| Hierarchical Methods: Undulative Electrodynamical Systems, Volume 2 2002 Edition Contributor(s): Kulish, V. (Author) |
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ISBN: 1402009682 ISBN-13: 9781402009686 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: October 2002 Annotation: This monograph consists of two volumes and provides a unified comprehensive presentation of a new hierarchical paradigm and discussions of various applications of hierarchical methods for nonlinear electrodynamic problems. Volume 1 is the first book, in which a new hierarchical model for dynamic non-linear systems is described and analysed and a set of new hierarchical principles is discussed. The modern hierarchical asymptotic methods are set forth systematically, taking into account specific features of electrodynamic problems, and the phenomenon of hierarchy in electrodynamics, in itself, is thoroughly discussed from a new point of view. A set of hierarchical asymptotic calculative methods of two types is discussed in detail. The methods of the first type are destined for asymptotic integration of non-linear differential equations with total derivatives and with multifrequency (including multi-scale) non-linear right hand parts. These are the Van der Pol method, Krylov-Bogolyubov method, Bogolyubov-Zubarev method and their hierarchical versions. The methods of the second type include the method of slowly varying amplitudes, the method of averaged characteristics, the methods of averaged kinetic and quasihydrodynamic equations, and some others. These methods are intended for asymptotic integration of non-linear differential equations with partial derivatives and multifrequency (including multi-scale) right hand parts. Detailed calculative technologies for practical application of all mentioned methods are illustrated by examples of real electrodynamic systems (free electron lasers, undulative induction accelerators, systems for transformation of laser signals, etc.). Volume 2 is the first book in which a hierarchical treatment of Undulative Electrodynamic Systems is given and in which such systems like EH-accelerators, EH-formers, EH-coolers, the klystron and multi-harmonic Two-Stream Superheterodyne Free Electron Lasers (TSFELs) are described and analysed. The hierarchical one-particle and self-consistent theory of Undulative Eletrodynamic Systems of different types is set forth. Those include, the single-particle theory of EH-accelerators, EH-formers, EH-coolers, traditional (parametrical) Free Electron Lasers (FELs) with H-ubitron, Dopplertron and EH-ubitron pumping which are exposed from the hierarchical point of view. The self-consistent nonlinear hierarchical theory of parametrical and two-stream superheterodyne FELs is developed. Special attention is paid to phenomena such as explosive instability, phase and polarization discrimination, nonlinear generation of electric and magnetic fields, superheterodyne amplification of electromagnetic waves. The nonlinear theory of multi-harmonic two-stream superheterodyne FELs is given as a demonstration of high practical efficacy of the presented hierarchical methods. The monograph is intended, mainly, for students and postgraduates who specialize in computer calculations in the field of physical electronics, plasma physics and radio physics, optical and electronic engineering, acceleration and various space technologies, as well as applied mechanics. However, the book will also be of great interest to experts, since a significant part is dedicated to a relatively new point of view of some calculation technologies and discusses some new applied systems. Hierarchical Methods is alsoavailable as a two-volume set: ISBN 1-4020-0758-2, (Volume 1: ISBN 1-4020-0757-4). |
| Additional Information |
| BISAC Categories: - Technology & Engineering | Electrical - Medical - Science | Physics - Mathematical & Computational |
| Dewey: 519 |
| LCCN: 2002034372 |
| Series: Undulative Electrodynamical Systems |
| Physical Information: 0.92" H x 6.32" W x 9.86" (1.85 lbs) 382 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The book consists of two Volumes. The first (the preceding volume) is devoted to the general nonlinear theory of the hierarchical dynamic oscillative-wave systems. This theory has been called the theory of hi- archical oscillations and waves. Here two aspects of the proposed theory are discussed. The first aspects concern the fundamental nature and the basic c- cepts and ideas of a new hierarchical approach to studying hierarchical dynamic systems. A new hierarchical paradigm is proposed as a - sis of a new point of view of such types of systems. In turn, a set of hierarchical principles is formulated as the fundamental basis of this paradigm. Therein the self-resemblance (holographic) principle plays a key role here. An adequate mathematic description (factorization) of the proposed paradigm is carried out. The concepts of structural and dynamic (functional) operators are put into the basis of this descr- tion. Electrodynamics is chosen as a convenient basis for an obvious demonstration of some key points of the proposed new theory. The second aspect has a purely mathematical nature. It is related to the form of factorization (i.e., mathematical description) of hier- chical types of dynamic models, and discussion of the methods of their mathematical analysis. A set of the hierarchical asymptotic analytical- numerical methods is given as an evidence of the practical effectiveness of the proposed version of hierarchical theory. |