A finite element model of the LHC dipole cold mass with hysteretic, non-linear behavior and single turn description

In one of its acceptation, the word quench is synonym of destruction. And this is even more consistent with reality in the case of the Large Hadron Collider dipole magnets, whose magnetic field and stored energy are unprecedented: the uncontrolled transition from the superconducting to the resistive state can be the origin of dramatic events. This is why the protection of magnets is so important, and why so many studies and investigations have been carried out on quench origin. The production, cold testing and installation of the 1232 arc dipole magnets is completed. They have fulfilled all the requirements and the operation reliability of these magnets has already been partially confirmed. From an academic standpoint, nevertheless, the anomalous mechanical behaviour, which was sometimes observed during power tests, has not yet been given a clear explanation. The work presented in this thesis aims at providing an instrument to better understand the reasons for such anomalies, by means of finite element modelling of the cross-section of the dipole cold mass. During the investigation on quench phenomenology and its characterization, a distinction can be done between the two main quench origins during cold test without beam: the local degradation of the conductor and the frictional heating resulting from mechanical disturbances (such as conductor motion under the effects of the Lorentz forces). Concerning the second type, it is illustrated how important a good positioning of the cables is in a magnet cross-section and which is the fundamental role of azimuthal pre-stress. There are numerous studies of the consequences of conductor motion under the effect of electro-magnetic forces and of the loss of pre-stress during energization. However, no model has ever been able to reproduce in detail and predict such phenomena. The present model, developed in ANSYS® environment, was initiated with the idea of representing the real behaviour of an LHC-type dipole coil, by taking into account each turn individually, reproducing the non-linear and hysteretic mechanical behaviour observed on a stack of insulated cables and inserting friction between mating surfaces. The representation of the mechanical complexity of the composite material is certainly one of the originalities of this study. To validate the model, a comparison with elastic modulus measurements, systematically performed in industry, was carried out, both for single layers and for assembled poles. The agreement is certainly worth the effort lavished and justifies the following steps in simulation, which are the modelling of the collaring mechanism and the cool-down process. These are other important and original elements. The last one, in particular, requires progressively changing the mechanical properties of the superconductor, following the temperature profile. This implied some simplifications to comply with the enhanced convergence difficulties, but does not invalidate the goodness of the description and the results obtained. This is a faithful reproduction of a magnet life-cycle, uncommon in this kind of studies.

Stability modeling of the LHC Nb-Ti Rutherford cables subjected to beam losses

Luca Bottura, Enrico Felcini

The Large Hadron Collider (LHC) at CERN is being prepared for its full energy exploitation during Run III, i.e. an increase of the beam energy beyond the present 6.5 TeV, targeting the maximum discovery potential attainable. This requires an increase of the operating field of the superconducting dipole and quadrupole magnets, which in turn will result in more demanding working conditions due to a reduction of the operating margin while the energy deposited by particle loss will increase. Beam-induced magnet quenches, i.e. the transition to normal conducting state, will become an increasing concern, because they could affect the availability of the LHC. It is hence very important to understand and be able to predict the quench levels of the main LHC magnets for the required values of current and generated magnetic fields. This information will be used to set accurate operating limits of beam loss, with sufficient but not excessive margin, so to achieve maximal beam delivery to the experiments. In this study we used a one dimensional, multi-strand thermal-electric model to analyze the maximum beam-losses that can be sustained by the LHC magnets, still remaining superconducting. The heat deposition distribution due to the beam losses is given as an input for the stability analysis. Critical elements of the model are the ability to capture heat and current distribution among strands, and heat transfer to the superfluid helium bath. The computational model has been benchmarked against energy densities reconstructed from beam-induced MB (Main Bending) dipole quenches during LHC operation at 6.5 TeV. The model was then used to evaluate the stability margin of both MB and MQ (Main Quadrupole) magnets at different beam energies, up to the expected ultimate operating energy of the LHC, 7.5 TeV. The comparison between the quench levels underlines how the increase of beam energy implies a substantial reduction of magnets stability and will require much stricter setting on the allowable beam losses to avoid resistive transitions during operation.

