Modern Problems in Classical Electrodynamics

Designed as an upper-level undergraduate/beginning graduate text and as a reference for research scientists, Modern Problems in Classical Electrodynamics addresses a wide range of topics in modern physics--including lasers and nonlinear optics--that are not found in other texts. The book begins with relativistic mechanics and field theory, partly because they lend unity and beauty to electrodynamics, and also because relativistic concepts appear frequently throughout the book. Electrostatics and magnetostatics, waves, continuous media, nonlinear optics, diffraction, and radiation by moving particles are then covered in depth. The book concludes by returning to basics, discussing the fundamental problems inherent in the classical theory of electrons. Modern Problems in Classical Electrodynamics features examples and homework exercises drawn from condensed-matter physics, particle physics, optics, and atomic physics. Many of these are experimentally oriented and help to make the book interesting and relevant to a broad audience. An instructor's manual including answers to the homework exercises is available to adopters. An accompanying website, http://www.physics.vanderbilt.edu/brau/book/Index.html, contains errata and additional homework exercises that instructors can use to supplement the exercises in the text.

Table of Contents:
Preface 0 Prologue 0.1: Introduction 0.2: Electrostatics 0.2.1: Charges 0.2.2: Forces and Electric Fields 0.3: Magnetostatics 0.3.1: Currents 0.3.2: Forces and Fields 0.3.3: Vector Potential 0.4: Electrodynamics 0.4.1: Conservation of Charge 0.4.2: Faraday's Law 0.4.3: Energy in the Magnetic Field 0.5: The Maxwell Equations and Electromagnetic Waves 0.5.1: The Maxwell--Ampere Law 0.5.2: Electromagnetic Waves 0.5.3: Potentials and Gauges 0.6: Conservation Laws 0.6.1: Poynting's Theorem 0.6.2: Conservation of Momentum 1. Relativistic Kinematics 1.1: The Principles of Special Relativity 1.1.1: Historical Overview 1.1.2: Einstein's Postulate 1.1.3: Intervals 1.1.4: Proper Time 1.2: The Lorentz Transformation 1.2.1: Rotation in 4-Spave 1.2.2: Time Dilation and Length Contraction 1.2.3: Velocity Transformation 1.3: 4-Vectors and 4-Tensors 1.3.1: Cartesian Tensors 1.3.2: Relativistic Metric and Lorentz Transformation 1.3.3: 4-Vector Calculus 1.4: Electromagnetic Fields 1.4.1: The 4-Tensor Electromagnetic Field 1.4.2: Transformation of Electromagnetic Fields 2. Relativistic Mechanics and Field Theory 2.1: Relativistic Free Particle 2.1.1: Hamilton's Principle and the Calculus of Variations 2.1.2: Langrangian for a Free Particle 2.1.3: Energy and Momentum 2.1.4: de Broglie Waves 2.1.5: Rotational Invariance and Angular Momentum 2.2: Charged Particle in a Vector Potential 2.2.1: Langrangian Mechanics 2.2.2: Canonical Momentum 2.2.3: Canonical Equations of Motion 2.3: The Maxwell Equations 2.3.1: Equations of Motion of a Vector Field 2.3.2: Proca Mass Term 2.4: Invariance and Conservation Laws 2.4.1: Gauge Transformations 2.4.2: Symmetric Stress Tensor for the Electromagnetic Field 3. Time-Independent Electromagnetic Fields 3.1: Electrostatics 3.1.1: Coulomb's Law 3.1.2: Energy in Electrostatic Fields 3.1.3: Multipole Moments 3.2: Boundary-Value Problems with Conductors 3.2.1: Boundary Conditions and Uniqueness Theorems 3.2.2: Energy and Capacitance 3.2.3: Method of Images 3.2.4: Separation of Variables 3.2.5: Spheroidal Coordinates 3.2.6: Spherical Harmonics 3.2.7: Variational Methods 3.2.8: Numerical Methods 3.2.9: Green Functions 3.3: Magnetostatics 3.3.1: Biot-Savart Law 3.3.2: Forces and Energy 3.3.3: Multipole Moments 3.3.4: Magnetic Scalar Potential 4. Electromagnetic Waves 4.1: Plane Waves 4.1.1: Electric and Magnetic Fields in Plane Waves 4.1.2: Charged Particle in a Plane Wave 4.2: Canonical Equations of an Electromagnetic Field 4.2.1: Fourier Decomposition of the Field 4.2.2: Spontaneous Emission by a Harmonic Oscillator 4.2.3: Canonical Equations of the Electromagnetic Field 4.2.4: Blackbody Radiation and the Einstein Coefficients 4.3: Waves in Plasmas 4.3.1: Transverse Electromagnetic Waves 4.3.2: Longitudinal Electrostatic Waves 5. Fourier Techniques and Virtual Quanta 5.1: Fourier Transformation 5.1.1: Fourier's Theorem 5.1.2: Asymptotic Behavior of Fourier Transforms 5.1.3: -Functions 5.1.4: Autocorrelation Functions and the Wiener-Khintchine Theorem 5.1.5: Pulse Compression 5.2: