The level of knowledge accumulated to date in the physics and technologies of controlled thermonuclear fusion (CTF) makes it possible to begin designing fusion—fission hybrid systems that would involve a fusion neutron source (FNS) and which would admit employment for the production of fissile materials and for the transmutation of spent nuclear fuel. Modern Russian strategies for CTF development plan the construction to 2023 of tokamak-based demonstration hybrid FNS for implementing steady-state plasma burning, testing hybrid blankets, and evolving nuclear technologies. Work on designing the DEMO-FNS facility is still in its infancy. The Efremov Institute began designing its magnet system and vacuum chamber, while the Kurchatov Institute developed plasma-physics design aspects and determined basic parameters of the facility. The major radius of the plasma in the DEMO-FNS facility is R = 2.75 m, while its minor radius is a = 1 m; the plasma elongation is k 95 = 2. The fusion power is P FUS = 40 MW. The toroidal magnetic field on the plasma-filament axis is B t0 = 5 T. The plasma current is I p = 5 MA. The application of superconductors in the magnet system permits drastically reducing the power consumed by its magnets but requires arranging a thick radiation shield between the plasma and magnet system. The central solenoid, toroidal-field coils, and poloidal-field coils are manufactured from, respectively, Nb3Sn, NbTi and Nb3Sn, and NbTi. The vacuum chamber is a double-wall vessel. The space between the walls manufactured from 316L austenitic steel is filled with an iron—water radiation shield (70% of stainless steel and 30% of water).