The reversed field pinch (RFP) could be a valid basis for the 14.1-MeV neutron source as required in fusion–fission hybrid reactors (FFHRs). The use of superconductors in an RFP reactor, although mandatory in the magnetizing/equilibrium coils, could represent an issue due to their limitations in the allowed magnetic field derivative, which is quite high during the initial plasma current phase of the RFP operation. A new concept is proposed based on a double-coil system: the first made with superconductors and the other with conventional copper coils. The basic principle is first introduced with the help of a simplified model that allows understanding the double-coil system operation. A feasibility study applying this solution has been carried out in the design of the poloidal magnetic system of a pilot RFP ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> = 4 m and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a\,\,=0.8$ </tex-math></inline-formula> m) as a fusion core for an FFHR. This article presents the preliminary results and, in particular, the possibility of obtaining high initial loop voltage for a fast rise of the RFP plasma current with a magnetic field derivative within the superconductor limits.