The Kinetic Theory of Inert Dilute Plasmas (Springer 2009)

Leopoldo S. García-Colín, Leonardo Dagdug9781402093296, 1402093292

This book results from recent studies aimed at answering questions raised by astrophycists who use values of transport coefficients that are old and often unsatisfactory. The few books dealing with the rigorous kinetic theory of a ionized plasma are based on the so called Landau (Fokker-Planck) equation and they seldom relate the microscopic results with their macroscopic counterpart provided by classical non-equilibrium thermodynamics. In this book both issues are thoroughly covered. Starting from the full Boltzmann equation for inert dilute plasmas and using the Hilbert-Chapman-Enskog method to solve the first two approximations in Knudsen´s parameter, we construct all the transport properties of the system within the framework of linear irreversible thermodynamics. This includes a systematic study of all possible cross effects (which, except for a few cases, were never treated in the literature) as well as the famous H-theorem. The equations of magneto-hydrodynamics for dilute plasmas, including the rather surprising results obtained for the viscomagnetic effects, may be now fully assessed. This book will be of immediate interest to the plasma physics community, as well as to astrophysicists. It is also likely to make an impact in the field of cold plasmas, involving laser cooled Rydberg atoms.

---

Table of contents :
The Kinetic Theory
of a Dilute Ionized Plasma
……Page 1
Acknowledgement……Page 6
Contents……Page 7
Introduction……Page 9
Part I.
Vector Transport Processes……Page 11
1. Non-equilibrium
Thermodynamics……Page 12
2.
The Problem……Page 19
3. Solution of the Boltzmann
Equation
……Page 29
4.
Calculation of the Currents……Page 43
5.
Solution of the Integral Equations……Page 51
6.
The Transport Coefficients……Page 60
7.
Discussion of the Results……Page 71
Part II.

Tensorial Transport Processes……Page 78
8. Viscomagnetism
……Page 79
9. Magnetohydrodynamics
……Page 102
A.
Calculation of M……Page 118
B. Linearized Boltzmann Collision
Kernels……Page 121
C.
The Case when B = 0……Page 124
D.
The Collision Integrals……Page 135
E.
Calculation of the Coefficients a(0), a(1), d(0) and d(1)……Page 142
F.
The proof of the equalities given in Eq. (8.7)……Page 144
G.
List of useful integrals……Page 145
Appendix H……Page 146
I. List of Marshall’s Equations
and Notation……Page 148
Index……Page 151