Magnetic Model of the CERN Proton Synchrotron

In this thesis, we present development of the first magnetic model of the main Proton Synchrotron magnets. The operation of the machine and conducting research on increasing its performance require a significant amount of the magnetic field data for the optics modelling. For magnets of the Proton Synchrotron, such amount of data cannot be provided by the magnetic measurements, therefore, we have to rely on magnetic models. We have developed the model based on the numerical analysis of the magnetic field in the magnet and performed the validation with the use of the available magnetic measurements data. The results of the 2D quasi-static analysis were used to decompose the multipolar contributions of different magnet circuits on different levels fo the iron core magnetization within the whole range of the PS operation energies. Established formulas of every circuit contributions take into account the global magnetization of the yoke and its saturation as well as a local magnetization changes caused by contributions of other circuits. The 3D numerical analysis was setup to study the influence of the magnet stray field and gaps between the magnet blocks on the integrated multipolar field. Its results were used to derive appropriate model corrections of the integrated multipolar field with respect to the field in the reference cross-section and to approximate the effective magnetic lengths of the auxiliary circuits of the PS magnet. In order to perform a non-linear chromaticity analysis and to take the full advantage of the developed model, we have modified the existing optics model of the PS lattice. We have integrated magnetic model into the optics calculation with two simulation adjustment methods, which optimize the main coil current in similar way as it is done for the real magnets and adjust four free parameters to match the measured parameters of the initial working point. We have successfully validated the combined magnetic and optics models for various beam momentum levels and magnet powering conditions. With the use of the new magnetic model, for the first time in the history of the PS we are able to predict a higher-order chromaticity function for any energy. Base on the optics modelling results, we have derived working point transfer matrices for the non-linear chromaticity, which allow to predict a set of powering current offsets required to apply foreseen working point adjustment. We were also able to model an offset of the measured transfer matrices due to a change of the radial position chosen for the beam production.

Electron Spin Resonance Magnetometers for Particle Accelerators

Anthony Jean Beaumont

CERN is the European Organization for Nuclear Research located in Geneva, Switzerland. Its main goal is to explore fundamental physics and it exists primarily to provide physicists the necessary tools for doing this, namely accelerators. These tools bring particles to almost the speed of light and then use them in different experiments. The CERN Accelerator Complex includes a chain of interconnected accelerators allowing the acceleration of charged particles up to 6.5 TeV per beam (for protons) in 2018 by the Large Hadron Collider (LHC). Different types of accelerator exist, but at CERN the most common are the synchrotrons. For those, the magnetic field is synchronous with the beam momentum. Magnetic models cannot be always used to predict the field within the required reproducibility, which may be as low as 10^(-5), due to non-linear effects (eddy currents, saturation and hysteresis). Therefore, most of the CERN's synchrotrons are equipped with a real time magnetic field measurement system, the so called "B-Train". The magnetic field measurement devices are composed of absolute field sensors (called "markers"), field tracking sensors (called "induction coils"), an acquisition system, a control system that calculates the magnetic field from the sensors, and a distribution system that delivers the field value to the users. Due to the configuration of the CERN accelerator chain, if one of the injectors fails, the LHC cannot have beam. Consequently, a huge consolidation program of the real time magnetic measurement systems was launched to guarantee operation in the long term. Thus the markers are critical devices for operations at CERN and must be carefully developed to fulfil the high performance and reliability requirements of the B-Train systems. This thesis propose new designs for electron spin resonance (ESR) field markers. We discuss in details the design, the operation, and performance of the ESR sensors based on resonator and oscillator structures including comparison between paramagnetic and ferrimagnetic samples. We propose four field marker levels at 36 mT, 106 mT, 360 mT and 710 mT that correspond to resonance frequencies of 1GHz, 3GHz, 10GHz and 20 GHz. Those measurement values cover most of the marker level requirements of the CERN accelerators and achieving resolution up to 0.1 nT/Hz^(1/2) for field ramps as fast as 5 T/s and field gradients as strong as 12 T/m. We conclude with measurements validation performed on the Proton Synchrotron (PS) and on the Low Energy Ion Ring (LEIR) accelerators.

