  Within the framework of the average approach and direct 3D PIC
(particle-in-cell) simulations we demonstrate that the gyrotrons operating in
the regime of developed turbulence can sporadically emit "giant" spikes with
intensities a factor of 100-150 greater than the average radiation power and a
factor of 6-9 exceeding the power of the driving electron beams. Together with
the statistical features such as a long-tail probability distribution, this
allows the interpretation of generated spikes as microwave rogue waves. The
mechanism of spikes formation is related to the simultaneous cyclotron
interaction of a gyrating electron beam with forward and backward waves near
the waveguide cutoff frequency as well as with the longitudinal deceleration of
electrons.
