Electron beams and microwave vacuum electronics

599 Pages·2007·6.541 MB·English

by  Shulim E. Tsimring

Electron Beams
and Microwave
Vacuum Electronics
SHULIM E. TSIMRING
A JOHN WILEY & SONS, INC., PUBLICATION

Electron Beams
and Microwave
Vacuum Electronics

Electron Beams
and Microwave
Vacuum Electronics
SHULIM E. TSIMRING
A JOHN WILEY & SONS, INC., PUBLICATION
Copyright#2007byJohnWiley&Sons,Inc.Allrightsreserved.
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LibraryofCongressCataloging-in-PublicationData:
Tsimring,ShulimE.,1924–
Electronbeamsandmicrowavevacuumelectronics/byShulimE.Tsimring.
p.cm.
“AWiley-Intersciencepublication.”
Includesbibliographicalreferencesandindex.
ISBN-13:978-0-470-04816-0
ISBN-10:0-470-04816-6
1. Vacuummicroelectronics.2. Electronbeams.I.Title.
TK7874.9.T752006
621.3815012–dc22 2006044263
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
To my dear wife, Miroslava Sverdlova

Contents
PREFACE xix
Introduction 1
I.1 Outline ofthe Book 1
I.2 List of Symbols 5
I.3 Electromagnetic Fields andPotentials 6
I.4 Principle of Least Action. Lagrangian. Generalized
Momentum. Lagrangian Equations 7
I.5 Hamiltonian. Hamiltonian Equations 9
I.6 LiouvilleTheorem 10
I.6.1 Liouville Theorem for InteractionParticles 10
I.6.2 Liouville Theorem for Noninteraction Identical Particles 11
I.6.3 Liouville Theorem for aPhase Space of
Lesser Dimensions 12
I.7 Emittance. Brightness 12
I.7.1 Emittancein aZero MagneticField 12
I.7.2 Brightness 13
I.7.3 MaximumLangmuir Brightnessfor
Thermionic Emitters 14
PART I ELECTRON BEAMS 15
1 Motion of Electronsin ExternalElectricand Magnetic
StaticFields 17
1.1 Introduction 17
1.2 Energy of aCharged Particle 17
1.3 Potential–Velocity Relation (Static Fields) 18
vii
viii CONTENTS
1.4 Electronsin aLinearElectric Field e E¼kx 20
0
1.4.1 Nonrelativistic Approximation 20
1.4.2 Relativistic Oscillator 20
1.5 Motion ofElectrons inHomogeneous Static Fields 21
1.5.1 Electric Field 21
1.5.2 Magnetic Field 23
1.5.3 ParallelElectric and Magnetic Fields 25
1.5.4 PerpendicularFields E and B 27
1.5.5 Arbitrary Orientation ofFields E andB.
Nonrelativistic Approximation 30
1.6 Motion ofElectrons inWeakly Inhomogeneous Static Fields 31
1.6.1 SmallVariations inElectromagnetic Fields Acting
on MovingCharged Particles 32
1.6.2 Adiabatic Invariants 33
1.6.3 Motionof the Guiding Center 37
1.7 Motion ofElectrons inFields with Axial and Plane Symmetry.
Busch’sTheorem 41
1.7.1 Systems with Axial Symmetry. Busch’sTheorem 41
1.7.2 Formation ofHelical Trajectories at aJump ina
Magnetic Field 43
1.7.3 Systems with Plane Symmetry 44
2 ElectronLenses 47
2.1 Introduction 47
2.2 Maupertuis’s Principle. Electron-Optical Refractive Index.
Differential Equations ofTrajectories 48
2.2.1 Maupertuis’s Principle. Differential Equations
of Trajectories 48
2.2.2 General Properties ofCharged-ParticleTrajectories
in Electromagnetic Fields 50
2.3 Differential Equations ofTrajectories in Axially Symmetric Fields 51
2.4 Differential Equations ofParaxialTrajectories inAxially
Symmetric Fields Without aSpace Charge 53
2.5 Formationof Images by ParaxialTrajectories 56
2.5.1 Linearization ofTrajectoryEquations 56
2.5.2 Rotationofan Image. StigmaticImaging. Image Similarity 57
2.5.3 Magnifications 59
2.6 Electrostatic Axially Symmetric Lenses 61
2.6.1 Classification of Electrostatic Lenses 61
2.6.2 Immersion and UnipotentialLenses 63
2.6.3 Cardinal Elementsof aLens with LimitedField Extent 65
2.6.4 Focal Length ofThinUnipotential andImmersion Lenses 67