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.

CONTENTS

Preface xi

1 Introduction 1

1.1 Dense Plasmas in Nature 1

1.1.1 Astrophysical Dense Plasmas 2

1.1.2 Dense Plasmas in Laboratories 6

1.2 Basic Parameters 7

1.2.1 Classical OCP 8

1.2.2 Electron Liquids at Metallic Densities 9

1.3 Consequences on the Coulomb Interaction 10

1.3.1 Scattering by Coulomb Forces 10

1.3.2 Debye Screening 11

1.3.3 The Ion-Sphere Model 13

1.3.4 Plasma Oscillation 15

1.3.5 Collective Motion and Individual-Particles Behavior 17

2 Fundamentals 19

2.1 Density-Fluctuation Excitations 19

2.1.1 System of Identical Particles 19

2.1.2 Structure Factors and Correlation Energy 21

2.1.3 System of Electrons at Metallic Densities 22

2.2 Dielectric Formulation 23

2.2.1 Density–Density Response Functions 24

2.2.2 Correlations, Radial Distributions, and Statistical Thermodynamics 25

2.2.3 Spin-Density Response 26

2.2.4 The Hartree–Fock Approximation 26

2.2.5 The Random-Phase Approximation 27

2.2.6 Collective versus Individual-Particles Aspects of Fluctuations 28

2.2.7 Strong Coupling Effects 29

2.3 Density-Functional Theory 32

2.3.1 Kohn–Sham Self-Consistent Equations 32

2.3.2 Thermodynamic Potentials 34

2.4 Computer Simulation Methods 36

2.4.1 Monte Carlo Approaches 36

2.4.2 Molecular Dynamics Simulations 36

2.4.3 Other Approaches 37

3 Scattering of Electromagnetic Waves 39

3.1 Scattering by Individual Particles 39

3.1.1 Cross-Section of Thomson Scattering 40

3.1.2 Doppler Effect 40

3.2 Incoherent Scattering by Correlated Particles 42

3.3 Radar Backscattering from the Ionosphere 43

3.3.1 Observations by Bowles 43

3.3.2 Observations by Pineo, Kraft, and Briscoe 44

3.4 Collective Phenomena in Electron-and-Ion Plasmas 45

3.4.1 Dielectric Response Function 46

3.4.2 Dressed Particles 47

3.4.3 Ion-Acoustic Waves 48

3.5 Plasma Critical Opalescence 49

3.6 Observation of Plasma Waves in Warm Dense Matter 50

4 Charged Particles or X-Rays Injected in Plasmas 53

4.1 Characteristic Energy-Loss Spectroscopy 53

4.2 Plasmon Dispersion 55

4.2.1 Plasmon Dispersion Coefficient 56

4.2.2 Measured Values 57

4.2.3 Theoretical Estimates 57

4.3 Stopping Power and Wake Potential 58

4.3.1 Induced Density Variations 59

4.3.2 Induced Potential 61

4.3.3 Stopping Power 61

4.4 Ion Clusters Injected in Metals 62

4.4.1 Injection into Thin Foils

4.4.2 Advanced Wakefield Experiment

4.5 X-Ray Crystallography 62

4.6 Observation of Laue Patterns in Coulomb Glasses 63

4.6.1 Madelung Energy 63

4.6.2 Layered Structures at Various Quenches 64

4.6.3 Laue Patterns for Glasses 66

4.7 X-Ray Thomson Scattering and Time-Resolved XANES Diagnostic with High

Energy Density Plasmas 68

5 Thermodynamics of Classical OCP and Quantum Electron Liquids 71

5.1 Radial Distribution Functions and Correlation Energies 71

5.1.1 Correlation Energy in the RPA 72

5.1.2 Multi-Particle Correlation 73

5.2 OCP Thermodynamic Functions 73

5.2.1 OCP Free Energy 74

5.2.2 OCP pressure 74

5.2.3 Solid Free Energy 74

5.2.4 Wigner Crystallization 75

5.3 Equations of State for Quantum Electron Liquids 75

5.3.1 Ideal-Gas Contributions 75

5.3.2 Exchange–Correlation Contributions 76

5.3.3 Origin of Cohesive Forces 77

5.4 Freezing and Ferromagnetic Transitions in Electron Liquid 78

6 Phase Diagrams of Hydrogen 79

6.1 States of Hydrogen 79

6.1.1 Molecular Hydrogen 80

6.1.2 Pressure Ionization 80

6.1.3 Laboratory Realization of Metallic Hydrogen 81

6.1.4 Metallic Hydrogen in Astrophysical Objects 81

6.1.5 Nuclear Reactions 81

6.2 Equations of State for Hydrogen 82

6.2.1 Molecular Fluids 82

6.2.2 Molecular Solids 83

6.3 Phases of Hydrogen Matter 84

6.3.1 Equations of State for the Fluid Phase 84

6.3.2 Short-Range Screening by Electrons 85

6.4 Coexistence Curves and Thermodynamics 86

6.4.1 Phase Diagram and Coexistence Curves 87

6.4.2 Thermodynamics across the MI Transitions 88

6.5 Metal–Insulator Transitions 88

7 Transport Processes 91

7.1 Electric and Thermal Resistivity 91

7.1.1 Parameterized Formulae 92

