Micro DC ion thrusters have broad application prospects as the propulsion system of micro spacecrafts due to their advantages of high discharge reliability and efficiency. The experiments in the literature show that the plasma discharge under the Axial Ring Cusp Hybrid (ARCH) magnetic field has higher discharge efficiency in the discharge chamber of micro DC ion thruster. In this paper, a 2d-3v axisymmetric particle-in-cell/Monte Carlo collision (PIC/MCC) numerical model is developed for the ARCH discharge. This model takes the thermal electron emission including the Schottky effect, various collision processes including the Bohm-type anomalous conductivity and the uneven background gas density distribution in the cathode-anode gap into account. The spatial distributions of plasma characteristics are presented and the advantages of ARCH discharge compared with traditional 3-Ring discharge in the discharge chamber of the micro DC ion thruster are analyzed. The longer electron path length and the change of ionization region improve the discharge efficiency in small-scale discharge. Two primary methods for the discharge confinement in the miniature ion thrusters, that is, the magneto-static “cusp confinement” through magnetic cusps and the electrostatic “sheath refection confinement” through the backplate with the lower potential are investigated. The sensitivity of macroscopic current characteristics and microscopic plasma characteristics in the ARCH discharge to the magnetic field strength and backplate biased potential are explored. It is found that there is an optimal magnetic field to maximize the utilization of propellant and minimize the discharge loss. The electrostatic “sheath refection confinement” is conducive to the reduction of discharge loss, however, it is also accompanied by the decline of propellant utilization. The above results provide a further support for the design optimization of the micro DC ion thruster discharge chamber.