Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics

Modern Classical Physics
	Cover
	Title
	Copyright
	Dedication
	CONTENTS
	List of Boxes
	Preface
	Acknowledgments
	PART I FOUNDATIONS
		1 Newtonian Physics: Geometric Viewpoint
			1.1 Introduction
				1.1.1 The Geometric Viewpoint on the Laws of Physics
				1.1.2 Purposes of This Chapter
				1.1.3 Overview of This Chapter
			1.2 Foundational Concepts
			1.3 Tensor Algebra without a Coordinate System
			1.4 Particle Kinetics and Lorentz Force in Geometric Language
			1.5 Component Representation of Tensor Algebra
				1.5.1 Slot-Naming Index Notation
				1.5.2 Particle Kinetics in Index Notation
			1.6 Orthogonal Transformations of Bases
			1.7 Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl
			1.8 Volumes, Integration, and Integral Conservation Laws
				1.8.1 Gauss’s and Stokes’ Theorems
			1.9 The Stress Tensor and Momentum Conservation
				1.9.1 Examples: Electromagnetic Field and Perfect Fluid
				1.9.2 Conservation of Momentum
			1.10 Geometrized Units and Relativistic Particles for Newtonian Readers
				1.10.1 Geometrized Units
				1.10.2 Energy and Momentum of a Moving Particle
			Bibliographic Note
		2 Special Relativity: Geometric Viewpoint
			2.1 Overview
			2.2 Foundational Concepts
				2.2.1 Inertial Frames, Inertial Coordinates, Events, Vectors, and Spacetime Diagrams
				2.2.2 The Principle of Relativity and Constancy of Light Speed
				2.2.3 The Interval and Its Invariance
			2.3 Tensor Algebra without a Coordinate System
			2.4 Particle Kinetics and Lorentz Force without a Reference Frame
				2.4.1 Relativistic Particle Kinetics: World Lines, 4-Velocity, 4-Momentum and Its Conservation, 4-Force
				2.4.2 Geometric Derivation of the Lorentz Force Law
			2.5 Component Representation of Tensor Algebra
				2.5.1 Lorentz Coordinates
				2.5.2 Index Gymnastics
				2.5.3 Slot-Naming Notation
			2.6 Particle Kinetics in Index Notation and in a Lorentz Frame
			2.7 Lorentz Transformations
			2.8 Spacetime Diagrams for Boosts
			2.9 Time Travel
				2.9.1 Measurement of Time; Twins Paradox
				2.9.2 Wormholes
				2.9.3 Wormhole as Time Machine
			2.10 Directional Derivatives, Gradients, and the Levi-Civita Tensor
			2.11 Nature of Electric and Magnetic Fields; Maxwell’s Equations
			2.12 Volumes, Integration, and Conservation Laws
				2.12.1 Spacetime Volumes and Integration
				2.12.2 Conservation of Charge in Spacetime
				2.12.3 Conservation of Particles, Baryon Number, and Rest Mass
			2.13 Stress-Energy Tensor and Conservation of 4-Momentum
				2.13.1 Stress-Energy Tensor
				2.13.2 4-Momentum Conservation
				2.13.3 Stress-Energy Tensors for Perfect Fluids and Electromagnetic Fields
			Bibliographic Note
	PART II STATISTICAL PHYSICS
		3 Kinetic Theory
			3.1 Overview
			3.2 Phase Space and Distribution Function
				3.2.1 Newtonian Number Density in Phase Space, N
				3.2.2 Relativistic Number Density in Phase Space, N
				3.2.3 Distribution Function f (x, v, t) for Particles in a Plasma
				3.2.4 Distribution Function Iv/v^3 for Photons
				3.2.5 Mean Occupation Number n
			3.3 Thermal-Equilibrium Distribution Functions
			3.4 Macroscopic Properties of Matter as Integrals over Momentum Space
				3.4.1 Particle Density n, Flux S, and Stress Tensor T
				3.4.2 Relativistic Number-Flux 4-Vector S and Stress-Energy Tensor T
			3.5 Isotropic Distribution Functions and Equations of State
				3.5.1 Newtonian Density, Pressure, Energy Density, and Equation of State
				3.5.2 Equations of State for a Nonrelativistic Hydrogen Gas
				3.5.3 Relativistic Density, Pressure, Energy Density, and Equation of State
				3.5.4 Equation of State for a Relativistic Degenerate Hydrogen Gas
				3.5.5 Equation of State for Radiation
			3.6 Evolution of the Distribution Function: Liouville’s Theorem, the Collisionless Boltzmann Equation, and the Boltzmann Transport Equation
