Plasma Atomic Physics

Description

Plasma Atomic Physics provides an overview of the elementary processes within atoms and ions in plasmas, and introduces readers to the language of atomic spectra and light emission, allowing them to explore the various and fascinating radiative properties of matter. The book familiarizes readers with the complex quantum-mechanical descriptions of electromagnetic and collisional processes, while also developing a number of effective qualitative models that will allow them to obtain adequately comprehensive descriptions of collisional-radiative processes in dense plasmas, dielectronic satellite emissions and autoionizing states, hollow ion X-ray emissions, polarized atoms and ions, hot electrons, charge exchange, atomic population kinetics, and radiation transport. Numerous applications to plasma spectroscopy and experimental data are presented, which concern magnetic confinement fusion, inertial fusion, laser-produced plasmas, and X-ray free-electron lasers’ interaction with matter. Particular highlights include the development of quantum kinetics to a level surpassing the almost exclusively used quasi-classical approach in atomic population kinetics, the introduction of the recently developed Quantum-F-Matrix-Theory (QFMT) to study the impact of plasma microfields on atomic populations, and the Enrico Fermi equivalent photon method to develop the “Plasma Atom”, where the response properties and oscillator strength distribution are represented with the help of a local plasma frequency of the atomic electron density. Based on courses held by the authors, this material will assist students and scientists studying the complex processes within atoms and ions in different kinds of plasmas by developing relatively simple but highly effective models. Considerable attention is paid to a number of qualitative models that deliver physical transparency, while extensive tables and formulas promote the practical and useful application of complex theories and provide effective tools for non-specialist readers. Preface Contents About the Authors 1 Introduction to Atomic Physics in Plasmas Abstract 1.1 Atomic Physics and Plasma Physics 1.1.1 General Characteristics of Radiation Processes 1.1.2 Interrelation Between Radiation and Matter 1.1.3 Radiative Emission and Volume Plasma Radiative Losses 1.1.4 Radiation Trapping and Plasma Radiation Losses in the General Case 1.1.5 Excited Atoms Under Plasma Perturbations 1.2 Structure of Atoms and Ions 1.2.1 Symmetry Properties of the Coulomb Field 1.2.2 Allowed and Forbidden Transitions 1.2.3 Properties of Highly Charged Ion Spectra 1.3 Autoionizing Atomic States 1.3.1 Excitation of Core Hole States 1.3.2 The Interaction of Discrete States with a Continuum: Fano resonances 1.4 Rydberg Atomic Autoionizing and Non-Autoionizing States in Plasmas 1.4.1 Rydberg Atomic States 1.4.2 Autoionizing Rydberg Atomic States 1.4.3 Dielectronic Satellite Accumulation in ns-Laser-Produced Plasmas 1.4.4 Transient Three-body Recombination of Dielectronic Satellite Emission 1.5 Plasma Spectroscopy 1.5.1 Spatial Properties of Dielectronic Satellite Emission 1.5.2 Stark Broadening Analysis of Rydberg Dielectronic Satellites 1.5.3 Nonlinear Interference Effects in Stark Broadening of Multi-electron Configurations 1.5.4 Hollow Ion X-Ray Emission in Dense Plasmas References 2 Radiative Characteristics of