"This book presents the mathematical foundation for a range of applications that employ high-current free electron lasers. It provides an in-depth analysis of hierarchic plasma-like electrodynamic systems and femto-second clusters of electromagnetic energy. The author re-examines classic approaches in order to examine new insights and scientific breakthroughs. In this way, he explains the universal space in which optical entities are represented as a series of harmonic oscillators by analyzing the behavior of these structures from multiple relativistic perspectives. In addition to the free-electron laser, the text covers related topics such as lasing systems, femtosecond lasers, and parametric oscillators"--

"Preface It is a well-known fact that development of some key military programs during the last fifty years systematically provoked critical situations in different parts of the applied physics. This happened mainly in cases when the appetite of the military exceeded the possibility of the existing, at that time, levels of science and technologies. The paradox of the situation is that every time, researchers, trying to solve arisen applied problems, made ultimately a next important step in fundamental sciences. As a result, we obtained systematically various new applied-fundamental achievements, which, naturally, were not foreseen initially by any military technical tasks. We have a similar scenario in the case of the hierarchic electrodynamics and the theory of hierarchic oscillations and waves. It all began with ancient experiments with the powerful plasma-beam instability, which were accomplished in 1950s through the 1960s (the famous Thermonuclear Plasma fusion Program). Essentially multiharmonic wave processes were observed, which have been characterized by the generation of tens and even hundreds of plasma-wave harmonics with commensurable amplitudes (Chapters 13 and 14). At that time, however, the observed experimental physical picture did not get any satisfactory theoretical description. Especially difficult mathematical situation took place in cases when the amplitudes of higher harmonics exceeded the amplitudes of the lower ones"--