			3.7 Transport Coefficients
				3.7.1 Diffusive Heat Conduction inside a Star
				3.7.2 Order-of-Magnitude Analysis
				3.7.3 Analysis Using the Boltzmann Transport Equation
			Bibliographic Note
		4 Statistical Mechanics
			4.1 Overview
			4.2 Systems, Ensembles, and Distribution Functions
				4.2.1 Systems
				4.2.2 Ensembles
				4.2.3 Distribution Function
			4.3 Liouville’s Theorem and the Evolution of the Distribution Function
			4.4 Statistical Equilibrium
				4.4.1 Canonical Ensemble and Distribution
				4.4.2 General Equilibrium Ensemble and Distribution; Gibbs Ensemble; Grand Canonical Ensemble
				4.4.3 Fermi-Dirac and Bose-Einstein Distributions
				4.4.4 Equipartition Theorem for Quadratic, Classical Degrees of Freedom
			4.5 The Microcanonical Ensemble
			4.6 The Ergodic Hypothesis
			4.7 Entropy and Evolution toward Statistical Equilibrium
				4.7.1 Entropy and the Second Law of Thermodynamics
				4.7.2 What Causes the Entropy to Increase?
			4.8 Entropy per Particle
			4.9 Bose-Einstein Condensate
			4.10 Statistical Mechanics in the Presence of Gravity
				4.10.1 Galaxies
				4.10.2 Black Holes
				4.10.3 The Universe
				4.10.4 Structure Formation in the Expanding Universe: Violent Relaxation and Phase Mixing
			4.11 Entropy and Information
				4.11.1 Information Gained When Measuring the State of a System in a Microcanonical Ensemble
				4.11.2 Information in Communication Theory
				4.11.3 Examples of Information Content
				4.11.4 Some Properties of Information
				4.11.5 Capacity of Communication Channels; Erasing Information from Computer Memories
			Bibliographic Note
		5 Statistical Thermodynamics
			5.1 Overview
			5.2 Microcanonical Ensemble and the Energy Representation of Thermodynamics
				5.2.1 Extensive and Intensive Variables; Fundamental Potential
				5.2.2 Energy as a Fundamental Potential
				5.2.3 Intensive Variables Identified Using Measuring Devices; First Law of Thermodynamics
				5.2.4 Euler’s Equation and Form of the Fundamental Potential
				5.2.5 Everything Deducible from First Law; Maxwell Relations
				5.2.6 Representations of Thermodynamics
			5.3 Grand Canonical Ensemble and the Grand-Potential Representation of Thermodynamics
				5.3.1 The Grand-Potential Representation, and Computation of Thermodynamic Properties as a Grand Canonical Sum
				5.3.2 Nonrelativistic van der Waals Gas
			5.4 Canonical Ensemble and the Physical-Free-Energy Representation of Thermodynamics
				5.4.1 Experimental Meaning of Physical Free Energy
				5.4.2 Ideal Gas with Internal Degrees of Freedom
			5.5 Gibbs Ensemble and Representation of Thermodynamics; Phase Transitions and Chemical Reactions
				5.5.1 Out-of-Equilibrium Ensembles and Their Fundamental Thermodynamic Potentials and Minimum Principles
				5.5.2 Phase Transitions
				5.5.3 Chemical Reactions
			5.6 Fluctuations away from Statistical Equilibrium
			5.7 Van der Waals Gas: Volume Fluctuations and Gas-to-Liquid Phase Transition
			5.8 Magnetic Materials
				5.8.1 Paramagnetism; The Curie Law
				5.8.2 Ferromagnetism: The Ising Model
				5.8.3 Renormalization Group Methods for the Ising Model
				5.8.4 Monte Carlo Methods for the Ising Model
			Bibliographic Note
		6 Random Processes
			6.1 Overview
			6.2 Fundamental Concepts
				6.2.1 Random Variables and Random Processes
				6.2.2 Probability Distributions
				6.2.3 Ergodic Hypothesis
			6.3 Markov Processes and Gaussian Processes
				6.3.1 Markov Processes; Random Walk
				6.3.2 Gaussian Processes and the Central Limit Theorem; Random Walk
				6.3.3 Doob’s Theorem for Gaussian-Markov Processes, and Brownian Motion
			6.4 Correlation Functions and Spectral Densities
				6.4.1 Correlation Functions; Proof of Doob’s Theorem
				6.4.2 Spectral Densities
				6.4.3 Physical Meaning of Spectral Density, Light Spectra, and Noise in a Gravitational Wave Detector
				6.4.4 The Wiener-Khintchine Theorem; Cosmological Density Fluctuations
			6.5 2-Dimensional Random Processes
				6.5.1 Cross Correlation and Correlation Matrix
				6.5.2 Spectral Densities and the Wiener-Khintchine Theorem
			6.6 Noise and Its Types of Spectra
				6.6.1 Shot Noise, Flicker Noise, and Random-Walk Noise; Cesium Atomic Clock
