Low-energy medium-luminosity Muon Collider (MC) is being studied as a possible Higgs Factory (HF). Electrons from muon decays will deposit more than 300 kW in superconducting magnets of the HF collider ring. This imposes significant challenges to superconducting (SC) magnets used in the MC storage ring (SR) and interaction regions (IR). The magnet designs are proposed which provide high operating gradient and magnetic field in a large aperture to accommodate the large size of muon beams due to low b{eta}* as well as the cooling system to intercept the large heat deposition from the showers induced by decay electrons. Specific distribution of heat deposition in the lattice elements MC SR requires large aperture magnets to accommodate thick high-Z absorbers to protect the SC coils. Based on the developed MARS15 model and intense simulations, a sophisticated radiation protection system was designed for the collider SR and IR to bring the peak power density in the superconducting coils below the quench limit and reduce the dynamic heat deposition in the cold mass by a factor of 100. The system consists of tight tungsten masks in the magnet interconnect regions and elliptical tungsten liners in magnet aperture optimized for each magnet. It also reduces the background particle fluxes in the collider detector.
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