Gyro-traveling-wave amplifiers (gyro-TWAs) are types of gyrodevices, which take advantage of the cyclotron maser instability to produce coherent electromagnetic (EM) radiation from electrons gyrating in an external magnetic field and interacting with fast traveling waves. For high power applications, gyrodevices often require relativistic electron beams and operate at high cyclotron harmonics. In such conditions, if the EM wave is large enough, the electron cyclotron frequency can vary significantly in the process of interaction with the wave. This can lead to the overlapping of cyclotron resonances at different harmonics, which can cause electrons to exhibit stochastic trajectories.

In devices operating at cyclotron harmonics, it is possible for the electron beam to excite a wave at a given harmonic. This wave, in turn, can excite other waves at frequencies different from the operating frequency. The interaction between such waves is a nonlinear effect. In relativistic gyrodevices, this wave interaction may be affected by the overlapping of cyclotron resonances. This thesis presents theoretical analysis of (a) the effect of overlapping of cyclotron resonances on electron trajectories (b) wave interaction in relativistic gyro-TWAs.