Foundations of high-energy-density physics : physical processes of matter at extreme conditions

High-energy-density physics explores the dynamics of matter at extreme conditions. This encompasses temperatures and densities far greater than we experience on Earth. It applies to normal stars, exploding stars, active galaxies, and planetary interiors. High-energy-density matter is found on Earth in the explosion of nuclear weapons and in laboratories with high-powered lasers or pulsed-power machines. The physics explored in this book is the basis for large-scale simulation codes needed to interpret experimental results whether from astrophysical observations or laboratory-scale experiments. The key elements of high-energy-density physics covered are gas dynamics, ionization, thermal energy transport, and radiation transfer, intense electromagnetic waves, and their dynamical coupling. Implicit in this is a fundamental understanding of hydrodynamics, plasma physics, atomic physics, quantum mechanics, and electromagnetic theory. Beginning with a summary of the topics and exploring the major ones in depth, this book is a valuable resource for research scientists and graduate students in physics and astrophysics. Contents Preface 1 Introduction 1.1 High-Energy-Density on Earth 1.2 Some Connections to Prior Work 1.3 Outline 1.4 Notation, Variables, and Units 2 Characteristics of High-Energy-Density Matter 2.1 Landscape of High-Energy-Density Matter 2.2 Compressing Atoms 2.3 Electron Degeneracy 2.4 Equation of State 2.5 Collisionality and Equilibrium 2.6 Radiation 2.7 Magnetic Fields 2.8 Warm Dense Matter 2.9 Scaling from Astrophysics to the Terrestrial Laboratory 3 Fundamental Microphysics of Ionized Gases 3.1 Kinetic Theory 3.1.1 The Distribution Function 3.1.2 Evaluation of the Collision Term 3.1.3 Boltzmann’s H-Theorem 3.1.4 The Maxwell-Boltzmann Distribution Function 3.2 Statistical Mechanics 3.2.1 The Distribution Functions 3.2.2 The Maxwell-Boltzmann Distribution Function (Again) 3.3 Thermodynamics 3.3.1 First Law of Thermodynamics 3.3.2 Second Law of Thermodynamics 3.3.3 Helmholtz Free Energy 3.3.4 Maxwell’s Relations and Thermodynamic Consistency 3.4 The Fermi Gas 3.4.1 The Chemical Potential 3.4.2 The Grand Canonical Ensemble 3.5 Debye Shielding and Quasineutrality 3.6 Fluid Conservation Equations 3.7 Electron Plasma Frequency and Plasma Waves 3.8 Coulomb Collisions 3.8.1 The Scattering Angle 3.8.2 Scattering Cross Section 3.8.3 Energy Loss 3.8.4 Coulomb Logarithm 3.9 Multiple Coulomb Scattering 3.9.1 Velocity Decrements and Diffusion 3.9.2 Relaxation Times 3.10 Radiation as a Fluid 3.10.1 Planck’s Law 3.10.2 Stefan’s Law 3.10.3 Thermodynamics of Equilibrium Radiation 3.11 One-Electron Atom 3.11.1 Bohr’s Hypothesis 3.11.2 Bohr-Sommerfeld Quantization 3.11.3 Quantum Theory of Atomic Structure 3.12 Plane Electromagnetic Waves 3.12.1 Plane Electromagnetic Waves in a Good Conductor 3.12.2 Field Energy in a Dispersive Medium 3.13 Permittivity and Electrical Conductivity 4 Ionization 4.1 Saha 4.2 Thomas-Fermi 4.3 Pressure Ionization and Continuum Lowering 4.3.1 Debye-Hückel 4.3.2 Ion-Sphere 4.3.3 Stewart-Pyatt 4.3.4 Ecker-Kröll 4.4 Collisional-Radiative 4.5 Screened Hydrogenic Average-Atom 4.6 Time-Dependent Non-LTE Average-Atom 4.6.1 Population Rate Equations 4.6.2 Steady-State Non-LTE 4.6.3 Dielectronic Recombination 4.6.4 Reconstruction of Ionic States 4.7 Other Models 5 Entropy and the Equation of State 5.1 Two-Temperature Thermodynamics 5.2 Perfect Gas 5.3 Realistic Gas 5.4 Debye-Hückel 5.4.1 Thermodynamic Properties 5.4.2 Nonequilibrium Debye-Hückel 5.4.3 Density Fluctuations 5.5 Strongly Coupled Plasma 5.5.1 Static Properties 5.5.2 Scattering Experiments 5.5.3 Dynamic Properties 