Conceptual Electromagnetic and Mechanical Design of a Cos$\theta$ Dipole for the Muon Collider Study

Within the framework of the International Muon Collider Collaboration (IMCC), researchers are involved in a feasibility study to develop high-temperature superconducting (HTS) magnets for a 10 km collider ring, designed to reach a 10 TeV Center-of-Mass (CoM) energy. Due to the short lifetime of muons of only 2.2 μs, the machine must minimize their acceleration time, allowing them to collide before the decay. To optimize the machine cost and maximize the collider luminosity, the superconducting dipoles of the collider ring must be compact and generate high steady-state magnetic fields. In addition, they must feature large apertures for the insertion of a shielding structure needed to preserve the superconducting coils from muon decay products. These demanding specifications pose significant technological challenges for the design of the dipole magnets, both in terms of physics and engineering. In this contribution, we give an overview of the conceptual 2D electromagnetic design of the main collider dipoles, followed by a preliminary mechanical analysis for a first estimation of stresses due to the Lorentz forces. Since the coil design is based on REBCO tapes- whose magnetization effects must be taken into account- an analytical code was written in MATLAB to evaluate the magnet performances considering non-uniform current distribution according to the Brandt model. A validation study of the code by comparing its results with finite element method (FEM) simulations is also presented. In this comparison, the computational time of the analytical and numerical approaches will also be pointed out to better appreciate the importance of the work done in developing the new tool.