Electron Beams and Microwave Vacuum Electronics

Name: Electron Beams and Microwave Vacuum Electronics
Brand: Wiley
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Shulim E. Tsimring(Autor*in)

Wiley (Verlag)

11. Auflage

Erschienen am 20. November 2006

512 Seiten

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Intro
Electron Beams and Microwave Vacuum Electronics
Contents
PREFACE
Introduction
I.1 Outline of the Book
I.2 List of Symbols
I.3 Electromagnetic Fields and Potentials
I.4 Principle of Least Action. Lagrangian. Generalized Momentum. Lagrangian Equations
I.5 Hamiltonian. Hamiltonian Equations
I.6 Liouville Theorem
I.6.1 Liouville Theorem for Interaction Particles
I.6.2 Liouville Theorem for Noninteraction Identical Particles
I.6.3 Liouville Theorem for a Phase Space of Lesser Dimensions
I.7 Emittance. Brightness
I.7.1 Emittance in a Zero Magnetic Field
I.7.2 Brightness
I.7.3 Maximum Langmuir Brightness for Thermionic Emitters
PART I ELECTRON BEAMS
1 Motion of Electrons in External Electric and Magnetic Static Fields
1.1 Introduction
1.2 Energy of a Charged Particle
1.3 Potential-Velocity Relation (Static Fields)
1.4 Electrons in a Linear Electric Field e(0)E = kx
1.4.1 Nonrelativistic Approximation
1.4.2 Relativistic Oscillator
1.5 Motion of Electrons in Homogeneous Static Fields
1.5.1 Electric Field
1.5.2 Magnetic Field
1.5.3 Parallel Electric and Magnetic Fields
1.5.4 Perpendicular Fields E and B
1.5.5 Arbitrary Orientation of Fields E and B. Nonrelativistic Approximation
1.6 Motion of Electrons in Weakly Inhomogeneous Static Fields
1.6.1 Small Variations in Electromagnetic Fields Acting on Moving Charged Particles
1.6.2 Adiabatic Invariants
1.6.3 Motion of the Guiding Center
1.7 Motion of Electrons in Fields with Axial and Plane Symmetry. Busch's Theorem
1.7.1 Systems with Axial Symmetry. Busch's Theorem
1.7.2 Formation of Helical Trajectories at a Jump in a Magnetic Field
1.7.3 Systems with Plane Symmetry
2 Electron Lenses
2.1 Introduction
2.2 Maupertuis's Principle. Electron-Optical Refractive Index. Differential Equations of Trajectories
2.2.1 Maupertuis's Principle. Differential Equations of Trajectories
2.2.2 General Properties of Charged-Particle Trajectories in Electromagnetic Fields
2.3 Differential Equations of Trajectories in Axially Symmetric Fields
2.4 Differential Equations of Paraxial Trajectories in Axially Symmetric Fields Without a Space Charge
2.5 Formation of Images by Paraxial Trajectories
2.5.1 Linearization of Trajectory Equations
2.5.2 Rotation of an Image. Stigmatic Imaging. Image Similarity
2.5.3 Magnifications
2.6 Electrostatic Axially Symmetric Lenses
2.6.1 Classification of Electrostatic Lenses
2.6.2 Immersion and Unipotential Lenses
2.6.3 Cardinal Elements of a Lens with Limited Field Extent
2.6.4 Focal Length of Thin Unipotential and Immersion Lenses
2.6.5 Aperture Lenses
2.6.6 Applications of Cathode Lenses
2.7 Magnetic Axially Symmetric Lenses
2.7.1 Equations of Paraxial Trajectories. Classification of Magnetic Lenses
2.7.2 Short Magnetic Lenses
2.7.3 Strong Magnetic Lenses
2.7.4 Long Magnetic Lenses
2.8 Aberrations of Axially Symmetric Lenses
2.8.1 Geometric Aberrations
2.8.2 Chromatic Aberration
2.8.3 Disturbances of Axial Symmetry
2.8.4 Space-Charge Fields
2.8.5 Electron Diffraction
2.9 Comparison of Electrostatic and Magnetic Lenses. Transfer Matrix of Lenses
2.9.1 Comparison of the Optical Power of Electrostatic and Magnetic Lenses
2.9.2 Second-Order Focusing of Axially Symmetric Lenses
2.9.3 Transfer Matrix of Lenses
2.10 Quadrupole lenses
2.10.1 Introduction