Polarized Atoms and Ions Abstract 2.1 Oscillator Strengths 2.2 Classical and Quantum Expressions for Einstein Coefficients 2.3 Dynamic Polarizability of Atoms 2.4 General Relations of Atomic Polarizability 2.5 Static Polarizability of Atoms and Ions 2.6 Local Plasma Frequency Model of Polarizability of Many Electron Systems 2.7 Dynamic Polarizability of Nanoparticles References 3 Probabilities of Radiative Transitions Abstract 3.1 Radiative Transition Cross Sections 3.2 Spectral Line Shapes of Atomic Radiative Transitions 3.3 Quasi-classical and Quantum Radiative Transition Probabilities 3.3.1 Kramers Electrodynamics 3.3.2 Discrete Energy Spectrum 3.4 Radiative Recombination 3.4.1 Kramers Photorecombination Cross Section 3.4.2 Radiative Recombination Rates 3.4.3 Radiative Losses 3.4.4 Generalized Scaled Empirical Formulas for Radiative Recombination Rates 3.4.5 Enhanced Radiative Recombination in Storage Rings 3.5 Two-Channel Bremsstrahlung in Electron–Atom Collisions 3.6 Bremsstrahlung in Many Electron–Atom Collisions and Mass-Independent Radiation 3.7 Photoionization 3.7.1 General Relations 3.7.2 Hydrogen-like Approximation 3.7.3 Photoeffect Cross Section in the Born Approximation 3.7.4 Local Plasma Frequency Model 3.7.5 Approximate Quantum Methods of Calculation of Photoabsorption Cross Sections 3.7.6 Rost Hybrid Method 3.7.7 Generalized Scaled Empirical Photoionization Cross Sections from K-, L-, M-, N- and O-Shell 3.8 Photodetachment from Negative Ions 3.9 Phase Control of Photoprocesses by Ultrashort Laser Pulses References 4 Radiation Scattering on Atoms, Plasmas, and Nanoparticles Abstract 4.1 Photon Scattering by a Free Electron 4.2 Radiation Scattering on Atoms 4.2.1 Classical Description 4.2.2 Quantum Description 4.3 High-Frequency Radiation Scattering on Atoms 4.3.1 Non-dipole Character of Scattering 4.3.2 Dynamic Form Factor of an Atom 4.3.3 Impulse Approximation in the Theory of Compton Scattering 4.4 Scattering on Plasmas 4.4.1 General Expression for the Cross Section of Radiation Scattering in Plasmas 4.4.2 Radiation Scattering by Plasma Electrons 4.4.3 Transient Scattering of Radiation in Plasmas 4.4.4 Radiation Scattering by a Plasmon 4.5 Scattering on Nanoparticles 4.5.1 Mie Theory of Radiation Scattering and Absorption References 5 Electron–Atom Collisions Abstract 5.1 Fermi Equivalent Photon Method 5.1.1 Excitation by Electron Impact as Absorption of Equivalent Photons by an Ion 5.1.2 Autoionization Decay and Dielectronic Capture 5.2 Ionization by Electron Impact 5.2.1 Thomson Formula 5.2.2 Similarity Function Method for the Ionization Cross-Section 5.2.3 Comparison with Experimental Data 5.3 Analytical Empirical Formulas for Ionization, Single, and Total Recombination Rates 5.3.1 Ionization 5.3.2 Three-Body Recombination in Dense Plasmas 5.3.3 Radiative Recombination in Dense Plasmas 5.4 Classical Consideration of Collisional Excitation of an Atom 5.4.1 Fermi Photon Equivalent Method and Oscillator Strength Method 5.4.2 Similarity Function Method for Collisional Excitation of an Atom 5.4.3 Analytical Empirical Formulas for Excitation and De-excitation Rates 5.4.3.1 Dipole Excitation and De-excitation of Ions 5.4.3.2 Dipole Excitation and De-excitation of Neutral Atoms 5.5 Excitation of Dipole-Forbidden Transitions in Atoms 5.5.1 Intercombination Transitions 5.5.2 Intermediate Coupling Effects 5.6 Analytical Empirical Formulas for