Physical Kinetics

This volume is mainly concerned with a systematic development of the theory of plasmas, the authority being firmly rooted in the pioneering work of Landau. Corresponding results are also given for partially ionized plasmas, relativistic plasmas, degenerate or non-ideal plasmas and solid state plasmas.

Preface

ix

Natation

xi

I. KINETIC THEORY OF GASES

The distribution function

1

(3)

The principle of detailed balancing

4

(3)

The Boltzmann transport equation

7

(4)

The H theorem

11

(2)

The change to macroscopic equations

13

(4)

The transport equation for a slightly inhomogeneous gas

17

(4)

Thermal conduction in the gas

21

(3)

Viscosity in the gas

24

(2)

Symmetry of the kinetic coefficients

26

(4)

Approximate solution of the transport equation

30

(6)

Diffusion of a light gas in a heavy gas

36

(4)

Diffusion of a heavy gas in a light gas

40

(2)

Transport phenomena in a gas in an external field

42

(6)

Phenomena in slightly rarefied gases

48

(8)

Phenomena in highly rarefied gases

56

(11)

Dynamical derivation of the transport equation

67

(5)

The transport equation including three-particle collisions

72

(5)

The virial expansion of the kinetic coefficients

77

(2)

Fluctuations of the distribution function in an equilibrium gas

79

(5)

Fluctuations of the distribution function in a non-equilibrium gas

84

(5)

II. THE DIFFUSION APPROXIMATION

The Fokker-Planck equation

89

(4)

A weakly ionized gas in an electric field

93

(4)

Fluctuations in a weakly ionized non-equilibrium gas

97

(5)

Recombination and ionization

102

(4)

Ambipolar diffusion

106

(2)

Ion mobility in solutions of strong electrolytes

108

(7)

III. COLLISIONLESS PLASMAS

The self-consistent field

115

(3)

Spatial dispersion in plasmas

118

(3)

The permittivity of a collisionless plasma

121

(3)

Landau damping

124

(4)

Permittivity of a Maxwellian plasma

128

(5)

Longitudinal plasma waves

133

(3)

Ion-sound waves

136

(2)

Relaxation of the initial perturbation

138

(4)

Plasma echoes

142

(4)

Adiabatic electron capture

146

(3)

Quasi-neutral plasmas

149

(3)

Fluid theory for a two-temperature plasma

152

(2)

Solitons in a weakly dispersing medium

154

(7)

Permittivity of a degenerate collisionless plasma

161

(7)

IV. COLLISIONS IN PLASMAS

The Landau collision integral

168

(5)

Energy transfer between electrons and ions

173

(2)

Mean free path of plasma particles

175

(2)

Lorentzian plasmas

177

(4)

Runaway electrons

181

(3)

Convergent collision integrals

184

(9)

Interaction via plasma waves

193

(3)

Plasma absorption in the high-frequency limit

196

(3)

Quasi-linear theory of Landau damping

199

(6)

The transport equation for a relativistic plasma

205

(4)

Fluctuations in plasmas

209

(8)

V. PLASMAS IN MAGNETIC FIELDS

Permittivity of a collisionless cold plasma

217

(3)

The distribution function in a magnetic field

220

(4)

Permittivity of a magnetoactive Maxwellian plasma

224

(2)

Landau damping in magnetoactive plamas

226

(5)

Electromagnetic waves in a magnetoactive cold plasma

231

(7)

Effect of thermal motion on electromagnetic wave propagation in magnetoactive plasmas

238

(3)

Equations of fluid dynamics in a magnetoactive plasma

241

(4)

Transport coefficients of a plasma in a strong magnetic field

245

(10)

The drift approximation

255

(10)

VI. INSTABILITY THEORY

Beam instability

265

(3)

Absolute and convective instabilities

268

(5)

Amplification and non-transparency

273

(3)

Instability with weak coupling of the two branches of the oscillation spectrum

276

(5)

Instability in finite systems

281

(3)

VII. INSULATORS

Interaction of phonons

284

(4)

The transport equation for phonons in an insulator

288

(4)

Thermal conduction in insulators. High temperatures

292

(5)

Thermal conduction in insulators. Low temperatures

297

(4)

Phonon scattering by impurities

301

(1)

Phonon gas dynamics in insulators

302

(3)

Sound absorption in insulators. Long waves

305

(4)

Sound absorption in insulators. Short waves

309

(3)

VIII. QUANTUM LIQUIDS

Transport equation for quasi-particles in a Fermi liquid

312

(6)

Thermal conductivity and viscosity of a Fermi liquid

318

(2)

Sound absorption in a Fermi liquid

320

(4)

Transport equation for quasi-particles in a Bose liquid

324

(5)

IX. METALS

Residual resistance

329

(5)

Electron-phonon interaction

334

(5)

Transport coefficients in metals. High temperatures

339

(3)

Umklapp processes in metals

342

(4)

Transport coefficients in metals. Low temperatures

346

(7)

Electron diffusion on the Fermi surface

353

(5)

Galvanomagnetic phenomena in strong fields. General theory

358

(5)

Galvanomagnetic phenomena in strong fields. Particular cases

363

(5)

Anomalous skin effect

368

(8)

Skin effect in the infra-red range

376

(2)

Helicon waves in metals

378

(3)

Magnetoplasma waves in metals

381

(2)

Quantum oscillations of the conductivity of metals in a magnetic field

383

(8)

X. THE DIAGRAM TECHNIQUE FOR NON-EQUILIBRIUM SYSTEMS

The Matsubara susceptibility

391

(4)

Green's functions for a non-equilibrium system

395

(6)

The diagram technique for non-equilibrium systems

401

(3)

Self-energy functions

404

(4)

The transport equation in the diagram technique

408

(5)

XI. SUPERCONDUCTORS

High-frequency properties of superconductors. General formula

413

(6)

High-frequency properties of superconductors. Limiting cases

419

(5)

Thermal conductivity of superconductors

424

(3)

XII. KINETICS OF PHASE TRANSITIONS

Kinetics of first-order phase transitions. Nucleation

427

(5)

Kinetics of first-order phase transitions. Coalescence

432

(6)

Relaxation of the order parameter near a second-order phase transition

438

(3)

Dynamical scale invariance

441

(2)

Relaxation in liquid helium near the λ-point

443

(6)

Index

449

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