Nonlinear Electron-Wave Interaction Phenomena

Nonlinear Electron-Wave Interaction Phenomena

1st Edition - January 1, 1965

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  • Author: Joseph E. Rowe
  • eBook ISBN: 9781483225203

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Nonlinear Electron-Wave Interaction Phenomena explores the interaction between drifting streams of charged particles and propagating electromagnetic waves. Of particular concern are the situations in which the wave amplitude is large and there is strong coupling between the charged fluid and the wave. Emphasis is placed on those devices that utilize a defined injected stream of some type. Particle and electromagnetic wave velocities both small and comparable to the velocity of light are considered. Comprised of 16 chapters, this book begins with an introduction to the various classes of devices in which the drifting stream (charged fluid) is composed of electrons and/or ions coupled to a slow electromagnetic wave over an extended region. The discussion then turns to Eulerian versus Lagrangian formulation and radio-frequency equivalent circuits, along with space-charge-field expressions. Subsequent chapters focus on the interaction mechanisms in klystrons, traveling-wave amplifiers, and O-type backward-wave oscillators, as well as crossed-field forward- and backward-wave amplifiers, and traveling-wave energy converters. The book also evaluates multibeam and beam-plasma interactions; phase focusing of electron bunches; pre-bunched electron beams; collector depression techniques; and modulation characteristics. This monograph is designed to serve both as a research monograph for workers in the fields of microwave electron and plasma devices and as a text for advanced graduate students.

