Exploring Dipole-Quadrupole Combined Function Magnets for a Muon Collider

Over the past few years, interest in a Muon Collider as a potential post-LHC machine has grown significantly. By colliding muons, it is possible to achieve both precision and high energy, overcoming the limitations of synchrotron radiation in conventional lepton colliders. However, the very short muon lifetime at rest requires high beam intensity and fast acceleration rates limiting the collider ring dimensions. These limitations lead to several challenges in the design of superconducting magnets, which must generate high magnetic fields in large apertures to provide shielding from the radiation due to muon decay. This work explores the design of combined function magnets, which are essential to address the neutrino flux issue in straight sections by bending the particles during focusing/defocusing stages. The superconducting material selected for these magnets is REBCO, a High Temperature Superconductor (HTS), with operating temperatures ranging from 4.5 K to 20 K. Various configurations of combined function magnets are studied and simulated using a Python code interfaced with the Finite Element Method (FEM) software ANSYS, employing the sector coil approximation. The goal is to identify feasible designs that can accommodate substantial internal shielding while continuing to provide the high fields and gradients demanded by the lattice optics. To validate the manufacturability of such concepts, a preliminary winding test has been performed using 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 in a Canted-Cosine-Theta (CCT) geometry. While REBCO represents the most promising HTS conductor for future high-field applications, 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 remains one of the most mature options for large accelerator magnets, providing a valuable feasibility benchmark.