On the possibility of multiplying the frequency of a gigawatt ultrashort microwave pulse

It has been shown that the frequency of an ultrashort microwave pulse of a lowest axisymmetric electric mode at the interaction with a counterpropagating relativistic tubular electron beam under the cyclotron resonance conditions can be doubled due to re-emission into a mode having resonance at the second harmonic of the gyrofrequency. The conversion of the 3-cm 1-ns gigawatt microwave pulse in a circular waveguide from the TM$_{01}$ mode to the TM$_{02}$ mode with the doubling of the frequency, reduction of the duration to 0.22 ns, and the achievement of the peak power above the initial value has been demonstrated in a numerical experiment. The possibility of forming an intense ultrashort frontal splash of oscillations with the doubled frequency has been shown for longer initial pulses with a subnanosecond front.