2.10.2 Equation of Paraxial Trajectories
2.10.3 Transfer Matrix
2.10.4 Cardinal Elements
2.10.5 Quadrupole Doublets
2.10.6 Quadrupole Triplets
2.10.7 Applications of Quadrupole Lenses
3 Electron Beams with Self Fields
3.1 Introduction
3.2 Self-Consistent Equations of Steady-State Space-Charge Electron Beams
3.2.1 Single-Flow Approximation (Laminar Beams). Pinch Effect
3.2.2 Multistream Flows
3.2.3 Kinetic Description
3.3 Euler's Form of a Motion Equation. Lagrange and Poincaré Invariants of Laminar Flows
3.3.1 Equation of Motion in Euler Form. Regular Beams
3.3.2 Lagrange and Poincaré Invariants
3.3.3 Generalized Busch Theorem
3.4 Nonvortex Beams. Action Function. Planar Nonrelativistic Diode. Perveance. Child-Langmuir Formula. ?- and T-Modes of Electron Beams
3.4.1 Indications of Congruent Beams
3.4.2 Differential Equation of a Congruent Beam
3.4.3 Nonmagnetic Congruent Beams
3.4.4 Application of an Action Function to Analysis of a Planar Nonrelativistic Diode. Child-Langmuir Formula. ?- and T-Modes
3.4.5 Influence of Initial Velocities
3.4.6 Optical Definition of a Congruent Beam
3.5 Solutions of Self-Consistent Equations for Curvilinear Space-Charge Laminar Beams. Meltzer Flow. Planar Magnetron with an Inclined Magnetic Field. Dryden Flow
3.5.1 Forms of Representation of Solutions for Curvilinear Space-Charge Beams
3.5.2 Normal Congruent Nonrelativistic Beams. Single-Component Flows
3.5.3 Meltzer Flow
3.5.4 Laminar Noncongruent Beams
4 Electron Guns
4.1 Introduction
4.2 Pierce's Synthesis Method for Gun Design
4.3 Internal Problems of Synthesis. Relativistic Planar Diode. Cylindrical and Spherical Diodes
4.3.1 Relativistic Planar Diode in the ?-Mode
4.3.2 Nonrelativistic Cylindrical and Spherical Diodes in the ?-Mode
4.4 External Problems of Synthesis. Cauchy Problem
4.4.1 Cauchy Problem for Laplace's Equation
4.4.2 Synthesis of a Pierce Gun
4.5 Synthesis of Electrode Systems for Two-Dimensional Curvilinear Beams with Translation Symmetry (Lomax-Kirstein Method). Magnetron Injection Gun
4.5.1 Lomax-Kirstein Method of Synthesis of Two-Dimensional Systems
4.5.2 Design of Electrodes for a Meltzer Flow Gun
4.5.3 Design of Electrodes for a Magnetron Injection Gun
4.6 Synthesis of Axially Symmetric Electrode Systems
4.6.1 Statement of the Problem. Harker's Method. Conformal Transformation of a Boundary Trajectory. Field Equations in a Transformed Plane
4.6.2 Transformation of Beam Equations to a Hyperbolic Type. Numerical Realization of Harker's Method
4.7 Electron Guns with Compressed Beams. Magnetron Injection Gun
4.7.1 Electron Guns with Wedge-Shaped and Conic Beams
4.7.2 Magnetron Injection Electron Guns (Kino-Taylor Guns)
4.7.3 High-Convergence Electron Gun with a Magnetic Accompaniment
4.7.4 Centrifugal Electrostatic Guns
4.8 Explosive Emission Guns
4.8.1 Introduction
4.8.2 Planar Explosive Emission Diodes
4.8.3 Magnetically Insulated Diodes
5 Transport of Space-Charge Beams
5.1 Introduction
5.2 Unrippled Axially Symmetric Nonrelativistic Beams in a Uniform Magnetic field
5.2.1 Statement of the Problem. Equations of an Equilibrium Beam
5.2.2 Isovelocity Beams
5.2.3 Solid Brillouin Beams
5.2.4 Hollow Brillouin Beams
5.3 Unrippled Relativistic Beams in a Uniform External Magnetic Field
5.3.1 Introduction
5.3.2 Equations of Relativistic Equilibrium Electron Flow
5.3.3 Solid Relativistic Brillouin Beams
5.4 Cylindrical Beams in an Infinite Magnetic Field
5.4.1 Thin Annular Flows in an Infinite Magnetic Field
5.4.2 Cylindrical Solid Beams in an Infinite Magnetic Field
5.5 Centrifugal Electrostatic Focusing
5.5.1 Introduction