5.5.4 Thermodynamic Properties 5.5.5 Ornstein-Zernike 5.5.6 Hypernetted-Chain 5.5.7 One-Component Plasma (OCP) 5.6 Thomas-Fermi 5.7 Density Functional Theory 5.8 Solids 5.8.1 Debye Model 5.8.2 Mie-Grüneisen Model 5.8.3 Lindemann Melt Law 5.9 Quotidian Equation of State (QEOS) 5.9.1 Electronic EOS 5.9.2 Chemical Bonding Correction 5.9.3 Ionic EOS 5.10 Screened Hydrogenic Average-Atom 5.11 Tabular EOS 6 Hydrodynamics 6.1 Frames of Reference 6.1.1 Eulerian and Lagrangean Derivatives 6.1.2 Reynolds Transport Theorem 6.2 Conservation Equations for Ideal Fluids 6.2.1 The Equation of Continuity 6.2.2 The Equation of Momentum 6.2.3 The Equations of Energy 6.2.4 Bernoulli’s Equation 6.2.5 Vorticity 6.3 Method of Characteristics 6.3.1 Isothermal Expansion 6.3.2 Adiabatic Expansion 6.4 Acoustic Disturbances 6.5 Shocks 6.5.1 Nonlinear Acoustic Waves 6.5.2 Rankine-Hugoniot Equations 6.5.3 Jump Relations in a Polytropic Gas 6.5.4 The Shock Tube 6.5.5 Shock Reflection 6.5.6 Multiple Shock Reflections 6.5.7 Shocks Moving from Heavy into Light Media 6.5.8 Sedov-Taylor Blast Wave 6.6 Viscous and Heat Conducting Fluids 6.6.1 Damping of an Acoustic Wave 6.6.2 Structure of the Shock Front 6.6.3 The Relaxation Layer 6.7 Elastic-Plastic Behavior of Solids 6.7.1 Hooke’s Law 6.7.2 Homogeneous Deformations 6.7.3 Thermal Deformations 6.7.4 Elastic Deformations 6.7.5 Plastic Flow 6.7.6 Yield Strength 6.8 Transitioning from Planar to Elliptical Flow 6.9 Fluid Instabilities 6.9.1 Rayleigh-Taylor 6.9.2 Kelvin-Helmholtz 6.9.3 Richtmyer-Meshkov 7 Thermal Energy Transport 7.1 Linear Heat Conduction 7.2 Nonlinear Heat Conduction 7.3 The Heat Flux 7.4 Thermal and Electrical Conductivities 7.4.1 Onsager Relations 7.4.2 Transport Coefficients 7.4.3 Relaxation Times 7.4.4 Electron-Ion Coulomb Logarithm 7.5 Electron-Ion Energy Exchange 7.6 Electron Degeneracy Effects 7.7 Inhibited Thermal Transport 7.8 Nonlocal Heat Transport 8 Radiation and Radiative Transfer 8.1 The Radiation Field 8.1.1 Specific Intensity 8.1.2 Radiation Energy Density and Mean Intensity 8.1.3 Radiation Flux and Momentum Density 8.1.4 Radiation Pressure Tensor 8.2 Interaction of the Radiation Field with Matter 8.2.1 Absorption 8.2.2 Emission 8.2.3 Kirchhoff’s Law 8.2.4 Scattering 8.2.5 Stimulated Emission 8.3 The Equation of Transfer 8.3.1 Boundary Conditions on the Transfer Equation 8.3.2 Equation of Transfer in Various Coordinate Systems 8.4 Moments of the Transfer Equation 8.5 Optical Depth 8.6 Approximate Descriptions of the Radiative Transfer Equation 8.6.1 Free-Streaming Approximation 8.6.2 Diffusion Approximation 8.6.3 Telegrapher’s Equation 8.6.4 Eddington’s Approximation 8.6.5 Equilibrium Diffusion 8.6.6 Higher-Order Approximations 8.6.7 Multigroup Approximation 8.7 Opacity Averaging 8.8 Steady-State Transfer 8.8.1 Formal Solution 8.8.2 Slab Geometry 8.8.3 Milne’s Equation 8.8.4 Eddington-Barbier Relation 8.9 The Comoving Frame Representation 8.9.1 Doppler and Aberration Transformations 8.9.2 Transforming the Specific Intensity, Emissivity, and Absorptivity 8.9.3 Transforming the Transfer Equation 8.9.4 Transforming the Moment Equations 8.9.5 Comoving-Frame Transfer Equation 8.9.6 Comoving-Frame Moment Equations 8.9.7 Transforming the Radiation-Matter Coupling Terms 8.9.8 Diffusion in the Comoving Frame 8.10 View Factors 9 Transition Rates and Optical Coefficients 9.1 Radiative Transitions 9.1.1 Einstein Relations 9.1.2 Bound-Bound Optical Coefficients 9.1.3 Quantum Mechanics of Radiative Processes 9.1.4 Einstein-Milne Relations 9.1.5 Bound-Free Optical Coefficients 9.1.6 Free-Free Optical Coefficients 9.1.7 Thomson Scattering 9.1.8 Maximum Opacity Theorem 9.2 Collisional Transitions 9.2.1 Excitation and De-excitation 9.2.2 Ionization and Three-Body