge regime of future operation of CERN's circular particle accelerators is investigated andmitigation strategies are developed in the framework of the present thesis. The intensity upgrade of the injector chain of Large Hadron Collider (LHC) prepares the particle accelerators to meet the requirements of the High-Luminosity LHC project. Producing the specified characteristics of the future LHC beams imperatively relies on injecting brighter bunches into the Proton Synchrotron Booster (PSB), the downstream Proton Synchrotron (PS) and eventually the Super Proton Synchrotron (SPS). The increased brightness, i.e. bunch intensity per transverse emittance, entails stronger beam self-fields which can lead to harmful interaction with betatron resonances. Possible beamemittance growth and losses as a consequence thereof threaten to degrade the beam brightness. These space charge effects are partly mitigated by the upgrade of the PSB and PS injection energies. Nevertheless, the space charge tune spreads of the future injector beams are found to exceed the values reached by present LHC or other intense fixed target physics beams. This thesis project comprises three key tasks: detailed modelling of space charge effects, measurement at the CERN machines and mitigation of space charge impact. Throughout the course of this thesis, the simulation tool PyHEADTAIL has been developed and extended to model 3D space charge effects in circular accelerators across the wide energy range from PSB to SPS. The implementation for hardwareaccelerating GPU architectures enables extensive studies, especially when employing the self-consistent particle-in-cell algorithm. The implemented models have been benchmarked with analytical results for space charge beam dynamics. In particular, the spectra of quadrupolar pick-ups - which provide a direct measurement method for the space charge tune shift - have been simulated and compared with the derived theory. The space charge situation at the SPS injection plateau has been extensively investigated in the course of comprehensive measurement studies, resulting in the identification of an optimal working point region for the SPS. The interplay of space charge and the horizontal quarter-integer resonance has been scrutinised in measurement, theory and simulation. Last but not least, a new LHC beam type with a hollow longitudinal phase space distribution has been developed for the PSB and proved to substantially mitigate space charge impact on the PS injection plateau.

Space Charge Effects and Advanced Modelling for CERN Low Energy Machines

Accurate measurements of the focusing properties of an accelerator are essential for properoperation of a synchrotron, both for the machine protection and for the performance of the experiment. Measurement of linear optics functions based on turn-by-turn measurements has been developed continuously in pursuit of more accurate results [1, 2, 3, 4]. Optics functions that describe the focusing properties of the machine can be obtained from different observables: phase and amplitude of the transverse betatron oscillations and the change of the tune by modulating the current of quadrupoles (K-modulation) [5]. Reconstruction of linear optics using the phase, in combination with K-modulation, have been the main approaches for obtaining the function in accelerators all over the world [3, 6, 7]. Measurements of optics functions based on the amplitude [8], denoted as from amplitude, have not been used as widely as the other methods since it requires accurate beam-position-monitor (BPM) calibration...

Optics-measurement-based Beam Position Monitor calibration

PyHEADTAIL is a 6D tracking tool developed at CERN to simulate collective effects. We present recent developments of the direct space charge suite, which is available for both the CPU and GPU. A new 3D particle-in-cell solver with open boundary conditions has been implemented. For the transverse plane, there is a semi-analytical BassettiErskine model as well as 2D self-consistent particle-in-cell solvers with both open and closed boundary conditions. For the longitudinal plane, PyHEADTAIL offers line density derivative models. Simulations with these models are benchmarked with experiments at the injection plateau of CERN’s Super Proton Synchrotron.

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Space charge modules for PyHEADTAIL

As part of the LHC Injector Upgrade Project, the CERN PS Booster (PSB) will be upgraded with a H- charge exchange injection system and its injection energy will be raised from 50 MeV to 160 MeV to obtain the beam brightness required for the LHC High-Luminosity Upgrade. Space charge effects like beam losses and transverse emittance blow-up at injection are expected to be the main limitations towards the achievement of the required high brightness. Studies of beam dynamics in presence of space charge in order to evaluate the performances of the PSB after the Upgrade have been performed. The first part of the work consists of measurements in the present machine, to study the effects of space charge and its interplay with resonances and to have a good set of data for code benchmarking. The code chosen for the beam tracking in presence of space charge is PTC-Orbit (and PyOrbit). Necessary numerical convergence studies are presented together with a benchmark with the PSB measurements. Once assessed the code and its limitations, predictions for the 160 MeV injection with high- brightness beams are delivered in terms of beam losses and emittance blow-up. These studies include the optimization of the working-point, resonance compensation and/or chromaticity correction taking into account the expected magnetic errors in the machine.

