Physics of Nonneutral Plasmas,9781860943034

Physics of Nonneutral Plasmas

by
ISBN13: 9781860943034
ISBN10: 1860943039
Format: Paperback
Pub. Date: 2001-12-01
Publisher(s): Imperial College Pr
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Table of Contents

Author's Foreword vii
Preface ix
Acknowledgments xi
Introduction
1(14)
Exordium
1(1)
Historical Background
2(1)
Technical Advances
3(2)
Outline
5(10)
References
7(8)
Theoretical Models of Nonneutral Plasma
15(24)
Introduction
15(2)
Kinetic Description
17(5)
Macroscopic Fluid Description
22(4)
Conservation Relations
26(3)
Discrete Particle Effects
29(6)
Gravitational Analogue
35(4)
References
35(4)
Fundamental Properties of Nonneutral Plasma
39(40)
Cold-Fluid Equilibrium Rotation
39(8)
Single-Particle Trajectories
47(5)
Thermal Equilibrium
52(7)
Debye Shielding
59(2)
Spontaneous Emission from a Test Electron
61(4)
Strongly Coupled Nonneutral Plasma
65(14)
References
75(4)
Kinetic Equilibrium and Stability Properties
79(142)
Equilibrium Vlasov-Maxwell Equations for Axisymmetric Nonneutral Plasma
80(10)
Axisymmetric Confinement Geometries
80(4)
Nonneutral Plasma Column
84(4)
Axially Confined Equilibria
88(2)
Nonrelativistic Kinetic Equilibria
90(19)
Rigid-Rotor Vlasov Equilibria
91(6)
Density Inversion Theorem
97(2)
Uniform-Density Plasma Column
99(3)
Annular Electron Layer
102(7)
Axially-Confined Kinetic Equilibria
109(13)
Penning-Trap and Segmented Cylinder Equilibria
110(7)
Mirror-Confined Electron Layer
117(5)
Intense Relativistic Electron Beam Equilibria
122(8)
Kinetic Stability Theorem for Nonneutral Plasma
130(7)
Kinetic Confinement Theorem for Nonneutral Plasma
137(6)
Electrostatic Eigenvalue Equation
143(6)
Dispersion Relation for Body-Wave Perturbations
149(19)
Electrostatic Dispersion Relation
149(6)
Examples of Kinetic Waves and Instabilities
155(7)
Dispersion Relation for Transverse Electromagnetic Waves
162(6)
Dispersion Relation for Flute Perturbations
168(11)
Kinetic Equilibrium and Stability Properties of the Modified Betatron
179(42)
Introduction and Assumptions
179(5)
Self-Consistent Vlasov Equilibrium
184(11)
Linearized Vlasov-Maxwell Equations
195(9)
Negative-Mass and Surface-Kink Instabilities
204(8)
References
212(9)
Macroscopic Equilibrium and Stability Properties
221(68)
Equilibrium Force Balance Equation
222(3)
Examples of Macroscopic Equilibria
225(15)
Nonrelativistic Nonneutral Plasma Column
226(2)
Relativistic Diamagnetic Equilibria
228(5)
Relativistic Beam-Plasma Equilibria
233(3)
Bennett Pinch Equilibrium
236(4)
Electrostatic Eigenvalue Equation
240(3)
Dispersion Relation for Uniform-Density Plasma Column
243(5)
Nonneutral Plasma-Filled Waveguide
248(9)
Electrostatic Dispersion Relation
248(1)
Trivelpiece-Gould Modes in a Pure Ion Plasma
249(4)
Modified Two-Stream Instability
253(4)
Stability Properties for Flute Perturbations
257(8)
Electrostatic Dispersion Relation
257(2)
Stable Oscillations
259(1)
Ion Resonance Instability
260(5)
Two-Stream Instabilities in Relativistic Beam-Plasma Systems
265(6)
Electrostatic Dispersion Relation
265(2)
Beam-Plasma Filled Waveguide
267(2)
Thin-Beam Limit
269(2)
Electromagnetic Filamentation Instability
271(5)
Ordinary-Mode Dispersion Relation
272(3)
Filamentation Instability
275(1)
Equilibrium and Collective Oscillation Properties of Two-Dimensional Nonneutral Plasma