				6.6.2 Information Missing from Spectral Density
			6.7 Filtering Random Processes
				6.7.1 Filters, Their Kernels, and the Filtered Spectral Density
				6.7.2 Brownian Motion and Random Walks
				6.7.3 Extracting a Weak Signal from Noise: Band-Pass Filter, Wiener’s Optimal Filter, Signal-to-Noise Ratio, and Allan Variance of Clock Noise
				6.7.4 Shot Noise
			6.8 Fluctuation-Dissipation Theorem
				6.8.1 Elementary Version of the Fluctuation-Dissipation Theorem; Langevin Equation, Johnson Noise in a Resistor, and Relaxation Time for Brownian Motion
				6.8.2 Generalized Fluctuation-Dissipation Theorem; Thermal Noise in a Laser Beam’s Measurement of Mirror Motions; Standard Quantum Limit for Measurement Accuracy and How to Evade It
			6.9 Fokker-Planck Equation
				6.9.1 Fokker-Planck for a 1-Dimensional Markov Process
				6.9.2 Optical Molasses: Doppler Cooling of Atoms
				6.9.3 Fokker-Planck for a Multidimensional Markov Process; Thermal Noise in an Oscillator
			Bibliographic Note
	PART III OPTICS
		7 Geometric Optics
			7.1 Overview
			7.2 Waves in a Homogeneous Medium
				7.2.1 Monochromatic Plane Waves; Dispersion Relation
				7.2.2 Wave Packets
			7.3 Waves in an Inhomogeneous, Time-Varying Medium: The Eikonal Approximation and Geometric Optics
				7.3.1 Geometric Optics for a Prototypical Wave Equation
				7.3.2 Connection of Geometric Optics to Quantum Theory
				7.3.3 Geometric Optics for a General Wave
				7.3.4 Examples of Geometric-Optics Wave Propagation
				7.3.5 Relation to Wave Packets; Limitations of the Eikonal Approximation and Geometric Optics
				7.3.6 Fermat’s Principle
			7.4 Paraxial Optics
				7.4.1 Axisymmetric, Paraxial Systems: Lenses, Mirrors, Telescopes, Microscopes, and Optical Cavities
				7.4.2 Converging Magnetic Lens for Charged Particle Beam
			7.5 Catastrophe Optics
				7.5.1 Image Formation
				7.5.2 Aberrations of Optical Instruments
			7.6 Gravitational Lenses
				7.6.1 Gravitational Deflection of Light
				7.6.2 Optical Configuration
				7.6.3 Microlensing
				7.6.4 Lensing by Galaxies
			7.7 Polarization
				7.7.1 Polarization Vector and Its Geometric-Optics Propagation Law
				7.7.2 Geometric Phase
			Bibliographic Note
		8 Diffraction
			8.1 Overview
			8.2 Helmholtz-Kirchhoff Integral
				8.2.1 Diffraction by an Aperture
				8.2.2 Spreading of the Wavefront: Fresnel and Fraunhofer Regions
			8.3 Fraunhofer Diffraction
				8.3.1 Diffraction Grating
				8.3.2 Airy Pattern of a Circular Aperture: Hubble Space Telescope
				8.3.3 Babinet’s Principle
			8.4 Fresnel Diffraction
				8.4.1 Rectangular Aperture, Fresnel Integrals, and the Cornu Spiral
				8.4.2 Unobscured Plane Wave
				8.4.3 Fresnel Diffraction by a Straight Edge: Lunar Occultation of a Radio Source
				8.4.4 Circular Apertures: Fresnel Zones and Zone Plates
			8.5 Paraxial Fourier Optics
				8.5.1 Coherent Illumination
				8.5.2 Point-Spread Functions
				8.5.3 Abbé’s Description of Image Formation by a Thin Lens
				8.5.4 Image Processing by a Spatial Filter in the Focal Plane of a Lens: High-Pass, Low-Pass, and Notch Filters; Phase-Contrast Microscopy
				8.5.5 Gaussian Beams: Optical Cavities and Interferometric Gravitational-Wave Detectors
			8.6 Diffraction at a Caustic
			Bibliographic Note
		9 Interference and Coherence
			9.1 Overview
			9.2 Coherence
				9.2.1 Young’s Slits
				9.2.2 Interference with an Extended Source: Van Cittert-Zernike Theorem
				9.2.3 More General Formulation of Spatial Coherence; Lateral Coherence Length
				9.2.4 Generalization to 2 Dimensions
				9.2.5 Michelson Stellar Interferometer; Astronomical Seeing
				9.2.6 Temporal Coherence
				9.2.7 Michelson Interferometer and Fourier-Transform Spectroscopy
				9.2.8 Degree of Coherence; Relation to Theory of Random Processes
			9.3 Radio Telescopes
				9.3.1 Two-Element Radio Interferometer
				9.3.2 Multiple-Element Radio Interferometers
				9.3.3 Closure Phase
				9.3.4 Angular Resolution
			9.4 Etalons and Fabry-Perot Interferometers
				9.4.1 Multiple-Beam Interferometry; Etalons
				9.4.2 Fabry-Perot Interferometer and Modes of a Fabry-Perot Cavity with Spherical Mirrors
