Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neutrino emission during the gravitational collapse.
Author(s): Gregory V. Vereshchagin, Alexey G. Aksenov
Publisher: Cambridge University Press
Year: 2017
Language: English
Pages: 344
Contents......Page 5
Acknowledgments......Page 10
Acronyms and Definitions......Page 11
Introduction......Page 14
Part I Theoretical Foundations......Page 20
1.1 Nonrelativistic Kinetic Theory......Page 22
1.2 Special Relativistic Kinetic Theory......Page 23
1.3 General Relativistic Kinetic Theory......Page 24
1.4 One-Particle Distribution Function......Page 25
1.5 Invariance of One-Particle Distribution Function......Page 26
1.6 Macroscopic Quantities......Page 27
2.1 Formulation of Kinetic Equation......Page 29
2.2 Collision Integral for Particle Scattering......Page 31
2.3 Boltzmann Equation in General Relativity......Page 32
2.5 Radiative Transfer......Page 34
2.6 Cross Section......Page 37
2.7 Relaxation Time......Page 38
3.1 Covariant Statistical Averaging......Page 39
3.3 The Role of Averaging in Kinetic Theory......Page 41
4.1 Conservation Laws and Relativistic Hydrodynamics......Page 43
4.2 H-theorem......Page 45
4.3 Equilibrium......Page 46
4.4 Relativistic Maxwellian Distribution......Page 49
4.5 Generalized Continuity Equation......Page 50
5.1 The Hierarchy of Kinetic Equations......Page 53
5.2 The First and Second Approximations in Relativistic Transport Equations......Page 57
5.3 The Vlasov-Maxwell System......Page 58
5.4 The Vlasov-Einstein System......Page 61
6.1 Plasma Frequency......Page 63
6.2 Correlations in Plasma......Page 64
6.3 Coulomb Collisions......Page 65
6.4 Characteristic Distances......Page 66
6.5 Microscopic Scales in Kinetic Theory and Hydrodynamics......Page 68
6.6 Relativistic Degeneracy......Page 69
Part II Numerical Methods......Page 72
7.1 Finite Differences and Computational Grids......Page 74
7.2 Stability and Accuracy of Numerical Schemes......Page 76
7.3 Numerical Methods for Partial Differential Equations......Page 79
7.5 ODE Systems and Methods of Their Solution......Page 96
7.6 Stiff Systems and Gear’s Method......Page 98
7.7 Numerical Methods for Linear Algebra......Page 102
8.1 Finite Differences and the Method of Lines......Page 108
8.2 Monte Carlo Method......Page 112
9 Multidimensional Hydrodynamics......Page 119
9.1 High-Order Godunov Methods......Page 120
9.2 Multidimensional Multitemperature High-Order Godunov Code......Page 122
9.3 Riemann Problem Solver in Special Relativity......Page 136
9.4 Particle-Based Methods......Page 139
Part III Applications......Page 146
10 Wave Dispersion in Relativistic Plasma......Page 148
10.1 Collisionless Plasma......Page 150
10.2 Response in an Isotropic Case......Page 151
10.3 Dispersion in Relativistic Thermal Plasma......Page 152
10.4 Landau Damping......Page 154
10.5 Plasma Instabilities......Page 156
10.6 Weibel Instability......Page 157
10.7 Two-Stream Instability......Page 160
10.8 Collisionless Shock Waves......Page 161
11.1 Pair Plasma in Astrophysics and Cosmology......Page 164
11.2 Qualitative Description of the Pair Plasma......Page 166
11.3 Collision Integrals......Page 167
11.4 Relativistic Boltzmann Equation on the Grid......Page 179
11.5 Thermalization Process......Page 180
11.6 Thermalization Timescales......Page 186
11.7 Dynamics and Emission of Mildly Relativistic Plasma......Page 190
11.8 Kinetic Equilibrium and Chemical Potential of Photons......Page 194
12 Kinetics of Particles in Strong Fields......Page 195
12.1 Avalanches in Strong Crossing Laser Fields......Page 196
12.2 Creation and Thermalization of Pairs in Strong Electric Fields......Page 199
12.3 Emission from Hot Bare Quark Stars......Page 211
13.1 The Boltzmann Equation for Compton Scattering......Page 216
13.2 Mean Number of Scatterings......Page 217
13.3 Kompaneets Equation......Page 219
13.4 Sunyaev-Zeldovich Effect......Page 223
13.5 Comptonization in Static Media......Page 227
13.6 Comptonization in Relativistic Outflows......Page 229
13.7 Monte Carlo Simulations of the Photospheric Emission from Relativistic Outflows......Page 233
14 Self-Gravitating Systems......Page 239
14.1 Kinetic Theory of Self-Gravitating Systems......Page 241
14.2 Gravitational Instability......Page 249
14.3 Collisionless (Violent) Relaxation......Page 263
14.4 Quasi-stationary States......Page 266
14.5 Self-Gravitating Systems in Equilibrium......Page 268
14.6 Cosmic Structure Formation......Page 273
15.1 Supernova Models and Neutrinos......Page 275
15.2 Spherically Symmetric Collapse of a Stellar Iron Core with Neutrino Transport......Page 278
15.3 Supernova Explosion Mechanism with Large-Scale Convection and Neutrino Transport......Page 287
Appendix A Hydrodynamic Equations in Orthogonal Curvilinear Coordinates......Page 291
B.1 Collision Integrals for Binary Interactions......Page 294
B.2 Collision Integrals for Binary Reactions with Protons......Page 300
B.3 Collision Integrals for Triple Interactions......Page 302
B.4 Mass Scaling for the Proton-Electron/Positron Reaction......Page 304
C.1 Scattering of Neutrinos on Electrons......Page 306
C.2 Absorption of Neutrinos by Neutrons......Page 308
C.3 Creation of Neutrinos......Page 310
Bibliography......Page 312
Index......Page 339
