Hierarchical Methods

1. Front Matter

   Pages i-xvii

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2. Hierarchical Theory of Undulative Induction Accelerators (Eh-Accelerators)

   Pages 1-88

3. Free Electron Lasers as a Classical Electron Device with Long-Time Interaction

   Pages 89-122

4. Hierarchical Single-Particle Theory of Free Electron Lasers

   Pages 123-167

5. Hierarchical Self-Consistent Theory of Free Electron Lasers

   Pages 169-290

6. Hierarchical Theory of Two-Stream Superheterodyne Free Electron Lasers

   Pages 291-351

7. Back Matter

   Pages 353-382

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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.

• Klystron
• Phase
• Signal
• computer
• dynamical systems
• electromagnetic wave
• electronics
• laser
• magnetic field
• model
• polarization
• radio

• National Aviation University, Kiev, Ukraine

  Victor V. Kulish

• Sumy State University, Sumy, Ukraine

  Victor V. Kulish

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