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

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.