Kinetic theory is the link between the non--equilibrium statistical mechanics of many particle systems and macroscopic or phenomenological physics. Therefore much attention is paid in this book both to the derivation of kinetic equations with their limitations and generalizations on the one hand, and to the use of kinetic theory for the description of physical phenomena and the calculation of transport coefficients on the other hand. The book is meant for researchers in the field, graduate students and advanced undergraduate students. At the end of each chapter a section of exercises is added not only for the purpose of providing the reader with the opportunity to test his understanding of the theory and his ability to apply it, but also to complete the chapter with relevant additions and examples that otherwise would have overburdened the main text of the preceding sections. The author is indebted to the physicists who taught him Statistical Mechanics, Kinetic Theory, Plasma Physics and Fluid Mechanics. I gratefully acknowledge the fact that much of the inspiration without which this book would not have been possible, originated from what I learned from several outstanding teachers. In particular I want to mention the late Prof. dr. H. C. Brinkman, who directed my first steps in the field of theoretical plasma physics, my thesis advisor Prof. dr. N. G. Van Kampen and Prof. dr. A. N. Kaufman, whose course on Non-Equilibrium Statistical Mechanics in Berkeley I remember with delight.

Inhalt

1. Introduction.- 1.1. The nature and the goals of kinetic theory. Summary and related books..- 1.2. Some concepts from probability theory..- 1.3. Some properties of the Dirac delta function..- 1.4. Phase spaces, conservation of probability and the Liouville equation..- 1.5 Microscopic and macroscopic quantities..- 1.6. Exercises..- 2. Balance Equations.- 2.1. Conservation of particles.- 2.2. Momentum equation..- 2.3. Energy equation..- 2.4. Exercises..- 3. Klimontovich Equation, b.b.g.k.y.-hierarchy and vlasov-maxwell Equations.- 3.2. Densities in µ-space..- 3.2. Klimontovich equation..- 3.3. Vlasov-Maxwell equations..- 3.4. The first equation of the B.B.G.K.Y.-hierarchy..- 3.5. The complete hierarchy..- 3.6. Derivation of the B.B.G.K.Y.-hierarchy..- 3.7. Exercises..- 4. Derivation and Properties of the boltzmann equation.- 4.1. The small parameter of the Boltzmann gas..- 4.2. Multiple-time-scales formalism..- 4.3. Derivation of the Boltzmann equation..- 4.4. Dynamics of binary collisions..- 4.5. Boltzmann equation and Markov processes..- 4.6. Properties of the Boltzmann equation..- 4.7. Discussion of irreversibility..- 4.8. Exercises..- 5. Chapman-enskog theory: Asymptotic solution to the boltzmann equation; transport Coefficients.- 5.1. Introduction and table of characteristic quantities..- 5.2. Balance equations..- 5.3. Power series in the Knudsen number and the multiple time scale formalism revisited..- 5.4. The role of entropy and the thermodynamic identity..- 5.5. The eigenvalues of the linearized collision Operator and transport coefficients..- 5.6. The Maxwell gas..- 5.7. Non-Maxwellian intermolecular interaction..- 5.8. Exercises..- 6. Kinetic theory of Plasmas in the binary collision Approximation..- 6.1. Kinetic theory of gas mixtures. Lorentz gas..- 6.2.The electrons in a very weakly ionized gas..- 6.3. The Landau equation for a fully ionized plasma..- 6.4. Calculation of the electrical conductivity..- 6.5. Exercises..- 7. B.G.K.-Models and the slip problem..- 7.1. Linear B.G.K.-model. Its relation to the Boltzmann equation..- 7.2. The non-linear B.G.K.-model. Linearization..- 7.3. The slip problem of Kramers..- 7.4. Solution to the B.G.K. integro-differential equation..- 7.5. The singular integral equation and hydrodynamic slip..- 7.6. The microscopic slip velocity..- 7.7. Exercises..- 8. Kinetic theory of Plasmas, including dynamical screening..- 8.1. Collisions and screening in plasmas. The Lenard approach..- 8.2. The interaction between two charged particles in a dielectric medium..- 8.3. Properties of the Lenard-Balescu equation..- 8.4. The Landau equation as an approximation to the Lenard-Balescu equation..- 8.5. Completely convergent collision integrals..- 8.6. The electrical conductivity at rather high frequencies..- 8.7. Excercises..- 9. Linear Response Theory.- 9.1. Linearized Liouville equation..- 9.2. Kubo formulae..- 9.3. Electrical conductivity..- 9.4. Internal agencies..- 9.5. Longtime tail of autocorrelation functions..- 9.6. Exercises..- 10. Brownian Motion.- 10.1. Statistical description. Markov processes..- 10.2. Generalized theory of the velocity autocorrelation function..- 10.3. Hydrodynamic fluctuations and the generalized Langevin equation..- 10.4. Discussion of the velocity autocorrelation function..- 10.5. Exercises..- Appendix..- 11. Dense Gases, Renormalized kinetic theory.- 11.1. The Enskog equation for hard sphere dense gases..- 11.2. Limitations of Bogoliubov approach revisited. Hard-sphere gases..- 11.3. Renormalization of collisional effects..- 11.4. Memory effects in hard-sphere gasesand self-diffusion..- 11.5. Exercises..- 12. Theory of (Slightly) nonideal Plasmas.- 12.1. The Klimontovich equation revisited..- 12.2. The expansion scheme..- 12.3. The electrical conductivity at frequencies much lower than the plasma frequency..- 12.4. The electrical conductivity at high frequencies.- 12.5. The dispersion relation for plasma waves..- 12.6. Remarks about strongly non-ideal plasmas..- 12.7. Exercises..- References..- Index..