Dielectronic Recombination in Dense Plasmas 5.6.1 Autoionization, Dielectronic Capture, and Dielectronic Recombination 5.6.2 Total Rates of Dielectronic Recombination and Multichannel Approach 5.6.2.1 Burgess Formulas 5.6.2.2 Multichannel Approach 5.6.2.3 Excited State-Driven Dielectronic Recombination 5.6.3 Dense Plasma and Electric Field Effects on Dielectronic Recombination 5.6.3.1 Atomic Population Kinetics 5.6.3.2 Limitation of Bound States 5.6.3.3 Effects of Angular Momentum Changing Collisions 5.6.3.4 Electric Field Effects on Cross-Sections References 6 Atomic Population Kinetics Abstract 6.1 Generalized Atomic Kinetics of Non-Equilibrium Plasmas Containing Ions of Various Charge States 6.1.1 Principles of Atomic Line Emission: The Two-Level Atom 6.1.2 The Principles of Ionic Charge State Distributions in Plasmas 6.1.3 Characteristics of the Ionic Charge State Distribution 6.1.4 Generalized Atomic Population Kinetics 6.1.5 Statistical Charge State Distribution Based on Average Occupation Numbers 6.2 Characteristic Time Scales of Atomic and Ionic Systems 6.2.1 Characteristic Times to Establish Ionization Balance 6.2.2 Characteristic Times of Photon Emission 6.2.3 Collisional Mixing of Relaxation Time Scales 6.3 Reduced Atomic Kinetics 6.3.1 Ground States, Single-Excited and Autoionizing Levels: General Considerations 6.3.2 The Virtual Contour Shape Kinetic Theory (VCSKT) 6.3.2.1 Exact and Reduced Kinetics 6.3.2.2 The Probability Method for Boltzmann-like Populations 6.3.2.3 Maximum Recovery Properties and Convergence Properties 6.3.2.4 Broadening Properties of Complex Emission Groups 6.3.2.5 Response Properties of VCSKT to Hot Electrons 6.4 Two-Dimensional Radiative Cascades Between Rydberg Atomic States 6.4.1 Classical Kinetic Equation 6.4.2 Quantum Kinetic Equation in the Quasi-classical Approximation 6.4.3 Relationship of the Quasi-classical Solution to the Quantum Cascade Matrix. The Solution in the General Quantum Case 6.4.4 Atomic Level Populations for a Photorecombination Source. Quasi-classical Scaling Laws 6.5 Two-Dimensional Collisional–Radiative Model of Highly Excited Atomic States 6.5.1 Kinetic Model of Radiative–Collisional Cascades 6.5.2 The Classical Collision Operator 6.5.3 Numerical Solution for Delta-Function Source 6.5.4 Radiation Recombination Population Source 6.5.5 Intensities of Rydberg Spectral Lines References 7 Quantum Atomic Population Kinetics in Dense Plasmas Abstract 7.1 Rate Equation and Quantum Populations 7.2 Schrödinger Picture 7.3 Atomic Density Matrix: Open and Closed Systems 7.4 The Electron Collisional Operator \hat{{\varvec{\Phi }}} 7.4.1 Scattering Matrix Representation 7.4.2 Electron Collisional Operator in Second-Order Perturbation Theory 7.4.3 Reduced Matrix Element Representation 7.4.4 Symmetry Properties 7.5 Matrix Elements and Atomic Physics Processes 7.5.1 Line Strengths and Oscillator Strengths 7.5.2 Reduced Matrix Elements and Cross Sections 7.6 Magnetic Quantum Number Averages 7.6.1 The Rate Equation Case 7.6.2 Formal Solution for the Density Matrix Equations 7.6.3 The Failure of the Rate Equation Approach for Quantum Averages 7.6.4 The Cross Section Method for Quantum Averages 7.6.4.1 The Total Loss Rate from a Quantum Level: \Phi _{ {\rm aa}}^{{\rm aa}} 7.6.4.2 The Loss Rate of Coherences: \Phi _{ {\rm ab}}^{{\rm ab}} 7.6.4.3 The Transfer Rate Between Two Levels: \Phi _{ {\rm aa}}^{{\rm