				9.4.3 Fabry-Perot Applications: Spectrometer, Laser, Mode-Cleaning Cavity, Beam-Shaping Cavity, PDH Laser Stabilization, Optical Frequency Comb
			9.5 Laser Interferometer Gravitational-Wave Detectors
			9.6 Power Correlations and Photon Statistics: Hanbury Brown and Twiss Intensity Interferometer
			Bibliographic Note
		10 Nonlinear Optics
			10.1 Overview
			10.2 Lasers
				10.2.1 Basic Principles of the Laser
				10.2.2 Types of Lasers and Their Performances and Applications
				10.2.3 Ti:Sapphire Mode-Locked Laser
				10.2.4 Free Electron Laser
			10.3 Holography
				10.3.1 Recording a Hologram
				10.3.2 Reconstructing the 3-Dimensional Image from a Hologram
				10.3.3 Other Types of Holography; Applications
			10.4 Phase-Conjugate Optics
			10.5 Maxwell’s Equations in a Nonlinear Medium; Nonlinear Dielectric Susceptibilities; Electro-Optic Effects
			10.6 Three-Wave Mixing in Nonlinear Crystals
				10.6.1 Resonance Conditions for Three-Wave Mixing
				10.6.2 Three-Wave-Mixing Evolution Equations in a Medium That Is Dispersion-Free and Isotropic at Linear Order
				10.6.3 Three-Wave Mixing in a Birefringent Crystal: Phase Matching and Evolution Equations
			10.7 Applications of Three-Wave Mixing: Frequency Doubling, Optical Parametric Amplification, and Squeezed Light
				10.7.1 Frequency Doubling
				10.7.2 Optical Parametric Amplification
				10.7.3 Degenerate Optical Parametric Amplification: Squeezed Light
			10.8 Four-Wave Mixing in Isotropic Media
				10.8.1 Third-Order Susceptibilities and Field Strengths
				10.8.2 Phase Conjugation via Four-Wave Mixing in CS2 Fluid
				10.8.3 Optical Kerr Effect and Four-Wave Mixing in an Optical Fiber
			Bibliographic Note
	PART IV ELASTICITY
		11 Elastostatics
			11.1 Overview
			11.2 Displacement and Strain
				11.2.1 Displacement Vector and Its Gradient
				11.2.2 Expansion, Rotation, Shear, and Strain
			11.3 Stress, Elastic Moduli, and Elastostatic Equilibrium
				11.3.1 Stress Tensor
				11.3.2 Realm of Validity for Hooke’s Law
				11.3.3 Elastic Moduli and Elastostatic Stress Tensor
				11.3.4 Energy of Deformation
				11.3.5 Thermoelasticity
				11.3.6 Molecular Origin of Elastic Stress; Estimate of Moduli
				11.3.7 Elastostatic Equilibrium: Navier-Cauchy Equation
			11.4 Young’s Modulus and Poisson’s Ratio for an Isotropic Material: A Simple Elastostatics Problem
			11.5 Reducing the Elastostatic Equations to 1 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica
			11.6 Buckling and Bifurcation of Equilibria
				11.6.1 Elementary Theory of Buckling and Bifurcation
				11.6.2 Collapse of the World Trade Center Buildings
				11.6.3 Buckling with Lateral Force; Connection to Catastrophe Theory
				11.6.4 Other Bifurcations: Venus Fly Trap, Whirling Shaft, Triaxial Stars, and Onset of Turbulence
			11.7 Reducing the Elastostatic Equations to 2 Dimensions for a Deformed Thin Plate: Stress Polishing a Telescope Mirror
			11.8 Cylindrical and Spherical Coordinates: Connection Coefficients and Components of the Gradient of the Displacement Vector
			11.9 Solving the 3-Dimensional Navier-Cauchy Equation in Cylindrical Coordinates
				11.9.1 Simple Methods: Pipe Fracture and Torsion Pendulum
				11.9.2 Separation of Variables and Green’s Functions: Thermoelastic Noise in Mirrors
			Bibliographic Note
		12 Elastodynamics
			12.1 Overview
			12.2 Basic Equations of Elastodynamics; Waves in a Homogeneous Medium
				12.2.1 Equation of Motion for a Strained Elastic Medium
				12.2.2 Elastodynamic Waves
				12.2.3 Longitudinal Sound Waves
				12.2.4 Transverse Shear Waves
				12.2.5 Energy of Elastodynamic Waves
			12.3 Waves in Rods, Strings, and Beams
				12.3.1 Compression Waves in a Rod
				12.3.2 Torsion Waves in a Rod
				12.3.3 Waves on Strings
				12.3.4 Flexural Waves on a Beam
				12.3.5 Bifurcation of Equilibria and Buckling (Once More)
			12.4 Body Waves and Surface Waves—Seismology and Ultrasound
				12.4.1 Body Waves
				12.4.2 Edge Waves
				12.4.3 Green’s Function for a Homogeneous Half-Space
				12.4.4 Free Oscillations of Solid Bodies
				12.4.5 Seismic Tomography
				12.4.6 Ultrasound; Shock Waves in Solids
