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A high-power rising-sun magnetron oscillator (AX-9) operating at 9.50 GHz is examined by the use of a three-dimensional particle-in-cell (PIC) code, MAGIC3D. A mode spectrum of the 18 vanes rising-sun magnetron cavity is obtained from both an analytic field theory and the numerical code MAGIC3D. A large mode separation in the vicinity of a π-mode is observed in the rising-sun configuration. A time evolved electron flow exhibits nine space charge spokes in the PIC simulations, which confirms the π-mode oscillation in the 18 vanes rising-sun magnetron. When space charge spokes build up in the interaction region, a single frequency RF oscillation starts to grow and the leakage current escaping from the interaction region reduces to zero. Simulations predict that the saturated radiation power measured at the output waveguide is 250 kW at 9.50 GHz, corresponding to a magnetron efficiency of 53% where the external magnetic field is 0.52 T and the beam voltage and current are 28 kV and 17 A, respectively.