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Self-similarity of rogue wave generation in gyrotrons: Beyond the Peregrine breather
Within the framework of numerical simulations, we study the gyrotron dynamics under conditions of a significant
excess of the operating current over the starting value, when the generation of electromagnetic pulses with
anomalously large amplitudes (“rogue waves”) can be realized. The averaged shape of high-power pulses is
shown to be very close to the celebrated Peregrine breather. At the same time, we demonstrate that the relation
between peak power and duration of rogue waves is self-similar, but does not reproduce the one characteristic for
Peregrine breathers. Remarkably, the discovered self-similar relation corresponds to the exponential nonlinearity
of an equivalent Schr¨odinger-like evolution equation. This interpretation can be used as a theoretical basis for
explaining the giant amplitudes of gyrotron rogue waves.