			12.5 The Relationship of Classical Waves to Quantum Mechanical Excitations
			Bibliographic Note
	PART V FLUID DYNAMICS
		13 Foundations of Fluid Dynamics
			13.1 Overview
			13.2 The Macroscopic Nature of a Fluid: Density, Pressure, Flow Velocity; Liquids versus Gases
			13.3 Hydrostatics
				13.3.1 Archimedes’ Law
				13.3.2 Nonrotating Stars and Planets
				13.3.3 Rotating Fluids
			13.4 Conservation Laws
			13.5 The Dynamics of an Ideal Fluid
				13.5.1 Mass Conservation
				13.5.2 Momentum Conservation
				13.5.3 Euler Equation
				13.5.4 Bernoulli’s Theorem
				13.5.5 Conservation of Energy
			13.6 Incompressible Flows
			13.7 Viscous Flows with Heat Conduction
				13.7.1 Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear
				13.7.2 Navier-Stokes Equation
				13.7.3 Molecular Origin of Viscosity
				13.7.4 Energy Conservation and Entropy Production
				13.7.5 Reynolds Number
				13.7.6 Pipe Flow
			13.8 Relativistic Dynamics of a Perfect Fluid
				13.8.1 Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics
				13.8.2 Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets
				13.8.3 Nonrelativistic Limit of the Stress-Energy Tensor
			Bibliographic Note
		14 Vorticity
			14.1 Overview
			14.2 Vorticity, Circulation, and Their Evolution
				14.2.1 Vorticity Evolution
				14.2.2 Barotropic, Inviscid, Compressible Flows: Vortex Lines Frozen into Fluid
				14.2.3 Tornados
				14.2.4 Circulation and Kelvin’s Theorem
				14.2.5 Diffusion of Vortex Lines
				14.2.6 Sources of Vorticity
			14.3 Low-Reynolds-Number Flow—Stokes Flow and Sedimentation
				14.3.1 Motivation: Climate Change
				14.3.2 Stokes Flow
				14.3.3 Sedimentation Rate
			14.4 High-Reynolds-Number Flow—Laminar Boundary Layers
				14.4.1 Blasius Velocity Profile Near a Flat Plate: Stream Function and Similarity Solution
				14.4.2 Blasius Vorticity Profile
				14.4.3 Viscous Drag Force on a Flat Plate
				14.4.4 Boundary Layer Near a Curved Surface: Separation
			14.5 Nearly Rigidly Rotating Flows—Earth’s Atmosphere and Oceans
				14.5.1 Equations of Fluid Dynamics in a Rotating Reference Frame
				14.5.2 Geostrophic Flows
				14.5.3 Taylor-Proudman Theorem
				14.5.4 Ekman Boundary Layers
			14.6 Instabilities of Shear Flows—Billow Clouds and Turbulence in the Stratosphere
				14.6.1 Discontinuous Flow: Kelvin-Helmholtz Instability
				14.6.2 Discontinuous Flow with Gravity
				14.6.3 Smoothly Stratified Flows: Rayleigh and Richardson Criteria for Instability
			Bibliographic Note
		15 Turbulence
			15.1 Overview
			15.2 The Transition to Turbulence—Flow Past a Cylinder
			15.3 Empirical Description of Turbulence
				15.3.1 The Role of Vorticity in Turbulence
			15.4 Semiquantitative Analysis of Turbulence
				15.4.1 Weak-Turbulence Formalism
				15.4.2 Turbulent Viscosity
				15.4.3 Turbulent Wakes and Jets; Entrainment; the Coanda Effect
				15.4.4 Kolmogorov Spectrum for Fully Developed, Homogeneous, Isotropic Turbulence
			15.5 Turbulent Boundary Layers
				15.5.1 Profile of a Turbulent Boundary Layer
				15.5.2 Coanda Effect and Separation in a Turbulent Boundary Layer
				15.5.3 Instability of a Laminar Boundary Layer
				15.5.4 Flight of a Ball
			15.6 The Route to Turbulence—Onset of Chaos
				15.6.1 Rotating Couette Flow
				15.6.2 Feigenbaum Sequence, Poincaré Maps, and the Period-Doubling Route to Turbulence in Convection
				15.6.3 Other Routes to Turbulent Convection
				15.6.4 Extreme Sensitivity to Initial Conditions
			Bibliographic Note
		16 Waves
			16.1 Overview
			16.2 Gravity Waves on and beneath the Surface of a Fluid
				16.2.1 Deep-Water Waves and Their Excitation and Damping
				16.2.2 Shallow-Water Waves
				16.2.3 Capillary Waves and Surface Tension
				16.2.4 Helioseismology
			16.3 Nonlinear Shallow-Water Waves and Solitons
				16.3.1 Korteweg–de Vries (KdV) Equation
				16.3.2 Physical Effects in the KdV Equation
				16.3.3 Single-Soliton Solution
				16.3.4 Two-Soliton Solution
				16.3.5 Solitons in Contemporary Physics
			16.4 Rossby Waves in a Rotating Fluid
			16.5 Sound Waves
				16.5.1 Wave Energy
				16.5.2 Sound Generation
				16.5.3 Radiation Reaction, Runaway Solutions, and Matched Asymptotic Expansions
			Bibliographic Note
