Phase bunching in the harmonic multiplying gyrotron traveling wave amplifier

Summary form only given, as follows. In the harmonic-multiplying gyrotron traveling wave amplifiers (TWA), the electron-wave interaction process in the first TWA and subsequent drift sections is straight forward and should not cause any controversy. However, the frequency multiplying amplification process in the TWA output section is more involved and remains to be addressed. A time-dependent PIC code is used to investigate the phase bunching process in the output section. We first isolate the output section and inject a signal at the second harmonic cyclotron frequency and follow the spatial evolution of phase trajectories of 30 test electrons. In this situation, the electron phases start with uniform distribution and have the same slope in the phase space. As a result, the two bunches form at the same z-position and separate by p in the azimuthal phase. Both bunches are in the correct phase to amplify the injected signal together. On the other hand, in the harmonic multiplying gyro-TWA, before entering the output section the phase trajectories of test electrons were perturbed by the input signal at the fundamental frequency and try to form a single bunch in the azimuthal phase. As a result, in the output section, the slopes are different for each test electron. The reaction of the self-consistent second harmonic field on these electrons tends to produce two bunches at different z-position and separate by less than p in the azimuthal phase. As a consequence, the simulation result reveals that the early portion of the amplification is dominated by the second harmonic generation due to the fundamental bunching and in the latter portion, the wave amplification is taken over by the harmonic cyclotron maser instability but with reduced growth rate.