2019

Analysis of a Novel Toroidal Configuration for Hadron Therapy Gantries

Enrico Felcini

Hadron therapy refers to a medical treatment that uses hadron beams (i.e. protons and ions) to deliver localized energy that suppresses cancerous cells, sparing the neighbouring healthy tissues from unwanted radiation. The major technical components of a hadron therapy centre are the particle accelerator (cyclotron, synchrotron, or linac) and the beam delivery system that controls, shapes and orients the particles towards the area to be treated. The beam delivery can consist of fixed transfer lines, or it can include a gantry, a transfer line that rotates around the patient and allows radiation from multiple directions. The present work investigates a new toroidal gantry for hadron therapy, named GaToroid. This novel gantry configuration allows the dose delivery from a discrete number of angles avoiding magnets as well as patient rotation. Compared to traditional gantries that require rotating magnets, this improvement is made possible by a toroidal magnet operating in steady-state. This design constitutes the ideal conditions for the use of superconductors to generate a significantly higher magnetic field compared to normal-conducting solutions, as well as to reduce the weight and footprint of the magnets. The study of a GaToroid system requires the integration of several aspects of physics and engineering. In this framework, the focus of this research is on the design of the superconducting coils integrated with beam optics and particle tracking analyses. The first part of the thesis illustrates the optimization of the toroidal magnet. Coupling two-dimensional particle tracking and magnetic field calculations, an algorithm was developed to identify optimal gantry configurations that maximize the energy acceptance of the system. Two solutions composed of 16 coils, differing in high and low values of engineering current density, were investigated. In line with current clinical requirements, the beams converged at the isocenter within 1 mm over the whole treatment energy spectrum for both configurations. The second part of the thesis describes the algorithm implemented for the two- and three-dimensional particle tracking. Building upon the results of the magnetic optimization, a linear beam optics formalism was developed to determine the focusing properties of GaToroid. The third part of the thesis focuses on the engineering design of the low current density solution. Using two thermo-electric models, lumped and one-dimensional, the Nb-Ti and ReBCO cable geometries were validated, together with the quench protection system. Furthermore, analytical and numerical studies on mechanics made it possible to estimate the overall footprint and weight of the system. Results show that, compared with the state-of-the-art gantries, the proposed GaToroid solution has the potential to be more compact and lighter by at least a factor two. Finally, the last part of the thesis describes the design of a scaled-down demonstrator wound with ReBCO tapes. Studies on quench protection, mechanics and experimental implementation aimed at testing the use of ReBCO technology for GaToroid coils are discussed. In conclusion, this work presents the first overall description of a GaToroid system, ranging from the analytical definition, magnetic optimization, particle tracking and magnet engineering. The investigation of this new toroidal paradigm for gantries represents a quantum step toward more compact and less expensive solutions for hadron therapy centres.

EPFL2021

An early separation scheme for the LHC luminosity upgrade

Guido Sterbini

In this thesis we evaluate the potential of the Early Separation Scheme for the Luminosity Upgrade of the Large Hadron Collider (LHC). The main goal of the Early Separation Scheme is to reduce the crossing angle between the proton beams at the collision point in order to increase the luminosity performance of the machine and to alleviate, at the same time, the detrimental effects due to the electromagnetic interaction between the beams. The Early Separation Scheme consists of four dipoles for each of the two high luminosity Interaction Points of the LHC, corresponding to the ATLAS and CMS detectors. Two dipoles out of the four, the so-called D0 dipoles, have to be integrated in the experimental cavern. We show that, working in synergy with an increased beam current and with a stronger final focusing system, the Early Separation Scheme can provide an integrated luminosity of 3000 fb-1 over a period of 6.5 – 7 years with a leveled luminosity of 5.5 1034 cm-2 s-1. These figures are possible thanks to the luminosity leveling by using the crossing angle. We study the impact of the Early Separation Scheme from the beam dynamics point of view by evaluating its linear and non-linear effects. We show, using an analytical approach, that all induced linear effects are negligible. The non-linear effects, namely the electromagnetic interaction between the beams, are considered by means of numerical simulations and dedicated experiments. From the simulation and the experimental results, we have indications about the minimum beam crossing angle that is still compatible with the beam dynamics constraints. From these indications and by considering the different issues related to the integration of the scheme in the detectors, we propose to position the D0 dipole at 14 m from the Interaction Point. The integrated magnetic field required and the space constraints in the detectors imply the use of a superconducting D0 dipole: we optimize its aperture to reduce the power deposited on the magnet's coil by the collision debris. Due to the high power density impinging on the coil and to the 9 T magnetic field required, we propose a magnet cross-section using a Nb3Sn superconducting cable at the temperature of 4.2 K.

EPFL2010