High-Field Electrodynamics

by Hartemann; Fred V.

• ISBN13: 9780849323782
• ISBN10: 0849323789
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-12-27
• Publisher: CRC Press

Summary

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.

Table of Contents

Part I Foundations
Overview	3	(22)
Introduction	3	(1)
The Relativistic Intensity Regime	4	(1)
The Schwinger Critical Field	5	(1)
Maxwell's Equations	5	(2)
Fields and Inductions, the Minkowski Formalism	7	(1)
Potentials, Gauge Condition, and Wave Equation	8	(2)
The Coulomb Potential and Plane Waves	10	(7)
Notes to Chapter 1	17	(7)
References	24	(1)
The Lorentz Transformation	25	(64)
Introduction	25	(3)
The Special Lorentz Transform	28	(2)
Four-Vectors	30	(5)
Addition of Velocities	35	(5)
Four-Acceleration and Hyperbolic Motion	40	(4)
Variation of the Mass with Velocity	44	(2)
The Energy-Momentum Four-Vector	46	(2)
Transformation of Forces	48	(7)
Transformation of Energy	55	(1)
Transformation of Angular Momentum	56	(3)
Transformation of Length, Surface, Volume, and Density	59	(4)
Relativistic Plasma Frequency	63	(8)
The General Lorentz Transform	71	(9)
Thomas Precession	80	(5)
Schwinger's Approach	85	(3)
References	88	(1)
Covariant Electrodynamics	89	(86)
Four-Vectors and Tensors	89	(4)
The Electromagnetic Field Tensor	93	(4)
Covariant Form of the Maxwell-Lorentz Equations	97	(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