		17 Compressible and Supersonic Flow
			17.1 Overview
			17.2 Equations of Compressible Flow
			17.3 Stationary, Irrotational, Quasi-1-Dimensional Flow
				17.3.1 Basic Equations; Transition from Subsonic to Supersonic Flow
				17.3.2 Setting up a Stationary, Transonic Flow
				17.3.3 Rocket Engines
			17.4 1-Dimensional, Time-Dependent Flow
				17.4.1 Riemann Invariants
				17.4.2 Shock Tube
			17.5 Shock Fronts
				17.5.1 Junction Conditions across a Shock; Rankine-Hugoniot Relations
				17.5.2 Junction Conditions for Ideal Gas with Constant
				17.5.3 Internal Structure of a Shock
				17.5.4 Mach Cone
			17.6 Self-Similar Solutions—Sedov-Taylor Blast Wave
				17.6.1 The Sedov-Taylor Solution
				17.6.2 Atomic Bomb
				17.6.3 Supernovae
			Bibliographic Note
		18 Convection
			18.1 Overview
			18.2 Diffusive Heat Conduction—Cooling a Nuclear Reactor; Thermal Boundary Layers
			18.3 Boussinesq Approximation
			18.4 Rayleigh-Bénard Convection
			18.5 Convection in Stars
			18.6 Double Diffusion—Salt Fingers
			Bibliographic Note
		19 Magnetohydrodynamics
			19.1 Overview
			19.2 Basic Equations of MHD
				19.2.1 Maxwell’s Equations in the MHD Approximation
				19.2.2 Momentum and Energy Conservation
				19.2.3 Boundary Conditions
				19.2.4 Magnetic Field and Vorticity
			19.3 Magnetostatic Equilibria
				19.3.1 Controlled Thermonuclear Fusion
				19.3.2 Z-Pinch
				19.3.3 Θ-Pinch
				19.3.4 Tokamak
			19.4 Hydromagnetic Flows
			19.5 Stability of Magnetostatic Equilibria
				19.5.1 Linear Perturbation Theory
				19.5.2 Z-Pinch: Sausage and Kink Instabilities
				19.5.3 The Θ-Pinch and Its Toroidal Analog; Flute Instability; Motivation for Tokamak
				19.5.4 Energy Principle and Virial Theorems
			19.6 Dynamos and Reconnection of Magnetic Field Lines
				19.6.1 Cowling’s Theorem
				19.6.2 Kinematic Dynamos
				19.6.3 Magnetic Reconnection
			19.7 Magnetosonic Waves and the Scattering of Cosmic Rays
				19.7.1 Cosmic Rays
				19.7.2 Magnetosonic Dispersion Relation
				19.7.3 Scattering of Cosmic Rays by Alfvén Waves
			Bibliographic Note
	PART VI PLASMA PHYSICS
		20 The Particle Kinetics of Plasma
			20.1 Overview
			20.2 Examples of Plasmas and Their Density-Temperature Regimes
				20.2.1 Ionization Boundary
				20.2.2 Degeneracy Boundary
				20.2.3 Relativistic Boundary
				20.2.4 Pair-Production Boundary
				20.2.5 Examples of Natural and Human-Made Plasmas
			20.3 Collective Effects in Plasmas—Debye Shielding and Plasma Oscillations
				20.3.1 Debye Shielding
				20.3.2 Collective Behavior
				20.3.3 Plasma Oscillations and Plasma Frequency
			20.4 Coulomb Collisions
				20.4.1 Collision Frequency
				20.4.2 The Coulomb Logarithm
				20.4.3 Thermal Equilibration Rates in a Plasma
				20.4.4 Discussion
			20.5 Transport Coefficients
				20.5.1 Coulomb Collisions
				20.5.2 Anomalous Resistivity and Anomalous Equilibration
			20.6 Magnetic Field
				20.6.1 Cyclotron Frequency and Larmor Radius
				20.6.2 Validity of the Fluid Approximation
				20.6.3 Conductivity Tensor
			20.7 Particle Motion and Adiabatic Invariants
				20.7.1 Homogeneous, Time-Independent Magnetic Field and No Electric Field
				20.7.2 Homogeneous, Time-Independent Electric and Magnetic Fields
				20.7.3 Inhomogeneous, Time-Independent Magnetic Field
				20.7.4 A Slowly Time-Varying Magnetic Field
				20.7.5 Failure of Adiabatic Invariants; Chaotic Orbits
			Bibliographic Note
		21 Waves in Cold Plasmas: Two-Fluid Formalism
			21.1 Overview
			21.2 Dielectric Tensor, Wave Equation, and General Dispersion Relation
			21.3 Two-Fluid Formalism
			21.4 Wave Modes in an Unmagnetized Plasma
				21.4.1 Dielectric Tensor and Dispersion Relation for a Cold, Unmagnetized Plasma
				21.4.2 Plasma Electromagnetic Modes
				21.4.3 Langmuir Waves and Ion-Acoustic Waves in Warm Plasmas
				21.4.4 Cutoffs and Resonances
			21.5 Wave Modes in a Cold, Magnetized Plasma
				21.5.1 Dielectric Tensor and Dispersion Relation
				21.5.2 Parallel Propagation
				21.5.3 Perpendicular Propagation
				21.5.4 Propagation of Radio Waves in the Ionosphere; Magnetoionic Theory
				21.5.5 CMA Diagram for Wave Modes in a Cold, Magnetized Plasma
			21.6 Two-Stream Instability
