Abstract The upgrade project of the J-PARC MR (Main Ring) based on doubled repetition-rate scenario is in progress to deliver the beam power of 750 kW. The present RF section will be occupied by 9 sets of new magnetic alloy, FT3L, cavities using the direct water cooling scheme. The direct water cooling is the efficient scheme to cool the magnetic alloy core although it requires dedicated high-quality cooling water which does not contain copper oxide and copper ions because copper ions may cause the severe corrosion damage on the magnetic alloy cores. These cavities will be used for the fundamental RF for acceleration which requires high duty operation. The second harmonic RF is necessary to increase the bunch length. This allows to enlarge the beam current because it relaxes the space charge effects during the injection. Thanks to the high impedance FT3L and low duty operation of the second harmonic RF, the power loss in the second harmonic RF system becomes moderate. The air cooled cavity is designed to fit in any locations in the MR where the dedicated high-quality 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
