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A 16-vane millimeter-wave spatial-harmonic magnetron (SHM) with a cold secondary emission cathode is examined by the use of a 3-D particle-in-cell (PIC) code embedded in CST Particle Studio. Simulations of the SHM are performed without artificial RF priming and without assuming restrictive assumptions on the mode of operation or on the number of harmonics to be considered. Thus, in our simulations, the electromagnetic oscillations grow naturally from noise. Time-evolved space-charge simulations and gradual formation of a single-frequency RF oscillation are presented. Examination of space-charge profiles at saturation time reveals the presence of two different space-charge distributions that depend on the amount of primary emission current. This current is employed to model a bombarding current, which is used to initialize the cold cathode. It is shown that a small primary emission density results in nonperiodic distribution of space charge at saturation time, which is in accordance with the previously reported space-charge distribution in SHMs. The simulated current, power, and efficiency indicate good correlation with the experimental results.