5.5.2 Self-Consistent Centrifugal Focusing of an Annular Electron Beam
5.5.3 Electron Guns Formatting Harris Flow
5.6 Paraxial-Ray Equations of Axially Symmetric Laminar Beams
5.6.1 Paraxial-Ray Equations of Axially Symmetric Hollow Beams with Rectilinear Axis
5.6.2 Paraxial-Ray Equations of Axially Symmetric Solid Beams
5.6.3 Expansion of a Laminar Beam in a Uniform Drift Tube
5.6.4 Transfer of a Maximal Beam Current Through a Drift Tube Without External Fields
5.7 Axially Symmetric Paraxial Beams in a Uniform Magnetic Field with Arbitrary Shielding of a Cathode Magnetic Field
5.7.1 Paraxial-Ray Equation of an Axially Symmetric Laminar Beam in a Uniform Magnetic Field and Its First Integral
5.7.2 Equilibrium Radius of an Electron Beam
5.7.3 Stiffness of an Electron Beam. Frequency and Wavelength of Small Ripples
5.8 Transport of Space-Charge Beams in Spatial Periodic Fields
5.8.1 Introduction
5.8.2 Magnetic Periodic Focusing
PART II MICROWAVE VACUUM ELECTRONICS
6 Quasistationary Microwave Devices
6.1 Introduction
6.2 Currents in Electron Gaps. Total Current and the Shockley-Ramo Theorem
6.2.1 Total Current. Continuity of Total Current
6.2.2 Total Current and the Shockley-Ramo Theorem
6.2.3 Particular Cases
6.3 Admittance of a Planar Electron Gap. Electron Gap as an Oscillator. Monotron
6.3.1 Formulation of the Problem. Scheme of the Solution
6.3.2 Law of Charge Conservation
6.3.3 Calculation of Induced Current
6.3.4 Linearization of Induced Current. Complex Admittance of an Electron Gap
6.3.5 Equivalent Circuit of an Electron Gap. Electron Gap as an Oscillator. Monotron
6.4 Equation of Stationary Oscillations of a Resonance Self-Excited Circuit
6.5 Effects of a Space-Charge Field. Total Current Method. High-Frequency Diode in the ?-Mode. Llewellyn-Peterson Equations
6.5.1 Total Current Method
6.5.2 Analysis of a Diode for Current Limited by Space Charge
6.5.3 Llewellyn-Peterson Equations
7 Klystrons
7.1 Introduction
7.2 Velocity Modulation of an Electron beam
7.3 Cinematic (Elementary) Theory of Bunching
7.3.1 Qualitative Discussion
7.3.2 Bunching of a Convection Current
7.3.3 Fourier Expansion of a Convection Current
7.4 Interaction of a Bunched Current with a Catcher Field. Output Power of A Two-Cavity Klystron
7.4.1 Interaction of a Bunched Current with a Catcher Field
7.4.2 Output Power and Electron Efficiency in a Kinematic Approximation
7.5 Experimental Characteristics of a Two-Resonator Amplifier and Frequency-Multiplier Klystrons
7.6 Space-Charge Waves in Velocity-Modulated Beams
7.6.1 Formulation of the Problem
7.6.2 Equations of Space-Charge Waves
7.6.3 Fast and Slow Space-Charge Waves
7.6.4 Plasma Frequency Reduction Factor
7.6.5 Debunching of a Velocity-Modulated Beam by a Space Charge
7.7 Multicavity and Multibeam Klystron Amplifiers
7.7.1 Voltage Amplifier Mode (Maximum Gain)
7.7.2 Power Amplifier Mode
7.7.3 Bandwidth Amplifier Mode
7.7.4 Multibeam Klystrons
7.8 Relativistic Klystrons
7.9 Reflex Klystrons
7.9.1 Bunching of an Electron Beam in a Retarded Field
7.9.2 Calculation of Electron Power and Efficiency
7.9.3 Equation of Stationary Oscillations. Starting Current. Electronic Frequency Tuning. Oscillation Zones
7.9.4 Efficiency and Applications of Reflex Klystrons
8 Traveling-Wave Tubes and Backward-Wave Oscillators (O-Type Tubes)
8.1 Introduction
8.2 Qualitative Mechanism of Bunching and Energy Output in a TWTO
8.2.1 Scheme of a TWTO
8.2.2 Qualitative Mechanism of Bunching and Energy Radiation in a TWTO
8.3 Slow-Wave Structures
8.4 Elements of SWS Theory
8.4.1 Floquet's Theorem
8.4.2 Spatial Harmonics