276(13)
Two-Dimensional Disk Equilibrium
278(2)
Normal Modes of Oscillation
280(4)
References
284(5)
The Diocotron Instability
289(56)
Nonrelativistic Guiding-Center Model
290(2)
Electrostatic Stability Theorem
292(3)
Linear Stability Properties
295(11)
Electrostatic Eigenvalue Equation
295(2)
Diocotron Instability for an Annular Electron Layer
297(8)
Stable Oscillations for l = 1 and Arbitrary Density Profile
305(1)
Experimental Results
306(6)
Quasilinear Evolution
312(11)
Theoretical Model
312(3)
Quasilinear Kinetic Equations
315(4)
Stabilization Process
319(4)
Resonant Diocotron Instability
323(7)
Instability Growth Rate
324(3)
Quasilinear Stabilization Process
327(3)
Influence of Electromagnetic and Relativistic Effects
330(15)
References
340(5)
Coherent Electromagnetic Wave Generation by the Cyclotron Maser and Free Electron Laser Instabilities
345(116)
Introduction
345(2)
Cyclotron Maser Instability
347(18)
Stability Properties for a Tenuous Electron Beam
348(7)
Influence of Intense Equilibrium Self Fields
355(10)
Cyclotron Maser Instability for an Annular Electron Beam
365(8)
High-Power Step-Tunable Gyrotron Experiments
373(2)
Free Electron Laser Instability
375(8)
Introduction
375(2)
Spontaneous Emission from a Test Electron in a Helical Wiggler Magnetic Field
377(4)
Free Electron Laser Oscillator Experiments
381(2)
Kinetic Description of the Free Electron Laser Instability
383(9)
Theoretical Model
383(3)
Kinetic Dispersion Relation
386(6)
Cold-Beam Stability Properties
392(12)
Linear Dispersion Relation
392(2)
Conditions for Free Electron Laser Interaction
394(1)
Tunable Free Electron Laser Experiments
395(2)
Analysis of the Full Dispersion Relation
397(2)
Compton-Regime Approximation
399(3)
Raman-Regime Approximation
402(2)
Warm-Beam Compton-Regime Stability Properties
404(8)
Nonlinear Evolution for Multimode Excitation
412(7)
Sideband Instability
419(20)
Nonlinear Wave and Orbit Equations
420(8)
Macroclump Model of the Sideband Instability
428(4)
Analysis of the Sideband Instability
432(5)
Experimental Results
437(2)
Harmonic Generation in a Planar Wiggler Free Electron Laser
439(7)
High-Gain Free Electron Laser Amplifier Experiments
446(15)
References
449(12)
Equilibrium and Stability Properties of Intense Nonneutral Flow in High-Power Diodes
461(78)
Introduction
461(2)
Child-Langmuir Flow
463(10)
Nonrelativistic Planar Diode
463(6)
Relativistic Planar Diode
469(4)
Magnetically Insulated Brillouin Flow
473(18)
Nonrelativistic Planar Flow
473(7)
Nonrelativistic Cylindrical Flow
480(5)
Relativistic Planar Flow
485(6)
Magnetically Insulated Ion Diodes
491(6)
Magnetron Instability for Magnetically Insulated Electron Flow
497(14)
Extraordinary-Mode Eigenvalue Equation
497(6)
Linear Growth Properties
503(8)
Multiresonator magnetron Experiments
511(4)
Ion Resonance and Transit Time Instabilities in Magnetically Insulated Ion Diodes
515(6)
Applied-B Diodes with Virtual Cathode
521(18)
Theoretical Model and Basic Equations
523(2)
Solution for Uniform-Density Electron Layer
525(4)
Ion Current Enhancement at Peak Diode Power
529(3)
References
532(7)
Propagation and Stability of Intense Charged Particle Beams in a Solenoidal Focusing Field
539(120)
Introduction
539(1)
Propagation of Intense Nonneutral Electron Beams
540(29)
Envelope Equation for Beam Propagation
541(6)