7.1.2 Generalized Coulomb Logarithms 92

7.1.3 Screened Potentials 93

7.1.4 The IRS Parameter 94

7.2 Ultrahigh-Pressure Metal Physics Experiments 95

7.2.1 Interpreting the Experiments 95

7.2.2 Compression and Metallization 96

7.2.3 Examining the Data 97

7.2.4 The First-Order MI Transitions Justified 98

7.3 Jovian Interiors and Excess Infrared Luminosity 99

7.3.1 Structure of Jupiter 100

7.3.2 Origins of the Excess Luminosity 101

7.3.3 The MI Transitions and Luminosity 101

8 Stellar and Planetary Magnetism 103

8.1 Jovian Magnetic Activities 103

8.1.1 Metallic Hydrogen in Jupiter 103

8.1.2 Magnetic Reynolds Number 104

8.1.3 Magnetic Activities 104

8.2 Ferromagnetic and Freezing Transitions in Metallic Hydrogen 105

8.2.1 Equations of State with Spin Polarization 105

8.2.2 Phase Diagrams with Spin Polarization 105

8.3 Nuclear Ferromagnetism with Magnetic White Dwarfs 105

8.3.1 Hydrogen with Magnetic White Dwarfs 105

8.3.2 Origin of Strong Magnetization 107

8.3.3 Field Amplification by Stellar Rotation 107

9 Nuclear Fusion in Metallic Hydrogen 109

9.1 Thermonuclear and Pycnonuclear Reactions 110

9.1.1 Scattering by the Coulomb Potential 110

9.1.2 Probability of Penetration—Bare Coulomb Repulsion 111

9.1.3 Cross-Section Factor 112

9.1.4 Probability of Penetration—Screened Coulomb Repulsion 113

9.1.5 Rates of Thermonuclear Reactions 115

9.1.6 Rates of Pycnonuclear Reactions 116

9.2 Solar Processes and Inertial-Confinement Fusion 117

9.2.1 Inertial-Confinement Fusion 117

9.2.2 The p–p Chain 117

9.3 Enhancement of Nuclear Reactions in Metallic Fluids 118

9.3.1 Enhancement Due to Coulomb Correlation 118

9.3.2 Enhancement Factor 119

9.3.3 Rates of Nuclear Reactions in Dense Plasmas 121

9.4 “Supernova on the Earth” 121

9.4.1 Adiabatic Compression 121

9.4.2 Metallization 122

9.4.3 Feasibility Experiment 122

9.4.4 Power-Production Experiment 123

10 Phase Diagrams of Nuclear Matter 125

10.1 Deconfinement of Quarks from Nucleons 125

10.1.1 Relativistic Heavy Ion Collider Experiments 125

10.1.2 The Oldest Phase of Matter 126

10.2 Phases of Nuclear Matter 126

10.2.1 Phase Diagrams 126

10.2.2 Deconfinement versus Metallization 126

10.3 Structure of a Neutron Star 127

10.3.1 Three-Part Structure 127

10.3.2 Non-Radial Oscillations 128

10.3.3 Central Core 128

11 Plasma Phenomena around Neutron Stars and Black Holes 129

11.1 Pulsars 130

11.1.1 Discovery 130

11.1.2 Characteristic Features 130

11.1.3 Crab and Vela Pulsars 132

11.2 Rotating Magnetic Neutron Stars 132

11.2.1 What Are the Pulsars? 132

11.2.2 Pulsar Magnetic Field 133

11.2.3 Spinning Down of Pulsars by Magnetic Dipole Radiation 134

11.2.4 Spinning Down of Crab Pulsar and the Crab Nebula Activities 135

11.2.5 Constructing the Radio Beams 136

11.2.6 Creating the Plasmas 138

11.2.7 A Pulsar Emission Mechanism 139

11.3 X-Ray Pulsars 140

11.3.1 Close Binary Systems 140

11.3.2 Accretion 141

11.3.3 Cyclotron Resonance Scattering Feature 143

11.3.4 Accretion Model of X-ray Pulsars 143

11.4 Black Hole Model of Cygnus X-1 144

11.4.1 Energy Spectra and Variability of X-ray Emission 144

11.4.2 Mass Estimate 145

11.4.3 Plasma Accretion to a Black Hole 147

11.4.4 A Black Hole Model of Cyg X-1 Observation 148

11.5 Stellar-Mass Black Holes and Supermassive Black Holes 150

11.5.1 Microquasars 150

11.5.2 Supermassive Black Hole in the Galaxy 151

11.5.3 Burst of γ-ray from a Supermassive Black Hole Breaking Apart and

Swallowing a Nearby Star 152

12 Dawn of Gravitational-Wave Astronomy 155

12.1 Hulse–Taylor Binary Pulsars 156

12.2 GW150915: The First Signals for LIGO 156

12.2.1 Information Extracted from the Signals 157

12.2.2 Items to Be Ensured with the Signals 159

12.3 Observation of Colliding Binary Neutron Stars 159

Appendix I: The δ-Functions 163

Appendix II: Fourier Analyses and Application 165

Appendix III: The Fluctuation-Dissipation Theorem 169

Appendix IV: Fermi Integrals 173

Appendix V: Functional Derivatives 175

References 177

Index 185