Kinetic Theory of Gases and Plasmas

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..