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.

Hierarchic Electrodynamics and Free Electron Lasers: Concepts, Calculations, and Practical Applications presents intriguing new fundamental concepts in the phenomenon of hierarchical electrodynamics as a new direction in physics. Concentrating on the key theory of hierarchic oscillations and waves, this book focuses on the numerous applications of nonlinear theory in different types of high-current Free Electron Lasers (FEL), including their primary function in the calculation methods used to analyze various multi-resonant, multi-frequency nonlinear FEL models. This is considered the first book to: Completely and systematically describe the foundation of hierarchical electrodynamics as a new direction of physics Fully represent the physics of high-current FEL-and associated models-from the hierarchic oscillation wave perspective Cover the multi-harmonic nonlinear theory of new types of electronic devices, such as plasma-beam and two-stream FEL Formulate and substantiate the concept of cluster femtosecond FEL Analyze practical prospects for a new generation of a global "Star Wars" strategic defense systems These subjects involve a wide range of disciplines. Using numerous real-world examples to illustrate information and concepts, the book offers a mathematical foundation to explore FEL applications as well as analyze hierarchic plasma-like electrodynamic systems and femto-second clusters of electromagnetic energy. Assembling fragmented concepts from existing literature, the author re-examines classic approaches in order to develop new insights and achieve scientific breakthroughs.

Everybody is current in a world surrounded by computer. Computers determine our professional activity and penetrate increasingly deeper into our everyday life. Therein we also need increasingly refined c- puter technology. Sometimes we think that the next generation of c- puter will satisfy all our dreams, giving us hope that most of our urgent problems will be solved very soon. However, the future comes and il- sions dissipate. This phenomenon occurs and vanishes sporadically, and, possibly, is a fundamental law of our life. Experience shows that indeed 'systematically remaining' problems are mainly of a complex tech- logical nature (the creation of new generation of especially perfect - croschemes, elements of memory, etc. ). But let us note that amongst these problems there are always ones solved by our purely intellectual efforts alone. Progress in this direction does not require the invention of any 'superchip' or other similar elements. It is important to note that the results obtained in this way very often turn out to be more significant than the 'fruits' of relevant technological progress. The hierarchical asymptotic analytical-numerical methods can be - garded as results of such 'purely intellectual efforts'. Their application allows us to simplify essentially computer calculational procedures and, consequently, to reduce the calculational time required. It is obvious that this circumstance is very attractive to any computer user.

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.

Hierarchic Electrodynamics and Free Electron Lasers: Concepts, Calculations, and Practical Applications presents intriguing new fundamental concepts in the phenomenon of hierarchical electrodynamics as a new direction in physics. Concentrating on the key theory of hierarchic oscillations and waves, this book focuses on the numerous applications of nonlinear theory in different types of high-current Free Electron Lasers (FEL), including their primary function in the calculation methods used to analyze various multi-resonant, multi-frequency nonlinear FEL models.

This is considered the first book to:

• Completely and systematically describe the foundation of hierarchical electrodynamics as a new direction of physics
• Fully represent the physics of high-current FEL and associated models from the hierarchic oscillation wave perspective
• Cover the multi-harmonic nonlinear theory of new types of electronic devices, such as plasma-beam and two-stream FEL
• Formulate and substantiate the concept of cluster femtosecond FEL
• Analyze practical prospects for a new generation of a global "Star Wars" strategic defense systems

These subjects involve a wide range of disciplines. Using numerous real-world examples to illustrate information and concepts, the book offers a mathematical foundation to explore FEL applications as well as analyze hierarchic plasma-like electrodynamic systems and femto-second clusters of electromagnetic energy. Assembling fragmented concepts from existing literature, the author re-examines classic approaches in order to develop new insights and achieve scientific breakthroughs.