bb}} 7.7 About the Boltzmann Limit in Quantum Kinetics 7.7.1 The Two-Level M-Quantum-Number-Averaged Level System 7.7.2 The Principle of Detailed Balance and Microreversibility 7.7.3 Comments to a Two-Level Quantum Kinetics Resolved in M-Quantum Number 7.8 The Field Perturbation Operator \hat{{\varvec V}} 7.8.1 The Quasi-classical Electric Field Perturbation 7.8.2 The Ionic Field Mixing 7.8.3 Magnetic Quantum Number Averages and Symmetry Properties 7.9 The Quantum Mechanical F-Matrix Theory QFMT 7.9.1 Rate Equation and Quantum Populations 7.9.2 The Open Two-Level System 7.9.3 The Exact QFMT Solution for a Two-Level System 7.9.4 Successive Pair Coupling of Quantum Effects 7.9.5 QFMT and Statistical Boltzmann Populations 7.10 Application to Autoionizing Levels of Highly Charged Ions 7.10.1 Dielectronic Satellites Near H-like Lyman-Alpha 7.10.2 The Low-Frequency Plasma Microfield 7.10.3 The Screened Effective Pair Potential Method in Strongly Coupled Plasmas 7.10.4 The Relaxation Rate Approximation of QFMT: QFMT-W References 8 Ionization Potential Depression Abstract 8.1 The Atomic-Solid-Plasma ASP Model 8.2 Approximate Solid-State Core Hole Configuration Energies 8.3 Ionization Potential Depression Formulas 8.4 Optical Electron Finite Temperature Ion Sphere Model OEFTIS 8.4.1 Plasma Polarization Shift and Level Disappearance in Dense Hot Plasmas 8.4.2 Scaled Ion Sphere Radii and Lattice Structure 8.5 Strongly Compressed Matter and Fermi Surface-Rising 8.6 Discussion of Different Regimes of Ionization Potential Depression References 9 The Plasma Atom Abstract 9.1 The Thomas–Fermi Statistical Approach 9.2 The Local Plasma Frequency Approximation 9.2.1 Oscillator Strengths Distribution and Photoabsorption 9.2.2 Fermi Equivalent Photon Method and Local Plasma Oscillator Strength 9.3 Radiative Losses 9.3.1 General Relations 9.3.2 Density Effects 9.4 Statistical Ionization Cross Sections and Rates 9.5 Statistical Dielectronic Recombination Rates 9.5.1 General Formula 9.5.2 Orbital Quantum Number Averaged Dielectronic Recombination Rates 9.5.3 Statistical Burgess Formula 9.5.4 Statistical Vainshtein Formula 9.5.5 Numerical Comparison of Different Dielectronic Recombination Models References 10 Applications to Plasma Spectroscopy Abstract 10.1 The Emission of Light and Plasma Spectroscopy 10.2 Dielectronic Satellite Emission 10.2.1 Electron Temperature 10.2.1.1 Satellite to Resonance Lines 10.2.1.2 Rydberg Satellites 10.2.2 Ionization Temperature 10.2.3 Relaxation Times 10.2.4 Spatially Confined Emission 10.2.5 Electron Density 10.2.5.1 Collisional Redistribution 10.2.5.2 Stark Broadening of Dielectronic Satellites 10.2.5.3 Stark Broadening of Hollow Ions 10.2.5.4 Interference Effects in Stark Broadening of Hollow Ions 10.2.5.5 Non-statistical Line Shapes 10.3 Magnetic Fusion 10.3.1 Neutral Particle Background and Self-consistent Charge Exchange Coupling to Excited States 10.3.2 Natural Neutral Background and Neutral Beam Injection: Perturbation of X-ray Impurity Emission 10.3.3 Transient Phenomena in the Start-up Phase 10.3.4 Impurity Diffusion and τ-Approximation 10.3.5 Non-equilibrium Radiative Properties During Sawtooth Oscillations 10.3.5.1 Fluctuations and Atomic Level Populations 10.3.5.2 Histogram Technique 10.3.5.3 Time-Dependent Charge State Evolution 10.3.5.4 Time-Dependent Evolution of Line Intensities 10.3.5.5 Enhanced Radiation Heat Load 