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The T-15MD tokamak with the warm toroidal field coils, elongated plasma cross section, and a low aspect ratio was commissioned at the National Research Center Kurchatov Institute in 2021. An economically viable fusion reactor requires long discharges or even a steady-state mode. The short pulse of the toroidal field is among the main obstacles on the way to the steady state. Therefore, as a next step after T-15MD, it is proposed at the NRC Kurchatov Institute to consider the design of a superconducting tokamak (SCT), which holds the basic geometric parameters of the T-15MD: R/a = 1.5 m/0.67 m with a field on the axis of B0 < 5 T and a long pulse of current of Ip < 5 MA. The focus of the paper is the system of the toroidal magnetic field. A three-layer design of the toroidal field coil is proposed: an inner layer of a high-temperature superconductor (HTSC), a Nb3Sn middle layer, and a NbTi outer layer. On the basis of structural strength calculations, candidate materials for coil cases were selected. For cooling the coils, a semi-longitudinal pumping of low-pressure liquid helium is proposed. The design of the HTSC cable in conduit consisting of two halves is considered in detail. A mesh cryostat design that provides a convenient access for diagnostics and plasma heating is proposed. SCT systems similar to those used in the T-15MD are analyzed. [ABSTRACT FROM AUTHOR]