Statistical Physics of Dense Plasmas

Setsuo Ichimaru is Professor Emeritus at the University of Tokyo, where he was a faculty member for nearly fifty years. He earned his doctorate in physics from the University of Illinois at Urbana-Champaign. He is a world renowned expert in the area of statistical physics of plasmas, and was the 2014 recipient of the Subramanyan Chandrasekhar Prize of Plasma Physics from the Association of Asia-Pacific Physical Societies. He was also awarded the Humboldt-Forschungspreis prize from Alexander von Humboldt-Stiftung. He was a visiting member at The Institute for Advanced Study in Princeton, New Jersey, a Visiting Professor in the Department of Physics and Astronomy at the University of California, San Diego, and a guest professor at the Institute for Theoretical Physics at Johannes Kepler University, and the Max Planck Institute for Quantum Optics.

• CONTENTSPreface xi1 Introduction 11.1 Dense Plasmas in Nature 11.1.1 Astrophysical Dense Plasmas 21.1.2 Dense Plasmas in Laboratories 61.2 Basic Parameters 71.2.1 Classical OCP 81.2.2 Electron Liquids at Metallic Densities 91.3 Consequences on the Coulomb Interaction 101.3.1 Scattering by Coulomb Forces 101.3.2 Debye Screening 111.3.3 The Ion-Sphere Model 131.3.4 Plasma Oscillation 151.3.5 Collective Motion and Individual-Particles Behavior 172 Fundamentals 192.1 Density-Fluctuation Excitations 192.1.1 System of Identical Particles 192.1.2 Structure Factors and Correlation Energy 212.1.3 System of Electrons at Metallic Densities 222.2 Dielectric Formulation 232.2.1 Density–Density Response Functions 242.2.2 Correlations, Radial Distributions, and Statistical Thermodynamics 252.2.3 Spin-Density Response 262.2.4 The Hartree–Fock Approximation 262.2.5 The Random-Phase Approximation 272.2.6 Collective versus Individual-Particles Aspects of Fluctuations 282.2.7 Strong Coupling Effects 292.3 Density-Functional Theory 322.3.1 Kohn–Sham Self-Consistent Equations 322.3.2 Thermodynamic Potentials 342.4 Computer Simulation Methods 362.4.1 Monte Carlo Approaches 362.4.2 Molecular Dynamics Simulations 362.4.3 Other Approaches 373 Scattering of Electromagnetic Waves 393.1 Scattering by Individual Particles 393.1.1 Cross-Section of Thomson Scattering 403.1.2 Doppler Effect 403.2 Incoherent Scattering by Correlated Particles 423.3 Radar Backscattering from the Ionosphere 433.3.1 Observations by Bowles 433.3.2 Observations by Pineo, Kraft, and Briscoe 443.4 Collective Phenomena in Electron-and-Ion Plasmas 453.4.1 Dielectric Response Function 463.4.2 Dressed Particles 473.4.3 Ion-Acoustic Waves 483.5 Plasma Critical Opalescence 493.6 Observation of Plasma Waves in Warm Dense Matter 504 Charged Particles or X-Rays Injected in Plasmas 534.1 Characteristic Energy-Loss Spectroscopy 534.2 Plasmon Dispersion 554.2.1 Plasmon Dispersion Coefficient 564.2.2 Measured Values 574.2.3 Theoretical Estimates 574.3 Stopping Power and Wake Potential 584.3.1 Induced Density Variations 594.3.2 Induced Potential 614.3.3 Stopping Power 614.4 Ion Clusters Injected in Metals 624.4.1 Injection into Thin Foils4.4.2 Advanced Wakefield Experiment4.5 X-Ray Crystallography 624.6 Observation of Laue Patterns in Coulomb Glasses 634.6.1 Madelung Energy 634.6.2 Layered Structures at Various Quenches 644.6.3 Laue Patterns for Glasses 664.7 X-Ray Thomson Scattering and Time-Resolved XANES Diagnostic with HighEnergy Density Plasmas 685 Thermodynamics of Classical OCP and Quantum Electron Liquids 715.1 Radial Distribution Functions and Correlation Energies 715.1.1 Correlation Energy in the RPA 725.1.2 Multi-Particle Correlation 735.2 OCP Thermodynamic Functions 735.2.1 OCP Free Energy 745.2.2 OCP pressure 745.2.3 Solid Free Energy 745.2.4 Wigner Crystallization 755.3 Equations of State for Quantum Electron Liquids 755.3.1 Ideal-Gas Contributions 755.3.2 Exchange–Correlation Contributions 765.3.3 Origin of Cohesive Forces 775.4 Freezing and Ferromagnetic Transitions in Electron Liquid 786 Phase Diagrams of Hydrogen 796.1 States of Hydrogen 796.1.1 Molecular Hydrogen 806.1.2 Pressure Ionization 806.1.3 Laboratory Realization of Metallic Hydrogen 816.1.4 Metallic Hydrogen in Astrophysical Objects 816.1.5 Nuclear Reactions 816.2 Equations of State for Hydrogen 826.2.1 