An Analytic Theory Of Multi-stream Electron Beams In Traveling Wave Tubes

by Alexander Figotin

Overview

The Traveling Wave Tubes (TWT) is a powerful vacuum electronic device used to amplify radio-frequency (RF) signals as well as numerous applications such as radar, television and telephone satellite communications. This monograph is devoted to the author's original theoretical developments in the theory of a traveling wave tube (TWT).Most of the monograph is the author's original work on an analytical theory of TWTs. It is a constructive Lagrangian field theory of TWT in which the electron beam (e-beam) is represented by one-dimensional multi-stream electron flow and the guiding slow-wave structure is represented by possibly non-uniform multi-transmission line (MTL). The proposed analytic theory accounts for a number of electron plasma phenomena including space-charge effects such as electron-to-electron repulsion (debunching), convective instabilities, wave-particle interaction, amplifying waves and more. It allows, in particular, to (i) identify origins of the wave-particle interaction and the system convective instability (exponential growth); (ii) evaluate the energy transfer rate from the e-beam to the electromagnetic radiation; (iii) identify instability modal branches which under condition of sufficiently strong coupling between the e-beam and the MTL can cover ideally all frequencies.

Product Details

ISBN-13:	9789811209192
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	11/13/2020
Pages:	500
Product dimensions:	6.69(w) x 9.61(h) x 1.06(d)

Table of Contents

Preface; List of Symbols and Acronyms; Review of the Theory and Its Key Elements: Introduction; Summary of the TWT-System Features and Effects; E-Beam and Multi-Transmission Line Parameters; System Lagrangian and Field Equations; Wave-Particle Interactions and Origins of Instability; Instability Concepts and their Graphical Representation; Instability Branches of the Characteristic Function; Circular Approximations; All-Frequency Modal Branches; Instability Phases via the Dispersion-Instability Graph; Instability Structure of Afm-Branches; Instability Nodes and the Degeneracy; Instability Critical States — 3rd-Order Degeneracy; Almost-Linear Unstable Modal Branches; Wave-Packet Propagation and Amplification; Single Stream E-Beam and MTL; Multi-Stream E-Beam Coupled to a Single TL; MTL as an Approximation and TWT Observables; Instability — Possibilities and Limitations; Traveling Wave Tube Components: Multi-Transmission Line; Multi-Stream E-Beam; Single Stream Uncoupled E-Beam; TWT with One-Stream or Two-Stream E-Beam: Single Stream E-Beam and Single TL; Two-Stream Uncoupled E-Beam; Two-Stream E-Beam Coupled to a Single TL; Traveling Tube (TWT) System: The E-Beam Interacting with MTL; Homogeneous MTL and Multi-Stream E-Beam; Detailed Energy Balance; Dielectric Medium Point of View; Instability of the TWT-System; Mathematical Subjects: Characteristic Functions and Equations; A Priori Bounds on the Characteristic Velocities; MTL Characteristic Function; Functions of the E-Beam; Nodal Function; Series Expansions; Circular Approximations; 2nd Order Degeneracy at Instability Nodes; 3rd Order Degeneracy at Critical States; Real-Valued Functions of Real Variable and their Zeros; Quasi-Concavity and Related Subjects; Pseudo-Parts of a Complex Number; Some Plasma Physics Subjects Concise Review: Kinetic Theory Basics for Cold Collisionless Plasma; Macroscopic Fluid Model of Plasma; Electron-Beam Steady States; Linearized Equations for the Plasma; The Pierce Model; Plasma Frequency Reduction; Velocity as a Function of the Gap Potential; Child's Law and Fedosov's Solution; Appendices: Fourier Transforms; Wave-Packet; The Rouche Theorem; Reversion, Inversion and Other Operations on Power Series; Fixed Point Theorem and the Contraction Principle; Inverse of an Analytic Function at Critical Points; Moebius (Linear-Fractional) Transformations; Dielectric Properties and Material Relations; Lagrangian Eld Theory; Block-Matrices; Time Averaging and Energy Conservation; Convexity, Quasi-Convexity and Log-Convexity; Polar Representation of a Curve in a Plane; Important Expressions and Equations; References; Index