Objective of the thesis: research using mathematical modeling methods of complex nonlinear dynamics of Volume Free Electron Laser (VFEL) with the aim of creating a tool for selecting optimal parameters and increasing the efficiency of using amplifiers and generators of tunable coherent radiation for various applications in science and commercial development, as well as creating information tools for preserving and popularising nuclear knowledge, including received in the frame of the dissertation work results. Generalised systems of equations are proposed that describe various variants of VFEL. The developed difference schemes can be used to simulate various VFEL geometries, as well as surface electromagnetic waves and surface plasmons. Computer program VOLC has been developed for express simulation of VFEL operation. The simulations carried out confirmed all the basic physical laws and operating principles of VFEL, and the generation thresholds for the experimental VFEL facilities of the Institute for Nuclear Problems of Belarusian State University were obtained. It is shown for the first time that the VFEL is a dynamic chaotic. The conducted modelling is important for future research in order to increase the efficiency of generators and sources of coherent radiation in different frequency ranges, implement control and methods of chaos management in experimental studies, and select more optimal VFEL operating modes. An electronic scientific and educational portal of nuclear knowledge BelNET has been created as an integral part of the Belarusian system of modern nuclear knowledge. The results can be used to develop powerful sources of electromagnetic radiation of different frequency ranges for the purpose of their use in high-energy physics and other fields of science and technology. The portal of nuclear knowledge BelNET can be used in the educational process of educational institutions, as well as to inform and to improve the Internet culture of the younger generation.

Based on the Doctoral thesis.