Molecular Fluids 826.2.2 Molecular Solids 836.3 Phases of Hydrogen Matter 846.3.1 Equations of State for the Fluid Phase 846.3.2 Short-Range Screening by Electrons 856.4 Coexistence Curves and Thermodynamics 866.4.1 Phase Diagram and Coexistence Curves 876.4.2 Thermodynamics across the MI Transitions 886.5 Metal–Insulator Transitions 887 Transport Processes 917.1 Electric and Thermal Resistivity 917.1.1 Parameterized Formulae 927.1.2 Generalized Coulomb Logarithms 927.1.3 Screened Potentials 937.1.4 The IRS Parameter 947.2 Ultrahigh-Pressure Metal Physics Experiments 957.2.1 Interpreting the Experiments 957.2.2 Compression and Metallization 967.2.3 Examining the Data 977.2.4 The First-Order MI Transitions Justified 987.3 Jovian Interiors and Excess Infrared Luminosity 997.3.1 Structure of Jupiter 1007.3.2 Origins of the Excess Luminosity 1017.3.3 The MI Transitions and Luminosity 1018 Stellar and Planetary Magnetism 1038.1 Jovian Magnetic Activities 1038.1.1 Metallic Hydrogen in Jupiter 1038.1.2 Magnetic Reynolds Number 1048.1.3 Magnetic Activities 1048.2 Ferromagnetic and Freezing Transitions in Metallic Hydrogen 1058.2.1 Equations of State with Spin Polarization 1058.2.2 Phase Diagrams with Spin Polarization 1058.3 Nuclear Ferromagnetism with Magnetic White Dwarfs 1058.3.1 Hydrogen with Magnetic White Dwarfs 1058.3.2 Origin of Strong Magnetization 1078.3.3 Field Amplification by Stellar Rotation 1079 Nuclear Fusion in Metallic Hydrogen 1099.1 Thermonuclear and Pycnonuclear Reactions 1109.1.1 Scattering by the Coulomb Potential 1109.1.2 Probability of Penetration—Bare Coulomb Repulsion 1119.1.3 Cross-Section Factor 1129.1.4 Probability of Penetration—Screened Coulomb Repulsion 1139.1.5 Rates of Thermonuclear Reactions 1159.1.6 Rates of Pycnonuclear Reactions 1169.2 Solar Processes and Inertial-Confinement Fusion 1179.2.1 Inertial-Confinement Fusion 1179.2.2 The p–p Chain 1179.3 Enhancement of Nuclear Reactions in Metallic Fluids 1189.3.1 Enhancement Due to Coulomb Correlation 1189.3.2 Enhancement Factor 1199.3.3 Rates of Nuclear Reactions in Dense Plasmas 1219.4 “Supernova on the Earth” 1219.4.1 Adiabatic Compression 1219.4.2 Metallization 1229.4.3 Feasibility Experiment 1229.4.4 Power-Production Experiment 12310 Phase Diagrams of Nuclear Matter 12510.1 Deconfinement of Quarks from Nucleons 12510.1.1 Relativistic Heavy Ion Collider Experiments 12510.1.2 The Oldest Phase of Matter 12610.2 Phases of Nuclear Matter 12610.2.1 Phase Diagrams 12610.2.2 Deconfinement versus Metallization 12610.3 Structure of a Neutron Star 12710.3.1 Three-Part Structure 12710.3.2 Non-Radial Oscillations 12810.3.3 Central Core 12811 Plasma Phenomena around Neutron Stars and Black Holes 12911.1 Pulsars 13011.1.1 Discovery 13011.1.2 Characteristic Features 13011.1.3 Crab and Vela Pulsars 13211.2 Rotating Magnetic Neutron Stars 13211.2.1 What Are the Pulsars? 13211.2.2 Pulsar Magnetic Field 13311.2.3 Spinning Down of Pulsars by Magnetic Dipole Radiation 13411.2.4 Spinning Down of Crab Pulsar and the Crab Nebula Activities 13511.2.5 Constructing the Radio Beams 13611.2.6 Creating the Plasmas 13811.2.7 A Pulsar Emission Mechanism 13911.3 X-Ray Pulsars 14011.3.1 Close Binary Systems 14011.3.2 Accretion 14111.3.3 Cyclotron Resonance Scattering Feature 14311.3.4 Accretion Model of X-ray Pulsars 14311.4 Black Hole Model of Cygnus X-1 14411.4.1 Energy Spectra and Variability of X-ray Emission 14411.4.2 Mass Estimate 14511.4.3 Plasma Accretion to a Black Hole 14711.4.4 A Black Hole Model of Cyg X-1 Observation 14811.5 Stellar-Mass Black Holes and Supermassive Black Holes 15011.5.1 Microquasars 15011.5.2 Supermassive Black Hole in the Galaxy 15111.5.3 Burst of γ-ray from a Supermassive Black Hole Breaking Apart andSwallowing a Nearby Star 15212 Dawn of Gravitational-Wave Astronomy 15512.1 Hulse–Taylor Binary Pulsars 15612.2 GW150915: The First Signals for LIGO 15612.2.1 Information Extracted from the Signals 15712.2.2 Items to Be Ensured with the Signals 15912.3 Observation of Colliding Binary Neutron Stars 159Appendix I: The δ-Functions 163Appendix II: Fourier Analyses and Application 165Appendix III: The Fluctuation-Dissipation Theorem 169Appendix IV: Fermi Integrals 173Appendix V: Functional Derivatives 175References 177Index 185