We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave (SCW) harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.

We construct a cubic nonlinear self-consistent theory of multiharmonic two-stream superheterodyne free electron lasers of a klystron type, intended to form powerful ultrashort clusters of an electromagnetic field. Plural three-wave parametric resonant interactions of wave harmonics have been taken into account. The two-stream superheterodyne free electron lasers mode in which the first harmonic of a space-charge wave is much smaller than the critical frequency of two-stream instability has been used for forming of the powerful ultrashort clusters of electromagnetic waves. We carry out amplitude, phase and spectral analyses of the processes occurring in such devices. We found out the conditions necessary for the forming of the ultrashort clusters of an electromagnetic field. We demonstrate the possibility of the ultrashort electromagnetic cluster formation in the multiharmonic two-stream superheterodyne free electron lasers-type systems.

This article deals with the development of the university activities model to ensure the quality of education and technology transfer (SDG 4) and to create a successful background in achieving SDG 7. We conduct an analysis of the literature on the achievement of SDGs through governmental instruments of influence, as well as the creation of effective university model ensuring the education quality and technology transfer. In addition, we demonstrate the role of the government in financing higher education in Ukraine. We also present the evaluation of the popularity of educational programs related to energy efficiency and a “clean” environment in Ukrainian universities after the adoption of the 2030 Agenda for Sustainable Development. The indicators of the use of various energy types by Ukraine are assessed, and a comparative analysis of these indicators with the data for EU-28 is performed. Based on the data presented, conclusions are drawn about the need to improve the quality of university training and to activate the university technology transfer. Successful practical approaches that can be of use for different higher education institutions are outlined. A combined model of quality assurance and technology transfer at the university is presented. An algorithm for testing the model and assessing the technological level of readiness for implementation is developed. The presented chain “combined model – model testing algorithm – determination of the technological level of readiness” is also assessed from the point of view of socio-economic impact on the main stakeholders. The use of the combined model lays background for the university’s own sustainable development as a tool for achieving SDGs.

We construct a cubically nonlinear theory of plural interactions between harmonics of the growing space charge wave (SCW) during the development of the two-stream instability. It is shown that the SCW with a wide frequency spectrum is formed when the frequency of the first SCW harmonic is much lower than the critical frequency of the two-stream instability. Such SCW has part of the spectrum in which higher harmonics have higher amplitudes. We analyze the dynamics of the plural harmonic interactions of the growing SCW and define the saturation harmonic levels. We find the mechanisms of forming the multiharmonic SCW for the waves with frequencies lower than the critical frequency and for the waves with frequencies that exceed the critical frequency.

We developed a cubic non-linear theory describing the dynamics of the multiharmonic spacecharge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.