Recombination 10 Radiation Hydrodynamics 10.1 Incorporating Radiation in Euler’s Equations 10.1.1 Fixed-Frame Equations 10.1.2 Comoving-Frame Equation 10.1.3 Consistency of the Equations in Both Coordinate Frames 10.1.4 Equilibrium Diffusion 10.1.5 Nonequilibrium Diffusion 10.1.6 Flux Limiting 10.2 Thermodynamic Relations in the Presence of Radiation 10.2.1 Equilibrium Radiation and a Perfect Gas 10.2.2 Equilibrium Radiation and an Ionizing Gas 10.3 Marshak Waves 10.4 Radiating Shock Waves 10.4.1 Radiative Precursors 10.4.2 Rankine-Hugoniot Relations and Jump Conditions 10.4.3 Fluid Dynamics of Radiating Shocks 10.4.4 Radiative Cooling of a Thin Layer 10.4.5 Shocks in Optically Thin Material 10.4.6 Optically Thick Shocks in the Flux Regime 10.4.7 Shocks in Optically Thin Upstream Material 10.4.8 Radiation-Dominated Shock Waves 10.5 Shock Structure 10.5.1 Subcritical 10.5.2 Supercritical 10.6 Ionization Fronts 11 Magnetohydrodynamics 11.1 Plasma Electrodynamics 11.2 Equations of Magnetohydrodynamics 11.2.1 Momentum Equation 11.2.2 Induction Equation 11.2.3 Electron Thermal Equation 11.2.4 Electron Degeneracy 11.2.5 Ion Thermal Equation 11.2.6 Bohm Diffusion 11.2.7 High-Frequency Plasma Oscillations 11.2.8 Magnetic Energy 11.2.9 Generalized Ohm’s Law 11.2.10 Hall Effect 11.2.11 One-Dimensional Cylindrically Symmetric Equations 11.3 Magnetic Reconnection 11.3.1 Biermann Battery 11.3.2 Sweet-Parker Reconnection 11.3.3 Hall MHD Reconnection 11.3.4 Plasmoid Formation 11.4 Magnetic Confinement 12 Electromagnetic Wav-Material Interactions 12.1 Electromagnetic Wave Propagation in Homogeneous Medium 12.1.1 Interaction of Free Electrons with an Electromagnetic Wave 12.1.2 Longitudinal Waves and Spatial Dispersion 12.2 Propagation in Inhomogeneous Isotropic Medium 12.2.1 Exact Solution in a Linear Density Gradient 12.2.2 Reflectivity and Phase Shift 12.2.3 Geometrical Optics Approximation 12.2.4 Weak Reflection 12.2.5 Oblique Incidence 12.2.6 Ponderomotive Force and Momentum Deposition 12.2.7 Ray-Trace “Equation of Motion” 12.3 Reflection at an Interface 12.4 Density Profile Modification 12.5 Absorption of Electromagnetic Energy 12.5.1 Collisional (Inverse Bremsstrahlung) 12.5.2 Nonlinear Inverse Bremsstrahlung 12.5.3 Resonance 12.6 Dielectric Permittivity (Revisited) 12.6.1 Plasma Conductivity 12.6.2 Near-Free Electron Metals 12.7 Kinetic Instabilities 12.7.1 Matching Conditions 12.7.2 Damping 12.7.3 Instability Threshold 12.7.4 Parametric Decay and Two-Stream Instabilities 12.7.5 Stimulated Raman Scattering 12.7.6 Two-Plasmon Decay 12.7.7 Stimulated Brillouin Scattering 12.7.8 Nonlinear Aspects 12.8 Magnetic Fields 12.8.1 Spontaneous Generation of Magnetic Fields 12.8.2 Faraday Rotation 12.9 Relativistic Considerations 12.9.1 Electromagnetic Wave Propagation 12.9.2 Interaction with Transparent Matter 12.9.3 Nonlinear Dynamics at the Vacuum Boundary References Index Introduction -- Characteristics Of High-energy-density Matter -- Fundamental Microphysics Of Ionized Gases -- Ionization -- Entropy And The Equation Of State -- Hydrodynamics -- Thermal Energy Transport -- Radiation And Radiative Transfer -- Transition Rates And Optical Coefficients -- Radiation Hydrodynamics -- Magnetohydrodynamics -- Electromagnetic Wave-material Interactions. Jon Larsen, Cascade Applied Sciences Inc., Colorado. Includes Bibliographical References (pages 726-732) And Index. A valuable and complete resource that brings together many of the branches of physics needed in high-energy-density physics. Targeted at research scientists and graduate students in physics and astrophysics, this book begins with basic concepts and develops a detailed explanation of the physics of hydrodynamics and energy transport in plasma.