Design of a Four-Layer Nb₃Sn Cos-Theta Dipole in the CERN High Field Magnet R&D Program

In the context of the High Field Magnet (HFM) R&D program at CERN, this paper introduces a design proposal for a four-layer cos-theta Nb<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula>Sn dipole. Collaboratively developed by the Italian Institute of Nuclear Physics (INFN) and CERN, the dipole aims to contribute to the advancement of high-field Nb<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula>Sn magnets for future particle colliders, particularly the post-Large Hadron Collider (LHC) era. The target bore field is 14 T, potentially reaching 16T with a reduced margin of operation. Featuring a single aperture, the design incorporates four layers of state-of-the-art Nb<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula>Sn Rutherford cable configured in cos-theta, using the grading technique to exploit the performance of the conductor in the low-field region. To mitigate challenges associated with Nb<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula>Sn cable strain sensitivity, the magnet incorporates the Bladder&Key technique during the pre-loading phase to minimize coil stress. This paper delves into the preliminary electromagnetic design of the dipole, emphasizing optimization for high field quality and performance required for High Energy Physics Particle Accelerator standards. Using 2D Finite Element Method (FEM) simulations, the coil layout is designed, the margins are computed, and a comparison between different designs is made. Furthermore, a 3D FEM analysis is employed to investigate the location of the peak field within the magnet, with a specific focus on the design of coil ends.