Space-Charge-Limiting Current
547(5)
Limiting Current in an Infinitely Long Drift Space
552(3)
Limiting Current in a One-Dimensional Drift Space
555(4)
Laminar Flow Equilibria in an Infinitely Long Drift Space
559(10)
Stability of Nonneutral Electron Flow in a One-Dimensional Drift Space
569(14)
Review of Nonrelativistic Equilibrium Flow
570(2)
Linearized Cold-Fluid-Poisson Equations
572(1)
Langrangian Representation
573(2)
Solution to the Eigenvalue Equation
575(4)
Analysis of Stability Properties
579(4)
Stability of Intense Nonneutral Ion and Electron Beams
583(32)
Theoretical Model and Assumptions
584(4)
Kapchinskij-Vladimirskij Beam Equilibrium
588(6)
Linearized Vlasov-Maxwell Equations
594(5)
Solution to the Eigenvalue Equation
599(6)
Transverse Stability Properties in a Solenoidal Focusing Field
605(5)
Transverse Stability Properties in a Quadrupole Focusing Field
610(5)
Resistive Hose Instability for Intense Electron Beam Propagation Through a Background Plasma
615(24)
Theoretical Model and Assumptions
615(3)
Equilibrium Properties
618(5)
Kinetic Eigenvalue Equation for l = 1 Perturbations
623(6)
Resistive Hose Instability for Sharp-Boundary Density Profile
629(8)
Resistive Hose Instability for a Diffuse Density Profile
637(2)
Resistive Sausage and Hollowing Instabilities for Intense Electron Beam Propagation Through a Background Plasma
639(20)
Theoretical Model and Assumptions
640(3)
Kinetic Eigenvalue Equation for Azimuthally Symmetric Perturbations
643(3)
Resistive Sausage Instability (n = 1)
646(4)
Resistive Hollowing Instability (n = 2)
650(3)
References
653(6)
Propagation and Stability of Intense Charged Particle Beams in an Alternating-Gradient Focusing Field
659(62)
Introduction
659(3)
Alternating-Gradient Field Configuration
662(4)
Equations of Motion in the Paraxial Approximation
666(3)
Orbit and Envelope Equations for a Periodic Quadrupole Field
669(4)
Particle Orbit Equations
669(3)
Beam Envelope Equations
672(1)
Orbit and Envelope Equations for a Solenoidal Focusing Field
673(7)
Particle Orbit Equations
673(3)
Beam Envelope Equations
676(1)
Beam Radius and Current for a Matched Beam
676(2)
Phase Advance σ
678(2)
Average Focusing Force and Phase Advance for a Periodic Quadrupole Field
680(10)
Envelope Equations for Small-Amplitude Modulation
680(2)
Phase Advance σ
682(6)
Average Quadrupole Focusing Force
688(1)
Beam Radius and Current for a Matched Beam
689(1)
Hamiltonian Formulation and Relationship to Kapchinskij-Vladimirskij Distribution Function
690(9)
Hamiltonian Formulation
691(3)
Kapchinskij-Vladimirskij Distribution Function
694(4)
Definition of Statistical Average and RMS Emittance
698(1)
Transverse Stability of the Kapchinskij-Vladimirskij Distribution Function
699(12)
Linearized Vlasov-Poisson Equations
699(3)
Transverse Stability Properties
702(5)
Generalization of the Eigenvalue Equation in the Low-Density Regime
707(4)
Emittance Growth
711(10)
Instability-Induced Emittance Growth
711(2)
Emittance Growth Caused by Charge Nonuniformity
713(4)
References
717(4)
Appendix A. Solution to the Eigenvalue Equation for Longitudinal Stability of the Modified Betatron 721(4)
Appendix B. Derivation of the Extraordinary-Mode Eigenvalue Equation for Relativistic Electron Flow in Planar Geometry 725(3)
Index 728

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