8.5 Linear Theory of a Nonrelativistic TWTO. Dispersion Equation, Gain, Effects of Nonsynchronism, Space Charge, and Loss in a Slow-Wave Structure
8.5.1 Statement of the Problem
8.5.2 Bunching of a Convection Current in a Traveling-Wave Field
8.5.3 Excitation of the Field E(w) in a Slow-Wave Structure by a Given Convection Current
8.5.4 Dispersion Equation of the TWTO
8.5.5 Dimensionless Parameters, Initial Conditions, and Gain of a Nonrelativistic TWTO
8.5.6 Particular Cases
8.6 Nonlinear Effects in a Nonrelativistic TWTO. Enhancement of TWTO Efficiency (Velocity Tapering, Depressed Collectors)
8.6.1 Introduction
8.6.2 Derivation of Nonlinear Equations of a TWTO
8.6.3 Phasing of Electrons and Trapping of Bunches in a Traveling Wave
8.6.4 Enhancement of TWTO Efficiency. Velocity Tapering. Depressed Collectors
8.7 Basic Characteristics and Applications of Nonrelativistic TWTOs
8.7.1 Introduction
8.7.2 TWTO Noises
8.7.3 Influence of Wave Reflections on Gain. Self-Excitation of TWTOs. Attenuation and Severing
8.7.4 Intermodulation Distortion
8.7.5 Characteristics of Helical and Coupled-Cavity TWTOs
8.8 Backward-Wave Oscillators
8.8.1 Traveling-Wave Tube as an Oscillator
8.8.2 Backward-Wave Amplifier Tubes: Principles of Operation
8.8.3 Gain in Backward Amplifiers and Starting Conditions of BWOs
8.8.4 Frequency Tuning in BWOs
8.8.5 Properties of Nonrelativistic BWOs for a Current Greater Than the Starting Value
8.9 Millimeter Nonrelativistic TWTOs, BWOs, and Orotrons
8.9.1 Structural Features of Millimeter Nonrelativistic TWTOs and BWOs
8.9.2 Clinotrons
8.9.3 Orotrons
8.10 Relativistic TWTOs and BWOs
8.10.1 Introduction
8.10.2 Equations of Relativistic BWOs and TWTOs. Relations of Similarity
8.10.3 Relativistic BWOs
8.10.4 Relativistic TWTOs
9 Crossed-Field Amplifiers and Oscillators (M-Type Tubes)
9.1 Introduction
9.2 Elementary Theory of a Planar MTWT
9.2.1 Scheme of a Planar MTWT. Electron Beam in DC Crossed Fields
9.2.2 Motion and Bunching of Electrons in a High-Frequency Field (Adiabatic Approximation)
9.2.3 Comparison of Basic Features of Bunching and Energy Transfer in MTWTs and TWTOs
9.3 MTWT Amplification
9.3.1 Equation of Excitation
9.3.2 Dispersion Equation
9.3.3 Gain of an MTWT
9.3.4 Effects of Space Charge and Losses
9.3.5 Nonlinear Gain of an MTWT
9.3.6 Efficiency of an MTWT
9.4 M-type Injected Beam Backward-Wave Oscillators (MWO, M-Carcinotron)
9.4.1 Introduction
9.4.2 Starting Conditions of an MBWO
9.4.3 Large-Signal Effects
9.4.4 Parameters and Construction of an MBWO
9.5 Magnetrons
9.5.1 Electromagnetic Field in a Magnetron Resonator
9.5.2 Electron Beam in a Magnetron
9.5.3 Dynamic Regime of a Magnetron. Threshold Voltage
9.5.4 Magnetron Efficiency
9.5.5 Magnetron Performance
9.5.6 Magnetron Frequency Tuning
9.6 Relativistic Magnetrons
9.6.1 Introduction
9.6.2 Hull and Buneman-Hartree Conditions
9.6.3 Performance of Relativistic Magnetrons
9.6.4 Pulse Duration, Repetitive Operations, and Phase Locking in Relativistic Magnetrons
9.7 Magnetically Insulated Line Oscillators
9.7.1 MILO Principles of Operation. Choke-Equipped MILOs
9.7.2 Tapered MILOs
9.8 Crossed-Field Amplifiers
9.8.1 Basic Types of CFAs
9.8.2 Slow-Wave Structures of CFAs
9.8.3 Amplification and Efficiency of Amplitrons
9.8.4 Amplitron Bandwidth
9.8.5 Amplitron Phase Characteristics
9.8.6 Electron Emission in CFAs
10 Classical Electron Masers and Free Electron Lasers
10.1 Introduction
10.2 Spontaneous Radiation of Classical Electron Oscillators
10.2.1 Introduction
10.2.2 Magnetic Bremsstrahlung. Doppler Frequency Up-Conversion
