The upgrade project of the J-PARC MR (Main Ring) is in progress to deliver the beam power of 750 kW based on doubled repetition-rate scenario. The present RF section will be occupied by 9 sets of new magnetic alloy, FT3L, cavity using the direct water cooling scheme. The direct water cooling requires dedicated high-quality cooling water. These cavities will be used for the fundamental RF for acceleration. The second harmonic RF is necessary to increase the bunch length. This allows to enlarge the beam current, and to relax the space charge effects during the injection. Thanks to the high impedance FT3L, the power loss in the second harmonic RF system becomes moderate. The air cooled cavity is designed to fit in any space in the MR where the dedicated water is not available. This paper reports the design of the second RF system, technical issues to produce the magnetic alloy cores to fit the air cooling, and construction of the system. Proceedings of the 5th Int. Particle Accelerator Conf., IPAC2014, Dresden, Germany
