[en] The J-PARC MR provides a coasting proton beam for nuclear physics experiments by slow extraction. The longitudinal emittance should be enlarged until the MR flat top to mitigate the microwave instability. We have investigated a phase modulation method by using a High Frequency Cavity (HFC) to increase the emittance. We have performed extensive simulation studies to find the appropriate parameters of the phase modulation. We found that the effective HFC frequency has a linear dependence with the modulation frequency where the emittance is smoothly enlarged. Furthermore, we confirmed that the required HFC voltage is inverse proportional to the square root of the duration time of the phase modulation. (author)