Design Optimization of the B5 Cooling Cell Demonstrator Solenoids for the Muon Collider

The muon collider is a promising candidate for future multi-TeV lepton colliders, with the possibility for high luminosity and center-of-mass energies of 10 TeV or more. Achieving this luminosity requires a high-brightness muon beam obtained through ionization cooling in the 6D cooling section. To demonstrate technological feasibility, the International Muon Collider Collaboration (IMCC) has started a Muon Cooling Demonstrator programme. The cooling cells are complex mechanical assemblies consisting of high field, large radius superconducting solenoids, absorbers and high- gradient RF cavities, tightly integrated. Among the different types of cells, the B5 has been selected as candidate demonstrator cell. The solenoids are based on metal-insulated high-temperature superconductors (HTS), operating at 20 K. These magnets pose multiple challenges, among which we identified: deliver a precise magnetic field profile with on-axis field swing of$\pm$7.3 T, in a compact integration, subjected to strong axial forces. Under these requirements, a design optimization strategy is needed. In this work, we present a custom design optimization tool to identify the optimal magnet configuration under specific operational constraints. The result of single-objective optimization has been compared to the Pareto optimal solutions from a multi-objective approach. Among the competing optimization targets, we considered minimum axial forces, conductor volume, adequate margins and coil protection, while guaranteeing the target field quality. A coupled electromagnetic-thermal model is employed to evaluate the maximum coil temperature in case of quench and is integrated into the optimization routine. The proposed design of the demonstrator magnets will be included in the next cell integration studies.