10.3 Stimulated Radiation of Excited Classical Electron Oscillators
10.3.1 Admittance of an Ensemble of Classical Oscillators
10.3.2 Linear Oscillators Near a Resonance
10.3.3 Stimulated Radiation of Nonlinear Oscillators Near Resonance on the nth Harmonic
10.3.4 Spatial Bunching of Classical Oscillators
10.4 Examples of Electron Cyclotron Masers
10.4.1 Oscillator of Barkhausen-Kurtz
10.4.2 Strophotron
10.4.3 Ubitron
10.4.4 Peniotron
10.4.5 Magnicon
10.4.6 Trochotron (ECM with Trochoidal Electron Beam)
10.4.7 Gyromonotron: Oscillator with a Helical Electron Beam in a Quasiuniform Waveguide Near Its Cutoff Frequency
10.5 Resonators of Gyromonotrons (Free and Forced Oscillations)
10.5.1 Construction and Basic Parameters of Resonators
10.5.2 Free Oscillations of Gyrotron Resonators
10.5.3 Energy Balance for Free and Forced Stationary Oscillations
10.6 Theory of a Gyromonotron
10.6.1 Equation of Electron Motion in a TE Wave at Quasi-Cutoff Frequency
10.6.2 Reducing Eqs. (10.72) and (10.73) to Slow Variables
10.6.3 Averaging of Equations
10.6.4 Hamiltonian Form of Averaged Equations
10.6.5 Energy Integral of Averaged Equations
10.6.6 Averaged Equations in Polar Coordinates
10.7 Subrelativistic Gyrotrons
10.7.1 Introduction
10.7.2 Derivation of Subrelativistic Averaged Equations
10.7.3 Results of Integration of Subrelativistic Gyrotron Equations
10.7.4 Linearization of Subrelativistic Gyrotron Equations
10.7.5 Starting Regime of a Gyromonotron
10.8 Elements of Gyrotron Electron Optics
10.8.1 Parameters of Helical Electron Beams
10.8.2 Systems of HEB Formation
10.8.3 Theory of an Adiabatic Magnetron-Injected Gun in a Nonrelativistic Approximation
10.8.4 Advanced Design of an MIG
10.8.5 Velocity, Energy Spread, and Instabilities of HEBs
10.8.6 Potential Depression and Limiting Current of HEBs
10.9 Mode Interaction and Mode Selection in Gyrotrons. Output Power Systems
10.9.1 Mode Interaction
10.9.2 Mode Selection
10.9.3 Output Power Systems
10.9.4 Output Windows
10.9.5 Depressed Collectors
10.10 Gyroklystrons
10.10.1 Introduction
10.10.2 Basic Model
10.10.3 Gyroklystron Equations
10.10.4 Efficiency, Gain, and Bandwidth of Gyroklystrons
10.11 Gyro-Traveling-Wave Tubes
10.11.1 Scheme of a Gyro-TWT. Resonance Condition
10.11.2 Linear Theory of Gyro-TWTs
10.11.3 Bandwidth of Gyro-TWTs
10.11.4 Reflective Instability of Gyro-TWTs
10.12 Applications of Gyrotrons
10.12.1 Introduction
10.12.2 Electron-Cyclotron Resonance Heating and Current Drive
10.12.3 Generation of Multiply Charged Ions and Soft X-rays. Electron Spin Resonance Spectroscopy
10.12.4 Microwave Procession of Materials
10.12.5 Millimeter Radar Systems
10.12.6 Gyroklystron RF Drivers for TeV Linear Electron-Positron Colliders
10.13 Cyclotron Autoresonance Masers
10.13.1 Moderately Relativistic Gyrotrons
10.13.2 Operation Principle and Some Properties of CARM Oscillators
10.14 Free Electron Lasers
10.14.1 Introduction
10.14.2 Scheme of an FEL
10.14.3 Linear Theory of FELs
10.14.4 Parameters of FELs
10.14.5 Applications of FELs
Appendixes
1. Proof of the 3/2 Law for Nonrelativistic Diodes in the ?-Mode
2. Synthesis of Guns for M-Type TWTs and BWOs
3. Magnetic Field in Axially Symmetric Systems
4. Dispersion Characteristics of Interdigital and Comb Structures
5. Electromagnetic Field in Planar Uniform Slow-Wave Structures
6. Equations of Free Oscillations of Gyrotron Resonators
7. Derivation of Eqs. (10.66) and (10.67)
8. Calculation of Fourier Coefficients in Gyrotron Equations
9. Magnetic Systems of Gyrotrons
References
Index

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