# Kinetic Theory of Nonideal Gases and Nonideal Plasmas

### International Series in Natural Philosophy

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Kinetic Theory of Nonideal Gases and Nonideal Plasmas presents the fundamental aspects of the kinetic theory of gases and plasmas. The book consists of three parts, which attempts to present some of the ideas, methods and applications in the study of the kinetic processes in nonideal gases and plasmas. The first part focuses on the classical kinetic theory of nonideal gases. The second part discusses the classical kinetic theory of fully ionized plasmas. The last part is devoted to the quantum kinetic theory of nonideal gases and plasmas. A concluding chapter is included, which presents a short account of the kinetic theory of chemically reacting systems and of partially ionized plasmas, in order to espouse further studies in the field. Physicists, scientific researchers, professors, and graduate students in various fields will find the text of good use.

## Table of Contents

Preface

Part I Kinetic Theory of Non-ideal Gases

Introduction

Chapter 1 The Method of Distribution Functions and the Method of Moments

Section 1 Equations for the Position and Momentum Distribution Functions in a Gas of Monatomic Particles

Section 2 The Approximation of Binary Collisions

Section 3 The Weak Coupling Approximation. The Polarization Approximation

Section 4 The Equation for the Phase Space Density in the Six-dimensional Position and Momentum Space

Section 5 The Method of Moments

Section 6 The Approximations of the First and Second Moments. The polarization approximation

Section 7 Transport Equations for the Mass Density, Momentum Density and Kinetic Energy Density

Chapter 2 The Boltzmann Kinetic Equation for Non-ideal Gases

Section 8 Some Results of the Equilibrium Statistical Theory of Non-ideal Gases

Section 9 Nonlinear Integral Equations for the Two-particle Correlation Function

Section 10 The Boltzmann Kinetic Equation for the Spatially Homogeneous Ideal Gas

Section 11 Properties of the Boltzmann Collision Integral for the Ideal Gas

Section 12 The Boltzmann Kinetic Equation for a Spatially Homogeneous Non-ideal Gas

Section 13 The Collision Integral in the Weak Coupling Approximation. The Landau Kinetic Equation

Section 14 Boltzmann's H-theory for the Non-ideal Gas

Section 15 The Boltzmann Equation for a Spatially Inhomogeneous Non-ideal Gas

Chapter 3 Kinetic Equations for Dense Gases

Section 16 Problems of the Kinetic Theory of Dense Gases

Section 17 Kinetic Equations for Non-ideal Gases Taking into Account Triple Collisions

Section 18 Kinetic Equations for the Smoothed Density of a Gas

Section 19 On the Statistical Description of Non-equilibrium Processes in Dense Gases

Section 20 Generalized Kinetic Equation

Chapter 4 Kinetic Theory of Fluctuations in Gases

Section 21 Equation for the Smoothed Distribution Functions in the Polarization Approximation

Section 22 Equation for the Smoothed Phase Density. The Method of Moments

Section 23 Random Sources in the Boltzmann Kinetic Equation and in the Hydrodynamical Equations

Part II Kinetic Theory of Non-ideal Fully Ionized Plasmas

Introduction

Chapter 5 The Microscopic Equations for a Fully Ionized Plasma and their Average

Section 24 Microscopic Equations for a Fully Ionized Plasma

Section 25 Microscopic Equations for a Coulomb Plasma

Section 26 Averaging of the Microscopic Equations

Section 27 Approximation of Binary Collisions and Polarization Approximation for Plasmas

Section 28 Transport Equations for the Density, the Momentum Density and the Energy Density of the Particles. Transport Equations for the Energy Density and the Momentum Density of the Electromagnetic Field

Chapter 6 Kinetic Equations for the Plasma in the First Moment Approximation. The Vlasov Equation

Section 29 Kinetic Description of the Processes in a Collision-less Plasma

Section 30 The Linear Approximation

Section 31 Electrical Conductivity and Dielectric Constant of a Collision-less Plasma

Section 32 Wave Properties of a Collision-less Plasma

Chapter 7 Kinetic Equations for the Ideal Fully Ionized Plasma

Section 33 Limitations Necessary for the Derivation of Kinetic Equations

Section 34 Spectral Densities of the Source Fluctuations in the Ideal Plasma

Section 35 Spectral Densities of Fluctuations in the Ideal Plasma

Section 36 Spectral Densities of the Fluctuations in the Equilibrium Plasma

Section 37 The Balescu-Lenard Kinetic Equation

Section 38 The Landau Kinetic Equation

Section 39 Spectral Densities of Fluctuations in a Relativistic Plasma

Section 40 Kinetic Equation for a Relativistic Plasma

Chapter 8 Effect of an External Field on the Kinetic Properties of Plasmas

Section 41 Equations for the Functions fa, δNa in the Presence of an External Field

