The Role of Azimuthal Prestress in the Longitudinal Degradation of Nb3Sn Superconducting Magnets

Superconducting magnet coils are subject to enormous electro-magnetic forces which push the cables away from the winding pole, and against the surrounding structure. This structure is usually optimized trying to limit the overall motion and the strains experienced by the superconducting elements. To achieve this, preload forces are applied both in the coil cross-section and along its length. If the e.m. forces overcome these preloads, separation between the coil and the pole occurs, resulting in an overall loss of rigidity. During the magnet design process, it is often tempting to treat the optimization of the azimuthal and longitudinal preload systems separately. However, the two are inextricably related: as the cross-section preload increases, friction can prevent any motion in the longitudinal plane, and decreasing it can instead allow dangerous motions in the conductor ends. The latter can result in very high strains and, in Nb₃Sn conductors, damage that can prevent the magnet to reach the desired performances. In an attempt to define design guidelines, in this paper we use simplified numerical models to compute, as a function of the in-plane prestress, the variation of the peak strains in the end region of the coils. Finally, we investigate the impact of the azimuthal prestress on a real magnet case, the High-Luminosity Nb₃Sn Quadrupole MQXF.