Table of Contents

  • Foreword

    Chapter I Introduction

    1 General Introduction

    2 Scope of the Book

    3 Classes and Description of Devices Analyzed

    4 Necessity for a Nonlinear Analysis


    Chapter II Eulerian Versus Lagrangian Formulation

    1 Introduction

    2 Eulerian Formulation of O-TWA Equations

    3 Lagrangian Formulation

    4 Composite Lagrangian System

    Chapter III Radio-Frequency Equivalent Circuits

    1 Introduction

    2 Equivalence of Maxwell and Kelvin Theories

    3 Equivalence for a Helical Wave Guiding Structure

    4 Transmission-Line Equivalent for Surface Wave Propagation on a Plasma Column

    5 Equivalent Transmission Lines for Multidimensional Propagating Structures

    6 Backward-Wave Equivalent Circuits

    7 Equivalent Circuits with Spatially Varying Line Parameters


    Chapter IV Space-Charge-Field Expressions

    1 Introduction

    2 Green's Function Method for Potential Problems

    3 Potential Functions for the Cartesian Coordinate System

    4 Potential Function for a Two-Dimensional Rectangular System

    5 Space-Charge Fields for Rods of Charge

    6 Replacement of Rf Structure by an Impedance Sheet

    7 Space-Charge Potentials for Cylindrical Systems

    8 Potential Function for a Ring of Charge in an Axially Symmetric System

    9 Potential Functions for Hollow Beams

    10 One-Dimensional Disk Space-Charge Model

    11 Harmonic Method for Calculating the One-Dimensional Space-Charge Field

    12 Equivalence of the Green's Function and Harmonic Methods for the One-Dimensional Problem

    13 Space-Charge Fields for Specialized Configurations


    Chapter V Klystron Analysis

    1 Introduction

    2 One-Dimensional Klystron Analysis

    3 One-Dimensional Klystron Results

    4 Two-Dimensional Klystron Analysis

    5 Three-Dimensional Klystron Interaction

    6 Radial and Angular Effects in Klystrons

    7 Relativistic Klystron Analysis

    8 Voltage Stepping in Klystrons


    Chapter VI Traveling-Wave Amplifier Analysis

    1 Introduction

    2 Mathematical Analysis of the One-Dimensional TWA

    3 One-Dimensional Results

    4 N-Beam TWA Analysis

    5 Two-Dimensional TWA Analysis

    6 Three-Dimensional O-TWA Analysis

    7 Two-Dimensional Circuit, Three-Dimensional Flow

    8 Effects of Transverse Variations on TWA Gain and Efficiency

    9 Relativistic O-TWA

    10 Integral Equation Analysis


    Chapter VII O-Type Backward-Wave Oscillators

    1 Introduction

    2 Backward-Wave Circuits

    3 Mathematical Analysis

    4 Solution Procedure

    5 Efficiency Calculations

    6 Relativistic Oscillator Analysis

    7 Radial and Angular Variations in BWO's


    Chapter VIII Crossed-Field Drift-Space Interaction

    1 Introduction

    2 Two-Dimensional Drift-Space Equations

    3 Gap Modulation of a Crossed-Field Stream

    4 Results for a Two-Dimensional Cf Drift Region

    5 Three-Dimensional Drift-Space Equations

    6 Adiabatic Motion in a Drift Region


    Chapter IX Crossed-Field Forward-Wave Amplifiers

    1 Introduction

    2 Two-Dimensional M-FWA with a Negative Sole

    3 Results for a Two-Dimensional M-FWA with a Negative Sole

    4 Two-Dimensional M-FWA with a Positive Sole

    5 Adiabatic Equations for a Two-Dimensional M-FWA with a Negative Sole

    6 Three-Dimensional M-FWA with a Negative Sole

    7 Effect of Cyclotron Waves

    8 Comparison with Sedin's Calculations

    9 Results of and Comparison of Various Nonlinear Theories for the M-FWA


    Chapter X Crossed-Field Backward-Wave Oscillators

    1 Introduction

    2 Two-Dimensional M-BWO with a Negative Sole

    3 Results for a Two-Dimensional M-BWO with a Negative Sole

    4 M-BWO with a Positive Sole

    5 Adiabatic Equations for an M-BWO with a Negative Sole

    6 Cyclotron Waves in M-BWO's

    7 Theory Versus Experiment


    Chapter XI Traveling-Wave Energy Converters

    1 Introduction

    2 O-Type Traveling-Wave Energy Converter

    3 M-Type Traveling-Wave Energy Converter


    Chapter XII Multibeam and Beam-Plasma Interactions

    1 Introduction

    2 Nonlinear Equations for Combined One-Dimensional Beam-Plasma Circuit

    3 Double-Beam Circuit Solutions

    4 Interaction Equations in the Absence of a Circuit

    5 Velocity Distributions

    6 Two-Dimensional Effects in Beam-Plasma Interactions


    Chapter XIII Phase Focusing of Electron Bunches

    1 Introduction

    2 Historical Background and Experimental Work

    3 Efficiency Improvement in Traveling-Wave Amplifiers

    4 Efficiency Improvement in O-Type Backward-Wave Oscillators

    5 Efficiency Improvement in Crossed-Field Amplifiers

    6 Efficiency Improvement in Crossed-Field Backward-Wave Oscillators


    Chapter XIV Prebunched Electron Beams

    1 Introduction

    2 Mathematical Formulation of the Lagrangian Equations

    3 Results for Klystrons

    4 Results for Traveling-Wave Amplifiers

    5 Results for Crossed-Field Amplifiers

    6 Rf Power Required to Bunch an Electron Beam


    Chapter XV Collector Depression Techniques

    1 Introduction

    2 Graphical Evaluation of Depressed Collectors

    3 Analysis of Output Energy Distribution for Collector Depression in O-Type Devices

    4 Results of Calculations for O-Type Devices

    5 Beam Current Flow Limitation in Collector Depression

    6 Depressed Collectors on Crossed-Field Devices


    Chapter XVI Modulation Characteristics

    1 Introduction

    2 Mathematical Analysis for O-Type Devices

    3 O-Type Nonlinear Modulation Results

    4 Mathematical Analysis for M-Type Devices

    5 Output Spectra for Low-Frequency Modulations

    6 Modulation by Multiple High-Frequency Signals


    Appendix A Rf Structure Impedance Variations

    1 Helical Line for O-FWA

    2 Helical Line for O-BWO

    3 Tapered Interdigital Line Characteristics


    Appendix B O-TWA Kompfner-Dip Conditions



    Appendix C M-FWA Kompfner-Dip Conditions



    Author Index

    Subject Index

Product details

  • No. of pages: 606
  • Language: English
  • Copyright: © Academic Press 1965
  • Published: January 1, 1965
  • Imprint: Academic Press
  • eBook ISBN: 9781483225203

About the Author

Joseph E. Rowe

About the Editors

Henry G. Booker

Nicholas Declaris

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