Section 42 Spectral Density of the Source Fluctuations in the Presence of a High-frequency Electric Field

Section 43 Spectral Density of the Electric Field Fluctuations

Section 44 Kinetic Equation of a Plasma in a High-frequency Electric Field

Section 45 Conductivity of a Plasma in a High-frequency Electric Field

Section 46 Low Frequencies

Section 47 The Effective Potential Originating from the Average Dynamical Polarization

Section 48 Electrical Conductivity and Effective Potential

Section 49 Fluctuations in the Presence of a Magnetic Field

Section 50 Kinetic Equation for a Plasma in the Presence of an External Magnetic Field

Chapter 9 The Spatially Homogeneous Non-ideal Plasma

Section 51 Spectral Densities of Non-stationary Processes

Section 52 Spectral Densities of the Source Fluctuations in a Non-ideal Plasma

Section 53 The Landau Kinetic Equation for a Non-ideal Plasma

Section 54 The Balescu-Lenard Equation for a Non-ideal Plasma

Section 55 The Collision Integral of the Non-ideal Plasma, Taking into Account the Averaged Dynamical Polarization

Section 56 Boltzmann Kinetic Equation for a Non-ideal Plasma

Section 57 Interaction of Charged Particles with Plasmons

Chapter 10 The Spatially Inhomogeneous Non-ideal Plasma

Section 58 Relation Between Collision Integral and Spectral Density of Fluctuations

Section 59 The Collision Integral

Section 60 Properties of the Collision Integral

Chapter 11 Kinetic Theory of Fluctuations in a Plasma

Section 61 Equations for the Smoothed Phase-space Density and Field

Section 62 The Method of Moments. The Polarization Approximation

Section 63 The Spectral Densities of the Long-range Fluctuations

Section 64 Kinetic Equations for Plasmas with Account of the Long-range Fluctuations

Section 65 Hydrodynamical Equations with Account of the Long-range Fluctuations

Part III Quantum Kinetic Equations for Non-ideal Gases and Non-ideal Plasmas

Introduction

Chapter 12 Quantum Kinetic Equations for Non-ideal Gases

Section 66 Hierarchy of Equations for the Quantum Distribution Functions. The Binary Collision Approximation

Section 67 Macroscopic Equations and Thermodynamic Functions for Non-ideal Gases

Section 68 Two Forms of the Quantum Collision Integral

Section 69 The Weak Coupling Approximation

Section 70 Quantum Boltzmann Collision Integral for Non-ideal Gases, with Account of the Exchange Effects

Chapter 13 Quantum Kinetic Equations for Plasmas

Section 71 The Phase-space Density Operator

Section 72 The Equations for the Moments

Section 73 The Polarization Approximation

Section 74 The Quantum Collision Integral in the Polarization Approximation

Section 75 The Effective Potential. The Pseudopotential

Section 76 The Quantum Boltzmann Equation for a Non-ideal Plasma

Section 77 Thermodynamic Functions of the Non-ideal Plasma

Section 78 Exchange Effects

Chapter 14 Kinetic Equations for Partially Ionized Plasmas and for Chemically Reacting Gases

Section 79 Partially Ionized Plasmas. Initial Model

Section 80 Kinetic Equations for the Distribution Functions of Electrons, Ions and Atoms

Section 81 Chemically Reacting Gases. Initial Model

Section 82 Kinetic Equations for Chemically Reacting Gases

Section 83 Equations for the Concentrations of Free and Bound Charged Particles. Ionization and Recombination Coefficients

Section 84 Effect of the Electromagnetic Field Fluctuations on the Kinetic Processes in a Partially Ionized Plasma

Section 85 Kinetic Theory of Fluctuations in Chemically Reacting Gases and in Partially Ionized Plasmas

References

Index

Other Titles in the Series

## Product details

- No. of pages: 328
- Language: English
- Copyright: © Pergamon 1982
- Published: January 1, 1982
- Imprint: Pergamon
- eBook ISBN: 9781483145440

## About the Author

### Yu L Klimontovich

## About the Editor

### D. ter Haar

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