Design of Nb3Sn magnetic devices to study the superconductor degradation under variable mechanical load

The Large Hadron Collider (LHC) is a two-ring, superconducting synchrotron accelerator and collider installed in a 27 km long tunnel aiming at the discovery of the Higgs particle and the study of rare events with center mass collision energies of up to 14 TeV. The number of collisions per unit of area and time in a collider are evaluated trough the Luminosity function. Inside the LHC, superconducting magnets aligned with a precision of a few tenths of millimeters are used to bend and focus the particle trajectories. The LHC can be considered as the state of the art for superconducting magnets using the Nb-Ti superconductor technology. Therefore, a higher luminosity and beam energy can be achieved in the LHC only by using a more performing superconductor, such as the Nb3Sn. This is considered as the most suitable superconductor to be used in high field magnets, allowing peak field of the order of 15 T. Nevertheless, the critical current jc variations in a Nb3Sn has been found as strongly dependent on the mechanical deformation provided. If the dependency of jc on the axial strain imposed along the wire axis is nowadays well known, the relation between jc reduction and transverse applied stress is not well described. Nowadays, the superconductor research community addresses the irreversible current degradation to a level of stress of about 150-200 MPa, referring to evidences of experimental tests on single cables rather than on Nb3Sn magnets. Nevertheless, this limit has not yet well understood, being the analysis results largely spread due to the influence of the cable features and of the test devices. Aim of this work is to design analytical and experimental tools that will allow studies on the correlation between applied mechanical stress and magnetic performances. The analytical approach presented in the first part of the thesis is intended in a preliminary understanding of the stress field distribution in cosθ-type coils, namely: quadrupoles and dipoles. A simple sector coil layout with constant current density is analyzed, as a representative of real coil cross sections. We focused in particular on the peak stress on coil mid-plane at short sample conditions, being the main responsible for cable current degradation. The peak stress has been correlated to the main 2 magnetic design parameters, i.e. the bore field for dipoles, and the field gradient for quadrupoles. This parametric analysis has been carried out considering firstly a simple coil in air, and then accounting for a magnetic screen which encloses the coil. This required a modification of the stress equations, and a reparameterization of the short sample current, carried out in an original and semi-analytic way. The value of 150 MPa as limit of Nb3Sn cables is nowadays assumed on the base of experimental evidence on magnets tests. Nevertheless, the lack of reproducible measurements and of a dedicated test facility led to the idea of developing a new sample holder. This will be used in the cable test facility FRESCA at CERN, capable of providing a 10 T dipole-like background field. It will be used to test cables up to widths of 16 mm, with a pressure variable from 50 to 200 MPa. The challenge has been to develop a device to be integrated in the FRESCA magnet bore (70 mm), avoiding any material plasticization and assuring a uniform stress distribution on the cable. The structure will adopt the same working philosophy as the magnets tested at LBNL. Part of the pre-load is transmitted at room temperature, whereas the total load is achieved by exploiting the thermal contraction between the sample holder elements. A short scale model has been built and tested at CERN, comparing the test results to a 3D FE model. The optimization of a racetrack dipole magnet is presented in the last part. The original model, called the SD01, required some structural and instrumentation improvements. In the thesis, we will focus on the magnetic and mechanical optimization. The project has been defined SMC (Short Model Coil) program, involving different European laboratories in a joint venture concerning: magnet design, cable optimization, and research on cable insulation. The project is part of the NED program. We will describe the models (2D and 3D) used for the magnetic design, giving details on the all optimization procedure, up to the final configuration. We will finally describe the mechanical parametric analysis by means of numerical models, aimed at defining the coil pre-load.