Second-Generation Coil Design of the Nb₃Sn low- $\beta$ Quadrupole for the High Luminosity LHC

As part of the Large Hadron Collider (LHC) Luminosity upgrade program, the U.S.-LHC Accelerator Research Program collaboration and CERN are working together to design and build a 150-mm aperture Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn quadrupole for the LHC interaction regions. A first series of 1.5-m-long coils was fabricated and assembled in a first short model. A detailed visual inspection of the coils was carried out to investigate cable dimensional changes during heat treatment and the position of the windings in the coil straight section and in the end region. The analyses allow identifying a set of design changes which, combined with a fine tune of the cable geometry and a field quality optimization, were implemented in a new second-generation coil design. In this paper, we review the main characteristics of the first generation coils, describe the modification in coil layout and discuss their impact on parts design and magnet analysis.