Method of Virtual Quanta 5.2.1: Fourier Decomposition of the Field of a Relativistic Charge 5.2.2: Bremsstrahlung 5.2.3: Excitation by a Fast Charged Particle 5.2.4: Transition Radiation 6. Macroscopic Materials 6.1: Polarization and Magnetization 6.1.1: The Macroscopic Form of the Maxwell Equations 6.1.2: The Constitutive Relations 6.1.3: Boundary Conditions 6.1.4: Magnetic Scalar Potentia 6.1.5: Conservation of Energy, and Poynting's Theorem 6.2: Properties of Dielectric and Magnetic Materials 6.2.1: Dielectric Materials 6.2.2: Magnetic Materials 7. Linear, Dispersive Media 7.1: Linear Media 7.1.1: Waves in a Nondispersive Medium 7.1.2: Constitutive Relations in Dispersive Media 7.1.3: Kramers-Kronig Relations 7.1.4: Plane Waves in Dispersive Media 7.1.5: Phase Velocity and Group Velocity 7.1.6: Conservation of Energy in Dispersive Media 7.1.7: Lorentz-Drude Model 7.2: Reflection and Refraction at Surfaces 7.2.1: Boundary Conditions 7.2.2: Dielectric Reflection 7.2.3: Metallic Reflection 7.2.4: Surface Waves 7.3: Energy Loss by Fast Particles Traveling Through Matter 7.3.1: Ionization and Excitation 7.3.2: Relativistic Limit and the Density Effect 8. Nonlinear Optics 8.1: Nonlinear Susceptibility 8.1.1: Nonlinear Polarization 8.1.2: Anisotropic Materials 8.2: Multiphoton Processes 8.2.1: Coupled-Wave Equation 8.2.2: Second-Harmonic Generation 8.2.3: Sum-Frequency Generation 8.3: Nonlinear Index of Refraction 8.3.1: Third-Order Susceptibility 8.3.2: Wave Equation with a Nonlinear Index of Refraction 8.3.3: Phase-Conjugate Reflection 8.4: Raman Processes 8.4.1: Raman Scattering 8.4.2: Coherent Raman Amplification 9. Diffraction 9.1: Geometrical Optics 9.1.1: Eikonal Approximation 9.1.2: Rays in Geometrical Optics 9.1.3: Integral Theorems 9.2: Gaussian Optics and Laser Resonators 9.2.1: Paraxial Approximation 9.2.2: Laser Resonators and Mode Spacing 9.2.3: Transverse Modes and Resonator Stability 9.3: Diffraction 9.3.1: Scalar Diffraction Theory 9.3.2: Fraunhofer Diffraction (Far Field) 9.3.3: Fresnel Diffraction (Near Field) 10. Radiation by Relativistic Particles 10.1: Angular and Spectral Distribution of Radiation 10.1.1: Fourier Decomposition of the Fields 10.1.2: Retarded Fields and Lienard-Wiechert Fields 10.1.3: Multipole Radiation 10.1.4: Spectral Distribution of Radiation from a Point Charge 10.1.5: Angular Distribution of Radiation from a Point Charge 10.1.6: Total Power Radiated by a Point Charge 10.2: Bremsstrahlung and Transition Radiation 10.2.1: Bremsstrahlung 10.2.2: Transition Raidiation 10.3: Thomson Scattering 10.3.1: Linear Thomson Scattering 10.3.2: Nonlinear Thomson Scattering 10.4: Synchrotron Radiation and Undulator Radiation 10.4.1: Synchrotron Radiation 10.4.2: Undulator Radiation 10.5: Coherent Emission from Multiple Particles 10.5.1: Coherence and Form Factor 10.5.2: Coherent Radiative Processes 10.6: Radiation from Relativistic Particles Traveling Through Matter 10.6.1: Angular Spectral Fluence 10.6.2: Cherenkov Radiation 11. Fundamental Particles in Classical Electrodynamics 11.1: Electromagnetic Mass and the Radiation Reaction 11.1.1: Difficulties in the Classical Theory 11.1.2: The 4/3 Problem and Poincaré Stresses 11.1.3: Point Particles and the Radiation Reaction 11.1.4: Extended Particles 11.2: Magnetic Monopoles 11.2.1: The Maxwell Equations 11.2.2: Magnetic Monopoles and Charge Quantization 11.3: Spin 11.3.1: Relativistic Equations of Motion 11.3.2: Thomas Precession and Spin-Orbit Coupling Appendix: Units and Dimensions A.1: Arbitrariness A.2: SI Units A.3: Gaussian Units A.4: Conversion of Formulas Between SI and Gaussian Units Index

About the Author :
Charles A. Brau received his B.A. in Engineering from Cornell University and his M.A. (in Engineering) and Ph.D. in Applied Physics from Harvard University. In the course of his career, he has been a theorist, an experimenter, a manager, and currently a professor of physics at the Vanderbilt University in Nashville, Tennessee. He focuses his research on free-electron lasers (FEL) and electron beams. He became a program manager of the FEL program at Los Alamos National Laboratory and then a director of the FEL Center at Vanderbilt University. In 1988 he was a visiting scientist in the Department of Nuclear Physics at the University of Oxford in England. He is an author of 7 patents and numerous publications, including 2 books. He is also a fellow of American Physical Society.