10.3.5.6 Time-Dependent Line Intensity Ratios 10.4 Suprathermal Electrons 10.4.1 Non-Maxwellian Elementary Atomic Physics Processes 10.4.2 Pathological Line Ratios 10.4.3 Bulk Electron Temperature 10.4.4 Hot Electron Fraction 10.4.4.1 Hot Electron Perturbed Satellite and Resonance Line Intensities 10.4.4.2 Qualitative Distortion of the Ionic Charge State Distribution 10.4.4.3 Temporal Shifts of the Hot Electron Fraction 10.5 Space-Resolved Measurements of Fast Ions 10.5.1 Spatial Resolution of Plasma Jets 10.5.2 Energy Distribution of Fast Ions 10.6 Atomic Physics in Dense Plasmas with X-ray Free Electron Lasers 10.6.1 Scaling Laws to Move Atomic Populations with XFEL 10.6.1.1 Description of Time- and Energy-Dependent XFEL Radiation 10.6.1.2 Photoionization 10.6.1.3 Photoexcitation 10.6.2 Atomic Kinetics Driven by Intense Short Pulse Radiation 10.6.3 Interaction of XFEL with Dense Plasmas 10.6.3.1 General Features of XFEL Interaction with Dense Plasmas: Simulations 10.6.3.2 X-ray Pumping of Dense Plasmas 10.6.4 Beating the Auger Clock 10.6.4.1 Photoionization Versus Autoionization 10.6.4.2 Hollow Ion Formation 10.6.4.3 X-ray Emission Switches for Ultrafast Dense Matter Investigations 10.6.4.4 Transparent Materials and Saturated Absorption 10.6.4.5 Exotic States of Dense Matter: Hollow Crystals 10.6.4.6 New Role of Elementary Processes: Auger Electron and Three-Body Recombination Heating 10.6.5 Generalized Atomic Physics Processes 10.6.5.1 Generalized Three-Body Recombination and Autoionization 10.6.5.2 Generalized Collisional Excitation, Ionization, and Dielectronic Capture 10.6.5.3 Generalized Fluorescence and Radiative Recombination 10.6.5.4 The Heated Solid and Generalized Atomic Fermi–Dirac Rate Coefficients 10.6.5.5 Fluorescence Emission of Warm Dense Matter References Annexes A.1 Summary of Simple General Formulae of Some Elementary Atomic Physics Processes Outline placeholder A.1.1 Transition Energies and Radiative Decay Rates A.1.2 Electron Collisional Excitation and De-excitation A.1.3 Electron Collisional Ionization and Three-Body Recombination A.1.4 Radiative Recombination A.1.5 Dielectronic Recombination A.1.6 Charge Exchange A.1.6.1 Single-electron Charge Exchange A.1.6.2 Multiple-electron Charge Exchange A.2 Simple General Formulae for Collisional–Radiative Processes in Hydrogen Outline placeholder A.2.1 Energies A.2.2 Spontaneous Transition Probabilities A.2.3 Radiative Recombination A.2.4 Electron Collisional Excitation and De-excitation A.2.5 Ionization and Three-Body Recombination A.2.6 Matrix Elements Including Phase Sign, Oscillator Strengths, and Energies of nlj-Split Levels A.3 Simple General Formulae for Collisional–Radiative Processes in He0+ and He1+ Outline placeholder A.3.1 Energies A.3.2 Spontaneous Transition Probabilities A.3.3 Radiative Recombination A.3.4 Dielectronic Recombination A.3.5 Electron Collisional Excitation and De-excitation A.3.6 Ionization and Three-Body Recombination A.3.7 Matrix Elements Including Phase Sign, Oscillator Strengths, and Energies of nlj-Split Levels A.4ƒIonization Potential Depression: Level Delocalization and Line Shifts Outline placeholder A.4.1 The Analytical b-potential Method A.4.2 Simple Analytical Formulas for Line Shifts A.4.3 Quantum Number Dependent Line Shift and Level Delocalization: High Precision 4th-order Analytical Formulas A.5 Atomic Units and Constants References Index