EPFL2020

High Intensity Beam Issues in the CERN Proton Synchrotron

Sandra Aumon

This PhD work is about limitations of high intensity proton beams observed in the CERN Proton Synchrotron (PS) and, in particular, about issues at injection and transition energies. With its 53 years, the CERN PS would have to operate beyond the limit of its performance to match the future requirements. Beam instabilities driven by transverse impedance and aperture restrictions are important issues for the operation and for the High-Luminosity LHC upgrade which foresees an intensity increase delivered by the injectors. The main subject of the thesis concerns the study of a fast transverse instability occurring at transition energy. The proton beams crossing this energy range are particularly sensitive to wake forces because of the slow synchrotron motion. This instability can cause a strong vertical emittance blow-up and severe losses in less than a synchrotron period. Experimental observations show that the particles at the peak density of the beam longitudinal distribution oscillate in the vertical plane due to a short range wake field and following a travelling wave of about 700 MHz. In order to perform measurements, a dedicated single bunch beam was set up with a zero chromaticity plateau around transition energy. Extensive measurements were performed of the dynamics of instability in order to compute rise times and intensity thresholds. These measurements were done for several peak densities and the results show that the longer the bunch length, the higher is the threshold in intensity. Other measurements performed with a small negative chromaticity and another working point show that the intensity threshold can be pushed at higher values—in this case, the threshold was increased by 20%. The particularity of this work is that the instability is triggered during the acceleration. At transition energy, the momentum compaction factor is zero and the exchange of particles between the head and the tail of the beam from synchrotron motion, which is a natural way to damp instabilities, vanishes for few turns. Therefore the measurements at which η the instability is triggered are fundamental to know in which longitudinal regime the instability develops. Macro particle simulations were performed in order reproduce the dynamics of the instability with the HEADTAIL code, that simulates the beam interaction with the impedance of the machine. In the case of the PS, a very detailed impedance model does not exist, therefore a very simple resonator impedance was considered. The parameters of the code were adapted in order to simulate the beam as close as possible to the experimental conditions. The simulations showed that the travelling wave is well reproduced and therefore rise times were extracted for different beam intensities and compared to the measurements. A good agreement is found for a such simple impedance model. The intensity thresholds are reproduced for zero chromaticity within 30% and it is clear that some damping mechanisms occurring in the measurements are not reproduced by the code. In particular, octupolar components of the field, non-linear coupling and transverse space charge are not taken into account. These limitations could cause some discrepancies between model and measurements. This study allows to establish a broadband impedance model which can be use to predict the dynamics of the instability. A few experiments were done also with the use a gamma transition jump. In this case, the instability appears in the adiabatic regime and the rising of the instability is following the peak density of the beam. Both the intensity threshold measurements and the simulations show that the gamma jump is by far the most efficient way to increase significantly the intensity threshold. The choice of adequate working point appears also to be a cure of the instability. This study with the support of measurements provides a rough impedance model confirmed by simulations and an understanding of the different mechanisms triggering the instability. The last part of the thesis is dedicated to proton beam losses studies at injection energy. An eventual upgrade of the high intensity beam is limited by large beam losses at injection in the PS. Losses were measured with the current beam loss monitor system of the PS that they occur while the incoming beam enters in the machine and then during several hundred turns while the beam is circulating. Optics measurements were performed to check the mismatch of the transfer line between the PSBooster and the PS. A significant horizontal dispersion mismatch was found and in particular a difference in optics between the four injection lines of the PS. Aperture bottlenecks were found at the injection septum in both transverse planes and at the maximum of the injection bump. With the help of Monte Carlo simulations, the high radiation outside the ring induced by the losses was understood. However, the mismatch does not explain the continuous losses after the beam is injected. A possible explanation is that the space charge forces contribute to make particles cross resonances and are lost while they are oscillating at high amplitudes. The transverse phase space is refilled due to the combination of the synchrotron motion and space charge. Several solutions were proposed to improve the situation. A new optics of the transfer line and at injection could make the beam size smaller. Some special quadrupoles already installed in the PS could be used to adapt the optics of the incoming beam. Increase the injection energy from 1.4 GeV to 2 GeV kinetic would cause a gain of 65% in space charge forces, and these studies are currently ongoing for the upgrade of the PS in the framework of high-intensity LHC upgrade project. High intensity beams are also perturbed by space charge forces and transverse instabilities. Coherent tune shift measurements were performed at injection and extraction in order to evaluate the transverse imaginary part of the impedance and the contribution of the space charge to betatron frequency shift with the beam intensity.

EPFL2012

Ultra Low Temperature Susceptometer and Magnetometer

Julian Piatek

The first part of this thesis discusses technical details relating to measurements of magnetic properties at ultra low temperatures. The implementation of AC susceptibility at temperatures down to 30 mK is introduced and used as a platform to showcase selected quantum magnets measured during the thesis. Each presented system illustrates a particular strength of AC susceptibility. This is followed by in-depth analysis of the design and implementation of a new solution for a SQUID magnetometer capable of running below 100 mK. The system employs a piezomotor to move the sample inside a dilution fridge, rather than the existing designs, which involve moving the entire dilution fridge. Furthermore, the system is completely modular, allowing for rapid removal from the fridge, and opening the possibility to use it on virtually any commercial dilution refrigerator. The latter part of the thesis presents a comprehensive study of a new family of model magnets, LiHox Er1−x F4, which combines the Ising spins of ferromagnetic LiHoF4 with the XY ones of antiferromagnetic LiErF4. The temperature-doping (T − x) phase diagram has been studied using AC susceptibility, and three key regions investigated in detail using additional neutron scattering experiments and mean-field calculations. The first region, x ≳ 0.6, corresponds to an Ising ferromagnet, where Tc (x) decreases linearly and faster than what mean-field predicts. At T < TC a so-called embedded spin-glass state is observed. The second region, 0.6 ≳ x ≳ 0.3, undergoes a spin-glass transition, where needle-like spin clusters form along the Ising axis below Tg (x) ∼ 0.4 − 0.5 K. Applying a field along the Ising axis at T < 200 mK produces a thermal runaway in the x = 0.50 sample, when the field reaches a value of H = 0.029 ± 0.002 T. The final region, x ≲ 0.3, corresponds to an antiferromagnetically coupled spin-glass, which shows archetypal spin-glass behaviour.

EPFL2012

Electron Spin Resonance Magnetometers for Particle Accelerators

Anthony Jean Beaumont

EPFL2020

High Intensity Beam Issues in the CERN Proton Synchrotron

Sandra Aumon

EPFL2012

Ultra Low Temperature Susceptometer and Magnetometer

Julian Piatek

EPFL2012