High-Field Electrodynamics

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ISBN: 9780849323782 | 0849323789
Cover: Hardcover
Copyright: 12/27/2001

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Tremendous technological developments and rapid progress in theory have opened a new area of modern physics: high-field electrodynamics, characterized by two fundamental scales: the relativistic intensity regime and the quantum electrodynamics (QED) scale. This text focuses on the theory of electromagnetic interactions near the relativistic intensity regime. It gives a comprehensive, detailed description of the theoretical tools needed to approach the subject and serves as a starting point for more advanced and specialized research. Written at a somewhat advanced level, the book includes many topics that have not been previously discussed within the context of high-field electrodynamics.

Part I Foundations

Overview

(22)

Introduction

(1)

The Relativistic Intensity Regime

(1)

The Schwinger Critical Field

(1)

Maxwell's Equations

(2)

Fields and Inductions, the Minkowski Formalism

(1)

Potentials, Gauge Condition, and Wave Equation

(2)

The Coulomb Potential and Plane Waves

(7)

Notes to Chapter 1

(7)

References

(1)

The Lorentz Transformation

(64)

Introduction

(3)

The Special Lorentz Transform

(2)

Four-Vectors

(5)

Addition of Velocities

(5)

Four-Acceleration and Hyperbolic Motion

(4)

Variation of the Mass with Velocity

(2)

The Energy-Momentum Four-Vector

(2)

Transformation of Forces

(7)

Transformation of Energy

(1)

Transformation of Angular Momentum

(3)

Transformation of Length, Surface, Volume, and Density

(4)

Relativistic Plasma Frequency

(8)

The General Lorentz Transform

(9)

Thomas Precession

(5)

Schwinger's Approach

(3)

References

(1)

Covariant Electrodynamics

(86)

Four-Vectors and Tensors

(4)

The Electromagnetic Field Tensor

(4)

Covariant Form of the Maxwell-Lorentz Equations

(7)

A Few Invariants, Four-Vectors, and Tensors Commonly Used

104

(3)

Transformation of the Fields

107

(3)

Electron and QED Units

110

(3)

Covariant Electromagnetic Lagrangian and Hamiltonian

113

(9)

Field Four-Momentum and Maxwell Stress Tensor

122

(15)

Metric and Christoffel Symbols

137

(8)

Solid in Rotation, Sagnac Effect

145

(7)

Dual Tensors and Spinors, Dirac Equation

152

(13)

Notes to Chapter 3

165

(8)

References

173

(2)

Gauge Condition and Transform

175

(64)

Introduction

175

(6)

Lorentz Gauge

181

(2)

Coulomb Gauge and Instantaneous Scalar Potential

183

(5)

Other Gauge Conditions

188

(3)

Charge Conservation

191

(2)

Noether's Theorem

193

(5)

Yang-Mills and Non-Abelian Gauge Fields

198

(5)

Weyl's Theory

203

(3)

Kaluza-Klein Five-Dimensional Space-Time

206

(3)

Charged Black Holes, Quantum Gravity, and Inflation

209

(11)

Superstrings and Dimensionality

220

(12)

The Bohm-Aharanov Effect

232

(4)

References

236

(3)

Part II Electromagnetic Waves

Green and Delta Functions, Eigenmode Theory of Waveguides

239

(128)

Introduction

239

(1)

The Dirac Delta-Function

240

(15)

Fourier, Laplace, and Hankel Transforms

255

(5)

Green Functions in Vacuum

260

(14)

Green Function for Poisson's Equation, Coulomb Potential

260

(5)

Green Function for the d'Alembertian, Photon Propagator

265

(9)

Lienard-Wiechert Potentials

274

(5)

Green Functions with Boundary Conditions: Cylindrical Waveguide

279

(42)

Cylindrical Vacuum Eigenmodes

279

(12)

Cylindrical Waveguide Eigenmodes

291

(5)

Orthogonality of Cylindrical Waveguide Eigenmodes

296

(3)

Eigenmode Decomposition of the Four-Current

299

(4)

Gauge Condition and Continuity Equation

303

(2)

Green Function in a Cylindrical Waveguide

305

(2)

Fast-Wave Excitation in a Cylindrical Waveguide

307

(4)

Slow-Wave Excitation in a Corrugated Waveguide

311

(10)

Point Charge in Rectilinear Motion in Vacuum

321

(7)

Coulomb Field and Lorentz Transform

322

(1)

Bessel Vacuum Eigenmode Excitation

323

(5)

Multipoles, Spherical Harmonics, and the Hydrogen Atom

328

(12)

Group Velocity Dispersion, Higher-Order Effects, and Solitons

340

(26)

References

366

(1)

Plane Waves and Photons

367

(48)

Introduction

367

(2)

