Kinetic Theory of Particles and Photons: Theoretical Foundations of Non-LTE Plasma Spectroscopy

ISBN-13: 9783642707308 / Angielski / Miękka / 2012 / 356 str.

Joachim Oxenius

Opis

Many laboratory and astrophysical plasmas show deviations from local ther- modynamic equilibrium (LTE). This monograph develops non-LTE plasma spectroscopy as a kinetic theory of particles and photons, considering the radiation field as a photon gas whose distribution function (the radiation in- tensity) obeys a kinetic equation (the radiative transfer equation), just as the distribution functions of particles obey kinetic equations. Such a unified ap- proach provides clear insight into the physics of non-LTE plasmas. Chapter 1 treats the principle of detailed balance, of central importance for understanding the non-LTE effects in plasmas. Chapters 2, 3 deal with kinetic equations of particles and photons, respectively, followed by a chapter on the fluid description of gases with radiative interactions. Chapter 5 is devoted to the H theorem, and closes the more general first part of the book. The last two chapters deal with more specific topics. After briefly discuss- ing optically thin plasmas, Chap. 6 treats non-LTE line transfer by two-level atoms, the line profile coefficients of three-level atoms, and non-Maxwellian electron distribution functions. Chapter 7 discusses topics where momentum exchange between matter and radiation is crucial: the approach to thermal equilibrium through interaction with blackbody radiation, radiative forces, and Compton scattering. A number of appendices have been added to make the book self-contained and to treat more special questions. In particular, Appendix B contains an in- troductory discussion of atomic line profile coefficients.

