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

Within the framework of the International Muon Collider Collaboration (IMCC), an innovative feasibility study on a Muon Collider accelerator complex is currently under development, granted by the European Union through Agreement 101094300. The proposed goal aims to develop a 10 km collider ring accelerating muons at approximately 10 TeV in the center-of-mass frame. To achieve this target, several requirements on the collider design arise to maximize the luminosity despite the short lifetime of this type of particle at rest. Despite being operated in steady-state mode, the superconducting magnet dipoles of the main collider are presently evaluated as the most challenging technological development of the design study. High levels of magnetic field above 10 T are presently foreseen with a magnet bore diameter around 150 mm to accommodate a tungsten shielding for the muon decay heat deposition. To minimize the radiation dose, coming from the collimated neutrino beams, different types of combined dipole and quadrupole are also considered in the lattice reducing the straight sections in the collider at the expense of the magnet performances and feasibility. An analytical analysis of possible magnet performances with the available technology has been already developed suggesting different working points for the magnet design. In this contribution, a first proposal of 2D cos$\theta$ electromagnetic and mechanical designs is provided comparing the analytical approach with FEM (Finite Element Method) - optimized configurations. HTS (High Temperature Superconductor) superconducting magnet designs have been evaluated to estimate the maximum possible expected performances of the collider, minimize the magnet cost, and deal with the requirements for the cryogenic cooling of the entire accelerator complex.