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FAST (Fusion Advanced Studies Torus), the Italian proposal for a European satellite facility to ITER, is a compact tokamak ( R0= 1.82 m, a= 0.64 m, triangularity δ = 0.4) able to investigate non linear dynamics effects of alpha-particle behavior in burning plasmas and to test technical solutions for the first wall/divertor directly relevant for ITER and DEMO (e.g.: full-tungsten wall and divertor and advanced liquid metal divertor). The machine is designed to operate with Deuterium plasmas in a dimensionless parameter range close to that of ITER and to access advanced tokamak regimes with long pulse duration with respect to the current diffusion time. It foresees a maximum magnetic field on plasma axis of 8.5 T and a maximum plasma current of 8 MA. In the present design phase, the feasibility of a superconducting solution for the magnet system is being investigated by ENEA. It consists of 18 Toroidal Field, 6 Poloidal Field and 6 Central Solenoid module coils, all of which wound by Nb3Sn and NbTi Cable-In-Conduit Conductors. All the main aspects driving the magnets' design, from mechanical to neutronic and thermal analyses, are here presented and discussed.