Spatio-Temporal Theory of Gyro-Devices Based on Microwave Systems Forming Curvilinear Operating Wave Beams

We submit the development of the quasianalytical spatio-temporal theory, which is able to describe two gyrotron-type auto-oscillators with similar features, namely, with a dense spectrum of eigenmodes which provides changing the operating frequency of the generated wave signal in the process of the broadband frequency tuning. First, we study various regimes of generation (stationary generation, autooscillations and superradiance) for a backward-wave gyrooscillator, but with an unusual wave trajectory resembling a zigzag. A sectioned system based on the use of quasi-optical mirrors provides the transportation of a wave beam from section to section, thereby its path resembles a zigzag. Then we switch to the development of the theory of a three-mirror gyrotron scheme. In fact, it is a resonant traveling-wave tube scheme based on the transverse amplifications of the operating wave and on the use of a remote delayed feedback. In the both cases, we study process of the frequency tuning, as well as competition of various modes of these systems. We show that at definite conditions, a broadband frequency tuning in the regime of stable single-frequency operation is possible.