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We investigate, using the 3-D particle-in-cell simulation code MAGIC, the millimeter-wavelength 20-vane magnetron operating at one of the spatial nonfundamental harmonics of the backward-traveling wave. This spatial harmonic is characterized by 16 (p = 16) RF electric field variations along the circumference of the magnetron interaction space (oscillation region). We call this magnetron as the “spatial-harmonic” magnetron operating in the “spatial-harmonic mode.” Calculated electron distribution reveals 16 electron spokes in the interaction space, which confirms the spatial-harmonic mode of the magnetron operation at p = 16. We observe a saturated output power of 3.2 kW, which corresponds to a power conversion efficiency of 12.3% when the applied voltage is 6.5 kV and the external magnetic field is 0.4 T. The operating frequency is 35.2 GHz. The collected anode current is 4 A when the current emitted from the cathode is 6.3 A. The dissipated power at each anode vane, depending on the anode vane position, is varied by the factor 1.8. The energy of back-bombarding electrons on the cathode increases from 305 to 503 eV while the spatial-harmonic magnetron operation is stabilized.