Performance of the CERN PSB at 160 MeV with $H^{-}$ charge exchange injection

The LHC injector upgrade project (LIU) [1] calls for a twofold increase in intensity of the SPS proton beam. In this paper, we present studies with a new SPS optics called Q22, which has a transition energy in between the one of the operationally used Q20 and Q26 optics. This new optics provides a compromise between the stability of Q20, due to the low transition energy, and the reduced requirements in terms of RF voltage and power in Q26. A non-linear effective model of Q22 has been extrapolated from beam based measurements and used to complement the SPS nonlinear optics model. Furthermore the studies of the TMCI threshold performed so far are discussed.

http://jacow.org/ipac2018/papers/tupaf022.pdf

Studies of a New Optics With Intermediate Transition Energy as Alternative for High Intensity LHC Beams in the CERN SPS

Good knowledge of the non-linear properties of the SPS lattice is crucial for modeling and optimizing the machine performance in the presence of collective effects leading to incoherent tune spreads such as space charge, e-cloud and beam coupling impedance. In view of the LHC injectors upgrade (LIU) project and the future SPS operation in a regime dominated by such collective effects, detailed measurements of the SPS non-linear chromaticity and detuning with amplitude have been performed for the two optics configurations presently available for LHC type beams. The measurement results are used to fit systematic multipole components to the main magnets of the SPS MADX model as a basis for the non-linear machine model that can be used for beam dynamics simulations. The implications for the operation of the SPS with the LIU beam parameters are discussed.

/pdf/improved-methods-for-the-measurement-and-simulation-of-the-2q798dyuii.pdf

Improved Methods for the Measurement and Simulation of the CERN SPS Non-linear Optics

At CERN we have ramped up a program to investigate space charge effects in the LHC pre-injectors with high brightness beams and long storage times. This in view of the LIU upgrade project for these accelerators. These studies require massive simulation over large number of turns. To this end we have been looking at all available codes and started collaborations on code development with several laboratories: pyORBIT from SNS, SYNERGIA from Fermilab, MICROMAP from GSI and our in-house MAD-X code with an space charge upgrade. We have agreed with our collaborators to bench-mark all these codes in the framework of the GSI bench-marking suite, in particular the main types of frozen space charge and PIC codes are being tested. We also include a study on the subclass of purely frozen and the adaptive frozen modes both part of MAD-X in comparison with the purely frozen MICROMAP code. Last, we will report on CERN's code development effort to understand and eventually overcome the noise issue in PIC codes.

https://inspirehep.net/files/9f616c1b6bedce3bc6aca4c1712239c3

JACoW : Code bench-marking for long-term tracking and adaptive algorithms

In order to reach the target beam parameters of the LHC injectors upgrade (LIU) project the beam degradation due to losses and emittance growth on the long injection plateau of the SPS needs to be minimized. A detailed study of the dependence of losses, transverse emittance blow-up and transverse beam tail creation as function of the working point is presented here for a high brightness single bunch beam with a vertical space charge tune spread of about 0.2 on the 26 GeV injection plateau. The beam behavior close to important betatron resonances is characterized and a region in the tune diagram with minimal beam degradation is identified. Implications about the performance for LIU beams are discussed.

http://jacow.org/ipac2016/papers/mopor021.pdf

Space Charge Studies with High Intensity Single Bunch Beams in the CERN SPS

The CERN PS Booster (PSB) is presently running with a space charge tune spread larger than 0.5 at injection. Since the High Luminosity LHC (HL-LHC) will require beams with twice the intensity and brightness of today, the LHC Injector Upgrade (LIU) Project is putting in place an upgrade program for all the injector chain and, in particular, it relies on the important assumption that the PS Booster can successfully produce these beams after the implementation of the 160 MeV H- injection from Linac4. This contribution describes the studies (measure- ments and simulations) that have been carried out to con- firm that the PSB can indeed perform as needed in terms of beam brightness for the future HL-LHC runs. The importance of the mitigation measures already in place, such as the correction of the half-integer line, and the effects of non-linear resonances on the beam are also discussed.

/pdf/space-charge-effects-and-mitigation-in-the-cern-ps-booster-1ep4e6aw78.pdf

Space Charge effects and mitigation in the CERN PS Booster, in view of the Upgrade

The paper presents the outstanding studies performed in 2016 in preparation of the PS Booster upgrade, within the LHC Injector Upgrade project (LIU), to provide twice higher brightness and intensity to the High-Luminosity LHC.Major changes include the increase of injection and extraction energy, the implementation of a H− charge-exchange injection system, the replacement of the present Main Power Supply and the deployment of a new RF system (and related Low-Level), based on the Finemet technology. Although the major improvements will be visible only after the upgrade, the present machine can already benefit of the work done, in terms of better brightness, transmission and improved reproducibility of the present operational beams. Studies address the space-charge limitations at low energy, for which a detailed optics model is needed and for which mitigation measurements are under study, and the blow-up reduction at injection in the downstream machine, for which the beams need careful preparation and transmission. Moreover they address the requirements and the reliability of new beam instrumentation and hardware that is being installed in view of LIU.

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Frank Schmidt

Papers

Improved Methods for the Measurement and Simulation of the CERN SPS Non-linear Optics

JACoW : Code bench-marking for long-term tracking and adaptive algorithms

Space Charge Studies with High Intensity Single Bunch Beams in the CERN SPS

Space Charge effects and mitigation in the CERN PS Booster, in view of the Upgrade

Machine Development Studies in the CERN PS Booster, in 2016