			Bibliographic Note
		22 Kinetic Theory of Warm Plasmas
			22.1 Overview
			22.2 Basic Concepts of Kinetic Theory and Its Relationship to Two-Fluid Theory
				22.2.1 Distribution Function and Vlasov Equation
				22.2.2 Relation of Kinetic Theory to Two-Fluid Theory
				22.2.3 Jeans’ Theorem
			22.3 Electrostatic Waves in an Unmagnetized Plasma: Landau Damping
				22.3.1 Formal Dispersion Relation
				22.3.2 Two-Stream Instability
				22.3.3 The Landau Contour
				22.3.4 Dispersion Relation for Weakly Damped or Growing Waves
				22.3.5 Langmuir Waves and Their Landau Damping
				22.3.6 Ion-Acoustic Waves and Conditions for Their Landau Damping to Be Weak
			22.4 Stability of Electrostatic Waves in Unmagnetized Plasmas
				22.4.1 Nyquist’s Method
				22.4.2 Penrose’s Instability Criterion
			22.5 Particle Trapping
			22.6 N-Particle Distribution Function
				22.6.1 BBGKY Hierarchy
				22.6.2 Two-Point Correlation Function
				22.6.3 Coulomb Correction to Plasma Pressure
			Bibliographic Note
		23 Nonlinear Dynamics of Plasmas
			23.1 Overview
			23.2 Quasilinear Theory in Classical Language
				23.2.1 Classical Derivation of the Theory
				23.2.2 Summary of Quasilinear Theory
				23.2.3 Conservation Laws
				23.2.4 Generalization to 3 Dimensions
			23.3 Quasilinear Theory in Quantum Mechanical Language
				23.3.1 Plasmon Occupation Number n
				23.3.2 Evolution of n for Plasmons via Interaction with Electrons
				23.3.3 Evolution of f for Electrons via Interaction with Plasmons
				23.3.4 Emission of Plasmons by Particles in the Presence of a Magnetic Field
				23.3.5 Relationship between Classical and Quantum Mechanical Formalisms
				23.3.6 Evolution of n via Three-Wave Mixing
			23.4 Quasilinear Evolution of Unstable Distribution Functions—A Bump in the Tail
				23.4.1 Instability of Streaming Cosmic Rays
			23.5 Parametric Instabilities; Laser Fusion
			23.6 Solitons and Collisionless Shock Waves
			Bibliographic Note
	PART VII GENERAL RELATIVITY
		24 From Special to General Relativity
			24.1 Overview
			24.2 Special Relativity Once Again
				24.2.1 Geometric, Frame-Independent Formulation
				24.2.2 Inertial Frames and Components of Vectors, Tensors, and Physical Laws
				24.2.3 Light Speed, the Interval, and Spacetime Diagrams
			24.3 Differential Geometry in General Bases and in Curved Manifolds
				24.3.1 Nonorthonormal Bases
				24.3.2 Vectors as Directional Derivatives; Tangent Space; Commutators
				24.3.3 Differentiation of Vectors and Tensors; Connection Coefficients
				24.3.4 Integration
			24.4 The Stress-Energy Tensor Revisited
			24.5 The Proper Reference Frame of an Accelerated Observer
				24.5.1 Relation to Inertial Coordinates; Metric in Proper Reference Frame; Transport Law for Rotating Vectors
				24.5.2 Geodesic Equation for a Freely Falling Particle
				24.5.3 Uniformly Accelerated Observer
				24.5.4 Rindler Coordinates for Minkowski Spacetime
			Bibliographic Note
		25 Fundamental Concepts of General Relativity
			25.1 History and Overview
			25.2 Local Lorentz Frames, the Principle of Relativity, and Einstein’s Equivalence Principle
			25.3 The Spacetime Metric, and Gravity as a Curvature of Spacetime
			25.4 Free-Fall Motion and Geodesics of Spacetime
			25.5 Relative Acceleration, Tidal Gravity, and Spacetime Curvature
				25.5.1 Newtonian Description of Tidal Gravity
				25.5.2 Relativistic Description of Tidal Gravity
				25.5.3 Comparison of Newtonian and Relativistic Descriptions
			25.6 Properties of the Riemann Curvature Tensor
			25.7 Delicacies in the Equivalence Principle, and Some Nongravitational Laws of Physics in Curved Spacetime
			25.7.1 Curvature Coupling in the Nongravitational Laws
			25.8 The Einstein Field Equation
				25.8.1 Geometrized Units
			25.9 Weak Gravitational Fields
				25.9.1 Newtonian Limit of General Relativity
				25.9.2 Linearized Theory
				25.9.3 Gravitational Field outside a Stationary, Linearized Source of Gravity
				25.9.4 Conservation Laws for Mass, Momentum, and Angular Momentum in Linearized Theory
				25.9.5 Conservation Laws for a Strong-Gravity Source
			Bibliographic Note
		26 Relativistic Stars and Black Holes
