Design optimization and evaluation of the 3 kA MgB$_2$ cable at 4.3 K for the superconducting link project at CERN

High-current superconducting links (SC links) are being developed at CERN for powering the superconducting magnets of the High-Luminosity Large Hadron Collider upgrade. The links contain MgB$_2$ cables, each about 100 m long, rated at currents of up to 18 kA. The assembly of the cables is carried out with reacted wires; cable geometry and cabling processes take into account the mechanical properties of the reacted MgB$_2$ conductor. The production of the cables as well as their final installation requires good mechanical stability, flexibility and electrical performance. The superconductor should have good mechanical strength in view of the stresses during cabling (tension and bending), operation at cryogenic temperatures (Lorentz forces and thermal contraction) and handling installation (tension and bending) at room temperature. Moreover, the electrical integrity of the MgB$_2$ wire ($I_C$ degradation ≤5%) should be ensured after the cabling process for the SC links. Therefore, the study of the mechanical properties of the MgB$_2$ wire and the definition of the cable design parameters are crucial for the project. In the present work we report on the optimization and validation of the design of the 18-strand, 3 kA MgB$_2$ cable by assessing the electromechanical behaviour of 3 kA MgB$_2$ superconducting cables produced with different cabling parameters. The critical current ($I_C$ ) of the MgB$_2$ wires was measured after triple bending and axial tensile load, and strands extracted from the cables were tested to quantify the critical current degradation. Electrical measurements of two, 2 m long, 18-strand MgB$_2$ cables were carried out in the FRESCA test facility at CERN and no degradation was observed. Cabling parameters such as the bending radius and the twist pitch were evaluated, and the most appropriate geometries for the MgB$_2$ 18-strand cables have been selected. Numerical simulations were performed to allow a detailed study of the strains developed in the MgB$_2$ strands due to the mechanical loading. The present results have been successfully transferred to industry for the first industrial production in the framework of the SC Link project.