Quantization of the Free Electromagnetic Field

369

(7)

Creation and Annihilation Operators

376

(2)

Energy and Number Spectra

378

(4)

Momentum of the Quantized Field

382

(3)

Angular Momentum of the Quantized Field

385

(5)

Classical Spin of the Electromagnetic Field

390

(3)

Photon Spin

393

(1)

Vacuum Fluctuations

394

(2)

The Einstein--Podolsky--Rosen Paradox

396

(4)

Squeezed States

400

(2)

Casimir Effect

402

(1)

Reflection of Plane Waves in Rindler Space

403

(10)

Background

404

(1)

Derivation of the Reflected Wave Using the Rindler Transform

405

(4)

Derivation of the Reflected Wave Using the Lorentz Transform

409

(3)

Mathematical Appendix

412

(1)

References

413

(2)

Relativistic Transform of the Refractive Index: Cerenkov Radiation

415

(30)

Introduction

415

(1)

Classical Theory of Cerenkov Radiation

416

(11)

Fields and Inductions, Polarization, and Nonlinear Susceptibilities

427

(5)

Transform of Linear Refractive Index: Minkowski Formulation

432

(3)

Anomalous Refractive Index and Cerenkov Effect

435

(3)

Linear Isotropic Medium: Induced-Source Formalism

438

(4)

Covariant Treatment of Nonlinear Effects

442

(1)

References

443

(2)

Three-Dimensional Waves in Vacuum, Ponderomotive Scattering, Vacuum Laser Acceleration

445

(60)

Introduction

445

(5)

Exact Solutions to the Three-Dimensional Wave Equation in Vacuum

450

(3)

The Paraxial Propagator

453

(4)

Bessel Functions and Hankel's Integral Theorem

457

(5)

Plane Wave Dynamics, Lawson-Woodward Theorem

462

(6)

Canonical Invariants: Phase and Light-Cone Variable

462

(4)

Fluid Invariants

466

(2)

Ponderomotive Scattering

468

(5)

Electron Dynamics in a Coherent Dipole Field

473

(8)

Chirped-Pulse Inverse Free-Electron Laser

481

(10)

Free-Wave Acceleration by Stimulated Absorption of Radiation

491

(6)

Plasma-Based Laser Acceleration Processes

497

(4)

References

501

(4)

Part III Relativistic Electrons and Radiation

Coherent Synchrotron Radiation and Relativistic Fluid Theory

505

(56)

Introduction

505

(4)

Coherent Synchrotron Radiation in Free-Space

509

(12)

Coherent Synchrotron Radiation in a Waveguide

521

(11)

Four-Current in a Helical Wiggler

522

(2)

Coupling to Cylindrical Waveguide Modes

524

(8)

Instantaneous Power Flow in the Waveguide

532

(1)

Time-Dependent Chirped Wavepacket

533

(8)

Propagation in Negative GVD Structure

541

(2)

Relativistic Eulerian Fluid Perturbation Theory

543

(17)

Covariant Linearized Fluid Theory

544

(6)

Cylindrical Waveguide Electrostatic Modes

550

(10)

References

560

(1)

Compton Scattering, Coherence, and Radiation Reaction

561

(66)

Introduction

561

(1)

Classical Theory of Compton Scattering

562

(7)

The HLF Radiation Theorem

563

(1)

Covariant Linearization

564

(1)

Nonlinear Plane Wave Dynamics

565

(3)

Radiation

568

(1)

Electron Beam Phase Space

569

(7)

Classical Compton Scattering Differential Cross-Section

569

(3)

Energy Spread

572

(2)

Emittance

574

(2)

Three-Dimensional Theory of Compton Scattering

576

(10)

The Cold Three-Dimensional Spectral Density

578

(2)

Three-Dimensional Effects

580

(2)

Three-Dimensional Compton Scattering Code

582

(4)

Stochastic Electron Gas Theory of Coherence

586

(8)

Comparison with a Fluid Model

590

(4)

Harmonics and Nonlinear Radiation Pressure

594

(1)

Radiative Corrections: Overview

595

(4)

Symmetrized Electrodynamics: Introduction

599

(1)

Symmetrized Electrodynamics: Complex Notation

600

(2)

Symmetrized Dirac-Lorentz Equation

602

(4)

Conceptual Difficulties: Electromagnetic Mass Renormalization, Runaways, Acausal Effects

606

(2)

Schott Term

608

(6)

Maxwell Stress Tensor

614

(2)

Hamiltonian Formalism

616

(2)

Symmetrized Electrodynamics in the Complex Charge Plane and the Running Fine Structure Constant

618

(1)

Notes to Chapter 10

619

(7)

References

626

(1)

Bibliography

627

(36)

Index

663

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High-Field Electrodynamics

Summary

Table of Contents

Supplemental Materials