The purpose of inventing a double stage Hall thruster is to control the propellant ionization and ion acceleration independently. In order to better understand the physics involved in such a thruster, an improved particle-in-cell method is used in this paper to simulate the discharge process. It is shown that the numerical features in the ionization stage accord well with the experimental results. It is also indicated that the ionization process and the acceleration process cannot be separated completely, as a relatively important ionization still occurs in the acceleration stage. Furthermore, an optimal threshold of ionization voltage in the ionization stage is existed to obtain the most favorable distributions of plasma parameters in the whole discharge channel.

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