Theory of injection locking and rapid start-up of magnetrons, and effects of manufacturing errors in terahertz traveling wave tubes

In this thesis, several contemporary issues on coherent radiation sources are examined. They include the fast startup and the injection locking of microwave magnetrons, and the effects of random manufacturing errors on phase and small signal gain of terahertz traveling wave amplifiers.;In response to the rapid startup and low noise magnetron experiments performed at the University of Michigan that employed periodic azimuthal perturbations in the axial magnetic field, a systematic study of single particle orbits is performed for a crossed electric and periodic magnetic field. A parametric instability in the orbits, which brings a fraction of the electrons from the cathode toward the anode, is discovered. This offers an explanation of the rapid startup observed in the experiments.;A phase-locking model has been constructed from circuit theory to qualitatively explain various regimes observed in kilowatt magnetron injection-locking experiments, which were performed at the University of Michigan. These experiments utilize two continuous-wave magnetrons; one functions as an oscillator and the other as a driver. Time and frequency domain solutions are developed from the model, allowing investigations into growth, saturation, and frequency response of the output. The model qualitatively recovers many of the phase-locking frequency characteristics observed in the experiments. Effects of frequency chirp and frequency perturbation on the phase and lockability have also been quantified.;Development of traveling wave amplifier operating at terahertz is a subject of current interest. The small circuit size has prompted a statistical analysis of the effects of random fabrication errors on phase and small signal gain of these amplifiers. The small signal theory is treated with a continuum model in which the electron beam is monoenergetic. Circuit perturbations that vary randomly along the beam axis are introduced through the dimensionless Pierce parameters describing the beam-wave velocity mismatch (b), the gain parameter (C), and the cold tube circuit loss ( d). Our study shows that perturbation in b dominates the other two in terms of power gain and phase shift. Extensive data show that standard deviation of the output phase is linearly proportional to standard deviation of the individual perturbations in b, C and d.