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A stretched particle-in-cell (PIC) code was used to carry out dynamic simulations of a mode-selective extended-interaction gyrotron oscillator. Simulation results show that using the same interaction length, increasing the number of coupled cavities tends to force the peak of the electric-field profile closer to the output plane. As a result, the radiation becomes easier to leak out and the cavity Q is reduced. Using three coupled cavities (TE02/TE03/TE04) with 10.6-cm total interaction length, the cavity Q of 260% and 25% efficiency can be attained in a second harmonic (31 GHz) gyrotron oscillator. Using the proposed cavity as the output cavity of an inverted gyrotwystron, the bandwidth without resistive loading attains 0.6%.