| This dissertation concerns itself with two important issues in the study of gyrotrons.; In Part I, we study the space charge instabilities in gyrotron electron beams via both solution of the linear dispersion equation and the nonlinear particle simulation. The linear analysis addresses the stabilizing effects of energy spread in the beams and the gradient of the external magnetic field. The nonlinear multi-frequency simulation demonstrates that the energy spread induced by multiple unstable waves in the nonlinear saturation stage is more significant than the corresponding spread induced by a single unstable wave. This indicates that the deleterious effect on the quality of the beam will be greater than previously expected, and emphasizes the need to design electron guns which are stable to this wave mode.; In Part II, we develope a generalized theory of gyro-traveling-wave tubes (gyro-TWTs) operating at arbitrary cyclotron harmonics. In the framework of small signal theory, we obtain and analyze the dispersion equation and discuss a problem of spurious counterpropagating waves excitation. In the large-signal study, we predict the possibility of achieving high efficiency of operation at the first four cyclotron harmonics and show that the orbital efficiency of the relativistic gyro-TWT operating at the second cyclotron harmonic with large frequency up-conversion may exceed 60%. The results obtained also demonstrate that the sensitivity of the harmonic gyro-TWT efficiency with respect to the electron velocity spread strongly depends on axial wavenumbers of the travelling waves. |
