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Heliotron reactors have attractive features for fusion power plants, such as no need for current drive and a wide space between the helical coils for the maintenance of in-vessel components. Their main disadvantage was considered the necessarily large size of their magnet systems. According to the recent reactor studies based on the experimental results in the Large Helical Device, the major radius of plasma of 14 to 17 m with a central toroidal field of 6 to 4 T is needed to attain the self-ignition condition with a blanket space thicker than 1.1 m. The stored magnetic energy is estimated at 120 to 140 GJ. Although both the major radius and the magnetic energy are about three times as large as ITER, the maximum magnetic field and mechanical stress can be comparable. In the preliminary structural analysis, the maximum stress intensity including the peak stress is less than 1,000 MPa that is allowed for strengthened stainless steel. Although the length of the helical coil is longer than 150 m that is about five times as long as the ITER TF coil, cable-in-conduit conductors can be adopted with a parallel winding method of five-in-hand. The concept of the parallel winding is proposed. Consequently, the magnet systems for helical reactors can be realized with small extension of the ITER technology.