Origin of Second-Harmonic Signals in Octave Bandwidth Traveling-Wave Tubes

In a helix traveling-wave tube (TWT) with a bandwidth exceeding one octave, the second harmonic of an input signal near the low end of the band will experience exponential growth. In such a case, we have found that the nonlinear electron orbits in the beam, as opposed to the orbital bunching exhibited in the linear electron orbits, are the main source for second-harmonic generation. This unexpected result is due to the synchronous amplification of the second harmonic. We demonstrate this phenomenon from the solution of the nonlinear equations that we have formulated that govern evolution of the second-harmonic field; these equations may include axial variations of the Pierce parameters. In several test cases, we compare the theory with simulation using the CHRISTINE large signal TWT code. Good agreement between theory and simulation is found.