New fusion devices are being discussed in Russia. One item is a superconducting magnet development for the demonstration hybrid facility—fusion neutron source based on a tokamak concept with the conventional aspect ratio ∼3. The magnetic parameters of this device are planned to be: 5 T on the plasma axis and about 12 T on the high field side of the toroidal field coils. Because of a high neutron flow and a thick shielding, the space remained for the inner legs of the toroidal field coil is very tight. Therefore, a very high current density is needed for the windings. Several magnet designs have been addressed up to now with required engineering critical current density ${\text{sim 1000 A/mm}}^{{\text 2}}$ at least. In this review, we present conceptual design of the magnet system, necessary strand parameters, and their irradiation properties. Few possible designs of the toroidal field, conductors are discussed. The R&D of efficient HTS current leads to be used for fusion machines are discussed as well.