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Within the framework of the average approach and direct 3D PIC (particle-in-cell) Many physical systems exhibit behavior associated with the emergence of the so-called rogue waves which represent dramatically high-amplitude events that occur with low probability but much more frequently than expected in ordinary (e.g., Gaussian or Rayleigh) wave statistics. can be suggested that, similar to lasers [5][6][7], the rogue waves can also occur in microwave oscillators representing active systems which are based on the interaction of electromagnetic waves with non-equilibrium electron beams.One of the widely studied microwave oscillators is a gyrotron in which a helical electron beam excites a waveguide mode near its cutoff frequency [10]. In this paper, we demonstrate that rogue waves can appear in gyrotrons operating in the regime of developed turbulence. It is well known that in electronic oscillators, including gyrotrons, an increase of the excess over the starting conditions leads to a complication of the radiation spectrum caused by the appearance of periodic self-modulation and then chaotic turbulent generation regimes [11][12][13][14][15][16][17]. Typically, realization of self-modulation regimes is a result of combination of a nonlinearity and delay effects [12].

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