An Analytic Theory of Multi-stream Electron Beams in Traveling Wave Tubes

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.Contents: Dedication 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, Field Equations, Characteristic Equation and Eigenmodes Wave-Particle Interactions and Origins of Instability Energy Transfer and Stream Velocities Instability Concepts and Their Graphical Representation Instability Branches of the Characteristic Function Circular Approximations to Sets of Admissible Phase Velocities All-Frequency Modal Branches Instability Phases via the Dispersion-Instability Graph Instability Structure of All-Frequency Modal Branches Instability Nodes and the Degeneracy of the Characteristic Function Instability at Critical States — The Third-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 Composed of a Single-Stream e-Beam and a Single Transmission Line: Lagrangian, Field Equations and Power Transfer Characteristic Function Characteristic Velocities and Wavenumbers Dispersion-Instability Graphs Asymptotic Expansions for Infinite-Frequency Limit Pierce Model as the Infinite-Frequency Limit Approximation Nodal Phase Velocities TWT with Two-Stream e-Beam and a Single TL: TWT Lagrangian and the Characteristic Equation Uncoupled Two-Stream e-Beam Infinite-Frequency Limit Approximation Instability Nodes and Nodal Velocities Complex-Valued Characteristic Velocities Complex-Valued characteristic Wavenumbers Critical Value of the TWT Principal Parameter All-Frequency Instability and Transition to It All-Frequency Almost-Linear Unstable Branch and Its Gain Single-Stream Approximation for Negative Phase Velocities Lagrangian Field Theory of TWTs: The e-Beam Interacting with Multi-Transmission Line Homogeneous Multi-Transmission Line Interacting with Multi-Stream e-Beam Detailed Energy Balance Dielectric Medium Point of View Mathematical Subjects: Characteristic Functions and Equations MTL Characteristic Function Properties Uncoupled e-Beam Related Quantities Uncoupled Two-Stream e-Beam Nodal Function and Its Critical Points Nodal and Critical Velocities Bounds on the Characteristic Velocities for TWT Series Expansions for the MTL and the e-Beam Functions Circular Approximations for Admissible Non-Real Phase Velocities Dispersion Relation at Instability Nodes — the Second-Order Degeneracy...