			26.1 Overview
			26.2 Schwarzschild’s Spacetime Geometry
				26.2.1 The Schwarzschild Metric, Its Connection Coefficients, and Its Curvature Tensors
				26.2.2 The Nature of Schwarzschild’s Coordinate System, and Symmetries of the Schwarzschild Spacetime
				26.2.3 Schwarzschild Spacetime at Radii r » M: The Asymptotically Flat Region
				26.2.4 Schwarzschild Spacetime at r ~ M
			26.3 Static Stars
				26.3.1 Birkhoff’s Theorem
				26.3.2 Stellar Interior
				26.3.3 Local Conservation of Energy and Momentum
				26.3.4 The Einstein Field Equation
				26.3.5 Stellar Models and Their Properties
				26.3.6 Embedding Diagrams
			26.4 Gravitational Implosion of a Star to Form a Black Hole
				26.4.1 The Implosion Analyzed in Schwarzschild Coordinates
				26.4.2 Tidal Forces at the Gravitational Radius
				26.4.3 Stellar Implosion in Eddington-Finkelstein Coordinates
				26.4.4 Tidal Forces at r = 0—The Central Singularity
				26.4.5 Schwarzschild Black Hole
			26.5 Spinning Black Holes: The Kerr Spacetime
				26.5.1 The Kerr Metric for a Spinning Black Hole
				26.5.2 Dragging of Inertial Frames
				26.5.3 The Light-Cone Structure, and the Horizon
				26.5.4 Evolution of Black Holes—Rotational Energy and Its Extraction
			26.6 The Many-Fingered Nature of Time
			Bibliographic Note
		27 Gravitational Waves and Experimental Tests of General Relativity
			27.1 Overview
			27.2 Experimental Tests of General Relativity
				27.2.1 Equivalence Principle, Gravitational Redshift, and Global Positioning System
				27.2.2 Perihelion Advance of Mercury
				27.2.3 Gravitational Deflection of Light, Fermat’s Principle, and Gravitational Lenses
				27.2.4 Shapiro Time Delay
				27.2.5 Geodetic and Lense-Thirring Precession
				27.2.6 Gravitational Radiation Reaction
			27.3 Gravitational Waves Propagating through Flat Spacetime
				27.3.1 Weak, Plane Waves in Linearized Theory
				27.3.2 Measuring a Gravitational Wave by Its Tidal Forces
				27.3.3 Gravitons and Their Spin and Rest Mass
			27.4 Gravitational Waves Propagating through Curved Spacetime
				27.4.1 Gravitational Wave Equation in Curved Spacetime
				27.4.2 Geometric-Optics Propagation of Gravitational Waves
				27.4.3 Energy and Momentum in Gravitational Waves
			27.5 The Generation of Gravitational Waves
				27.5.1 Multipole-Moment Expansion
				27.5.2 Quadrupole-Moment Formalism
				27.5.3 Quadrupolar Wave Strength, Energy, Angular Momentum, and Radiation Reaction
				27.5.4 Gravitational Waves from a Binary Star System
				27.5.5 Gravitational Waves from Binaries Made of Black Holes, Neutron Stars, or Both: Numerical Relativity
			27.6 The Detection of Gravitational Waves
				27.6.1 Frequency Bands and Detection Techniques
				27.6.2 Gravitational-Wave Interferometers: Overview and Elementary Treatment
				27.6.3 Interferometer Analyzed in TT Gauge
				27.6.4 Interferometer Analyzed in the Proper Reference Frame of the Beam Splitter
				27.6.5 Realistic Interferometers
				27.6.6 Pulsar Timing Arrays
			Bibliographic Note
		28 Cosmology
			28.1 Overview
			28.2 General Relativistic Cosmology
				28.2.1 Isotropy and Homogeneity
				28.2.2 Geometry
				28.2.3 Kinematics
				28.2.4 Dynamics
			28.3 The Universe Today
				28.3.1 Baryons
				28.3.2 Dark Matter
				28.3.3 Photons
				28.3.4 Neutrinos
				28.3.5 Cosmological Constant
				28.3.6 Standard Cosmology
			28.4 Seven Ages of the Universe
				28.4.1 Particle Age
				28.4.2 Nuclear Age
				28.4.3 Photon Age
				28.4.4 Plasma Age
				28.4.5 Atomic Age
				28.4.6 Gravitational Age
				28.4.7 Cosmological Age
			28.5 Galaxy Formation
				28.5.1 Linear Perturbations
				28.5.2 Individual Constituents
				28.5.3 Solution of the Perturbation Equations
				28.5.4 Galaxies
			28.6 Cosmological Optics
				28.6.1 Cosmic Microwave Background
				28.6.2 Weak Gravitational Lensing
				28.6.3 Sunyaev-Zel’dovich Effect
			28.7 Three Mysteries
				28.7.1 Inflation and the Origin of the Universe
				28.7.2 Dark Matter and the Growth of Structure
				28.7.3 The Cosmological Constant and the Fate of the Universe
			Bibliographic Note
	References
	Name Index
	Subject Index
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