Field quality in Nb3Sn superconducting accelerator magnets

Colliders of highly energetic particle beams are a crucial tool for high energy physics (HEP) and accelerator magnets are an essential component to steer and focus the particle beam. To enable highest energy hadron colliders, reliable and cost-effective magnet technologies are fundamental. Today Nb3Sn is the superconductor that reached a level of maturity enough to be considered as a candidate material to reach field levels above 10 T. This pursuit of higher magnetic fields translates into challenges for the magnet design. A major milestone for the technology will be the first-time implementation of Nb3Sn quadrupole accelerator magnets in the High Luminosity Upgrade of the Large Hadron Collider (HL-LHC). After more than 20 years of development, the production of the first mini-series of Nb3Sn accelerator-quality magnets is ongoing, paving the path towards the next generation magnets. The work presented in this thesis is focused on the magnetic performance, contributing to a better understanding of these magnets, needed to define targets for future generation accelerator magnets. HL-LHC Nb3Sn magnets are exploring an unprecedented operating current density in the strand of 700–800 A/mm2 and a magnetic energy density 50 % higher than the NbTi main dipoles of the LHC. In addition, fabrication of Nb3Sn coils requires a heat treatment to 650ºC after winding to form the superconducting phase. The formation of the superconducting phase produces a volume expansion leading to radial, azimuthal, and axial dimensional changes of the conductor. The position of the conductors must be controlled with a precision greater than 0.1 mm. Compared to the Nb-Ti, state-of-the-art Nb3Sn conductor features larger filament size and higher critical current density resulting on a strand magnetization about one order of magnitude larger, which has an impact on the field errors in particular at injection. A superconducting magnet is therefore a complex electro-magnetic-mechanical system and HL-LHC marks the start of a new era in particle accelerators. The aim of this work is to study the magnetic behaviour of the Nb3Sn magnets for the HL-LHC upgrade in order to stablish a solid background for future accelerators. Special focus is given to the intrinsic difficulties of Nb3Sn technology. After a brief introduction, the second chapter will describe the challenges to reach the 12 T field level and the main design features of the MBH-11 T dipoles and MQXF quadrupoles. Chapter three focuses on the geometric field errors with an assessment of the precision in the positioning of the conductors within the magnet cross section. Later on, the contribution of ferromagnetic materials is discussed including the capabilities to correct field errors through magnetic shimming. The last two chapters address the magnetization and coupling current effects (field distortions and AC losses), including the dynamic effects at injection (decay and snapback).