Physics of Nonneutral Plasmas

, by Davidson, Ronald C.

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ISBN: 9781860943034 | 1860943039
Cover: Paperback
Copyright: 12/1/2001

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Supplemental Materials

Author's Foreword

vii

Preface

Acknowledgments

Introduction

(14)

Exordium

(1)

Historical Background

(1)

Technical Advances

(2)

Outline

(10)

References

(8)

Theoretical Models of Nonneutral Plasma

(24)

Introduction

(2)

Kinetic Description

(5)

Macroscopic Fluid Description

(4)

Conservation Relations

(3)

Discrete Particle Effects

(6)

Gravitational Analogue

(4)

References

(4)

Fundamental Properties of Nonneutral Plasma

(40)

Cold-Fluid Equilibrium Rotation

(8)

Single-Particle Trajectories

(5)

Thermal Equilibrium

(7)

Debye Shielding

(2)

Spontaneous Emission from a Test Electron

(4)

Strongly Coupled Nonneutral Plasma

(14)

References

(4)

Kinetic Equilibrium and Stability Properties

(142)

Equilibrium Vlasov-Maxwell Equations for Axisymmetric Nonneutral Plasma

(10)

Axisymmetric Confinement Geometries

(4)

Nonneutral Plasma Column

(4)

Axially Confined Equilibria

(2)

Nonrelativistic Kinetic Equilibria

(19)

Rigid-Rotor Vlasov Equilibria

(6)

Density Inversion Theorem

(2)

Uniform-Density Plasma Column

(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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Physics of Nonneutral Plasmas

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