Hierarchical Methods: Undulative Electrodynamical Systems, Volume 2

ISBN-13: 9789401740609 / Angielski / Miękka / 2013 / 382 str.

V. Kulish

Opis

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."

Spis treści

Preface. 9: Hierarchical Theory of Undulative Induction Accelerators (EH-Accelerators). 1. EH-Accelerators: General Ideas and Properties. 2. EH-Accelerator as a Hierarchical Oscillative System. 3. Motion of Charged Particles in the Non-Stationary Linearly Polarized EH-Accelerator. 4. Picosecond Electron Bunch Formers. 5. Stationary EH-Accelerators. 6. Example: Project of an Especially Compact Stationary EH-Accelerator. 7. The Effect of 'Cooling' of Charged Particle Beams in EH-Accelerators. 8. Stationary EH-Coolers. 10: Free Electron Lasers as a Classical Electron Device with a Long-Time Interaction. 1. Free Electron Lasers: General Information. 2. Grouping (Bunching) Mechanisms in Free Electron Lasers. 11: Hierarchical Single-Particle Theory of Free Electron Lasers. 1. General Approach to the Single-Particle Theory of Free Electron Lasers. 2. Single-Particle Theory of the Free Electron Lasers of Dopplertron Type. 3. The Single-Particle Theory of the Free Electron Laser with EH-Pumping. 12: Hierarchical Self-Consistent Theory of Free Electron Lasers. 1. General Formulation of the Problem. 2. Self-Consistent Truncated Equations. Simplified Version of the Method of Slowly Varying Amplitudes. 3. Self-Consistent Truncated Equations. Method of the Averaged Kinetic Equation. The Cubic Dopplertron Model. 4. Self-Consistent Truncated Equations. The Method of the Averaged Kinetic Equation. The Cubic Nonlinear H-Ubitron Model. 5. Self-Consistent Truncated Equations. The Method of Slowly Varying Amplitudes. The Quadratic Kinetic Dopplertron Model with Arbitrarily Polarizations of the Electromagnetic Waves. 6. Self-Consistent Quadratic Fel Theory of The Simplest Linearly Polarized Quasi-Hydrodynamic model. 7. Analysis of the Wave Resonant Conditions. 8. Self-Consistent Quadratic Fel Theory of the Arbitrary Polarized Kinetic Model. The Approximation of a Given Pumping Field in the Case of the Raman Mode. 9. Self-Consistent Quadratic Fel Theory of the Arbitrarily Polarized Kinetic Model. The Approximation of the Given Pumping Field in the Case of Compton Mode. 10. Self-Consistent Quadratic Fel Theory. The Explosive Instability in the Linearly Polarized Raman Model. 11. Self-Consistent Quadratic Fel Theory. The Explosive Instability in the Arbitrarily Polarized Self-Consistent Raman Model. 12. The Self-Consistent Quadratic Fel Theory. The Explosive Instability in Linearly Polarized Self-Consistent Compton Model. 13. Self-Consistent Quadratic Fel Theory of the Effect of the Generation of the Transverse H-Ubriton Field. 14. The Dopplertron Cubic Nonlinear Model. The Effect of Nonlinear Generation of the Longitudinal Electric Field. 15. Dopplertorn Cubic Nonlinear Model. The Isochronous Model of a Dopplertron Amplifier. 16. H-Ubriton Cubic Nonlinear Model. The Effect of Nonlinear Generation of the Transverse Periodic Magnetic Field. 13: Hierarchical Theory of Two-Stream Superheterodyne Free Electron Lasers. 1. Two-Stream Superheterodyne Free Electron Lasers as a New Class of Relativistic Electron Devices. 2. Theory of the Two-Stream Instability. 3. The Essence of the Effect of Two Superheterodyne Amplification. 4. Formulation of the Cubic Nonlinear Two-Stream Superheterodyne Problem. 5. C