Odarenko I. Nonlinear three-dimensional theory of the hybrid O-type beam-wave systems of the mm and submm bands

The aim - developing the nonlinear theory of the beam-wave interaction in the hybrid millimeter wave devices at three-dimensional electrons motion in the non-uniform magnetostatic field. Object - process of the self-consistent interaction between directed charged particles beams and multicomponent electromagnetic fields in the resonant and non-resonant beam-wave systems. Methods - asymptotic methods of the oscillations theory, mathematical physics methods, theory of differential equations and special functions theory. Results - multidimensional self-consistent theory of the autonomous O-type beam-wave systems is developed for relativistic electron beam velocities and arbitrary spatial distribution of the focusing magnetic field; efficiency enhancement due to levelling of the bunching conditions at the electron beam thickness on the basis of the non-linear equations set solution for non-resonant sectioned systems has been revealed; enhancement of the frequency multiplication efficiency in the hybrid beam-wave system owing to transverse interaction is found under condition of focusing field induction decrease. Implementation - at Usikov Institute of Radiophysics and Electronics of the National Academy of Science of Ukraine, in a number of educational courses at higher education institutions of the Ministry Education and Science, Youth and Sports of Ukraine. Application - multidimensional simulation of the nonlinear processes of electron beam interaction with high-frequency electromagnetic fields.