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Abstract A 162.5 MHz, 7.2 MeV Radio Frequency Quadruples (RFQ) is being designed for the injector of a heavy ion medical machine, which is promoted by the Institute of Modern Physics (IMP), Chinese Academy of Science (CAS). The proposed RFQ will adopt the conventional 4-rod structure, which is most commonly used for the heavy ion linac at low energy section. RF design was based on a new fast-bunching beam dynamics design. Comparing with the conventional beam dynamics design, this design strategy makes the structure more compact and need less power consumption. To meet the requirements of beam dynamics, various methods were used to optimize the electric field distribution. The electric field fluctuation under 3.5% and the dipole field ratio under 3% were obtained simultaneously. Water temperature rise and cavity thermal deformation were also simulated based on the special water-cooling system design. Under the setting of the cooling parameters, the temperature rise of cooling water was kept below 2 °C in theory. Considering the possible frequency shift during assembling and operation, the tuning range of the movable plungers is 500 kHz to compensate frequency shift. [ABSTRACT FROM AUTHOR]