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The low thermodynamic cycle efficiency of the plasma synthetic jet actuator (PSJA) limits its application in flow control of supersonic aircraft. To improve the thermodynamic cycle efficiency of the PSJA, the energy conversion process of the PSJA under single discharge has been investigated by thermodynamic theory analysis and numerical simulation. The relations between thermodynamic cycle efficiency, specific heat ratio of gas medium, non-dimensional energy deposition and heating efficiency are established by theoretical deduction. Employing the three-dimensional nonconstant electrode center energy deposition model, energy conversion processes in the PSJA with six different gas mediums have been investigated. The simulation results show that the thermodynamic cycle efficiency of the PSJA with noble gas medium can exceed 3.2 %, which is 1.92 times of the PSJA with air medium due to their low volume specific heat. The maximum jet x-velocity of helium can reach 493.11 m/s, which is 3.3 times higher than that of air. Consequently, noble gases prove to be effective in improving the thermodynamic cycle efficiency of the PSJA and enhancing the strength of the synthetic jet. The advancement in the performance of the PSJA contributes to their enhanced capabilities in the field of active flow control. [ABSTRACT FROM AUTHOR]