Spis treści

1. Thermal Equilibrium and Detailed Balance.- 1.1 Introductory Remarks.- 1.2 The Principle of Detailed Balance.- 1.3 Proof of the Principle of Detailed Balance for a Special Case.- 1.4 Derivation of Thermal Distribution Functions from Detailed Balance.- 1.4.1 Maxwell Distribution.- 1.4.2 Boltzmann Distribution.- 1.4.3 Saha Distribution.- 1.4.4 Planck Distribution.- 1.5 Validity of the Reciprocity Relation w(i?f)= w(f?i).- 1.6 Explicit Forms of the Reciprocity Relation w(i?f) = w(f?i).- 1.6.1 Collisional Excitation and De-Excitation.- 1.6.2 Collisional Ionization and Three-Body Recombination.- 1.6.3 Autoionization and Radiationless Capture.- 1.6.4 Line Emission and Absorption.- 1.6.5 Photoionization and Radiative Recombination.- 1.6.6 Free-Free Emission and Absorption.- 1.6.7 Two-Photon Emission and Absorption.- 2. Kinetic Equations of Particles.- 2.1 Kinetic Equations.- 2.2 Elastic Collision Terms.- 2.2.1 Boltzmann Collision Terms.- 2.2.2 Fokker-Planck Collision Terms.- 2.2.3 General Properties of Elastic Collision Terms.- 2.3 Inelastic Collision Terms.- 2.3.1 Collisional Excitation and De-Excitation (Atoms).- 2.3.2 Collisional Ionization and Three-Body Recombination (Atoms).- 2.3.3 Collisional Excitation and De-Excitation (Electrons).- 2.3.4 Collisional Ionization and Three-Body Recombination (Electrons).- 2.3.5 Dielectronic Recombination.- 2.4 Collision Terms Due to Radiative Processes.- 2.4.1 Line Emission and Absorption.- 2.4.2 Photoionization and Radiative Recombination (Atoms).- 2.4.3 Photoionization and Radiative Recombination (Electrons).- 2.4.4 Bremsstrahlung and Inverse Bremsstrahlung (Electrons).- 3. The Kinetic Equation of Photons.- 3.1 The Equation of Radiative Transfer.- 3.2 Emission and Absorption.- 3.2.1 Bound-Bound Transitions.- 3.2.2 Free-Bound Transitions.- 3.2.3 Free-Free Transitions.- 3.3 Scattering.- 3.3.1 Scattering by Stationary Particles.- 3.3.2 Scattering by Moving Particles.- 4. Moment Equations and Fluid Description.- 4.1. Moment Equations for Particles.- 4.1.1 One Particle Type a.- 4.1.2 One Particle Species A.- 4.1.3 Several Particle Species.- 4.2 Moment Equations for Photons.- 4.3 Fluid Description of a Gas.- 4.4 Fluid Description of a Gas with Radiative Interactions.- 4.4.1 Preliminary Discussion.- 4.4.2 Covariant Form of the Transfer Equation and the Energy-Momentum Tensor of the Radiation Field.- 4.4.3 Radiation Pressure, Radiative Heat Conductivity, Radiative Viscosity.- 4.4.4 Hydrodynamic Equations with Radiative Terms.- 5. H Theorem for Gases and Radiation.- 5.1 Entropy and Entropy Production.- 5.1.1 General Definitions.- 5.1.2 Entropy of a Classical Gas.- 5.1.3 Entropy of Radiation.- 5.2 Proof of the H Theorem.- 5.2.1 Elastic Collisions (Identical Particles).- 5.2.2 Elastic Collisions (Unlike Particles).- 5.2.3 Emission and Absorption.- 6. Energy Exchange Between Matter and Radiation.- 6.1 General Remarks.- 6.2 Optically Thin Plasmas.- 6.2.1 Physical Reactions.- 6.2.2 Some Illustrative Results.- 6.3 Non-LTE Line Transfer by Two-Level Atoms (I): Basic Relations.- 6.3.1 Kinetic Equation of Photons.- 6.3.2 Kinetic Equations of Two-Level Atoms.- 6.3.3 Approximations.- 6.3.4 Line Profile Coefficients.- 6.3.5 Redistribution Functions.- 6.3.6 Stimulated Emission.- 6.4 Non-LTE Line Transfer by Two-Level Atoms (II): Results.- 6.4.1 The Standard Problem.- 6.4.2 Dimensionless Quantities.- 6.4.3 Boundary Conditions.- 6.4.4 Complete Redistribution: Static Approximation.- 6.4.5 Complete Redistribution: Diffusion Approximation.- 6.4.6 Exact Solutions.- 6.5 Multilevel Atoms.- 6.5.1 Atomic Line Profile Coefficients of a Three-Level Atom.- 6.5.2 Laboratory Line Profile Coefficients of a Three-Level Atom.- 6.6 Non-Maxwellian Electron Distribution Functions.- 7. Momentum Exchange Between Matter and Radiation.- 7.1 General Remarks.- 7.2 Approach to Thermal Equilibrium Through Interaction with Blackbody Radiation.- 7.2.1 Line Radiation of Two-Level Atoms.- 7.2.2 Thomson Scattering of Electrons.- 7.3 Radiative Forces.- 7.3.1 Scattering.- 7.3.2 Bound-Bound Transitions.- 7.3.3 Free-Bound Transitions.- 7.4 Compton Scattering.- 7.4.1 Kinematics of Compton Scattering.- 7.4.2 Reciprocity Relation.- 7.4.3 Compton Collision Term (Electrons).- 7.4.4 Compton Collision Term (Photons).- 7.4.5 Transformation of Cross Sections.- Appendices.- A. Transformation Formulas for Radiative Quantities.- A.1 Transformation Formulas.- A.2 Is the Distribution Function a Relativistic Invariant?.- B. Atomic Absorption and Emission Profiles.- B.1 Definitions and General Remarks.- B.2 Two-Level Atom (I): One Level Broadened.- B.3 Two-Level Atom (II): Two Levels Broadened.- B.4 Three-Level Atom.- B.5 Atomic Redistribution Functions.- B.6 Absorption and Emission Profiles in Terms of Generalized Redistribution Functions.- C. The Boltzmann Equation.- D. Brownian Motion and Fokker-Planck Equation.- D.1 Brownian Motion.- D.2 Fokker-Planck Equation.- E. Reciprocity Relations for Inelastic Collisions with Heavy Particles.- E.1 Excitation and De-Excitation.- E.2 Ionization and Three-Body Recombination. Dissociation and Recombination.- F. Elastic Collision Term of the Standard Problem.- General Bibliography.- References.