Stochasticity of electron trajectories in relativistic gyro-devices

Summary form only given. For many applications for relativistic gyro-devices the ultimate goal is to achieve the highest possible coherent electromagnetic (EM) power from the interaction of gyrating electrons with EM waves. When an EM wave of large amplitude and electrons of relativistic initial energy interact, the electron cyclotron frequency can vary significantly in the process, which may lead to the overlapping of cyclotron resonances at different harmonics. The current study shows that this resonance overlap, which is similar to one known in the theory of dynamic systems as Chirikov criterion, may cause electrons to exhibit stochastic trajectories. In this work, the particular case of electrons interacting with an initial resonant second harmonic field is considered. The study shows that depending on whether electrons lose or gain energy in the process of interacting with the large magnitude EM field their cyclotron frequency shifts from being close to the second harmonic towards fundamental or third resonant harmonic. Therefore, these particles can interact with the field at several harmonics simultaneously. It is shown that in the process of this interaction, electrons can exhibit stochastic orbits. This might explain why previous studies which were focused on isolated cyclotron resonance failed to observe this effect.