Plasma Astrophysics

by Somov, Boris V.

• ISBN13: 9780387349169
• ISBN10: 0387349162
• Format: Hardcover
• Copyright: 2006-10-30
• Publisher: Springer Verlag

Summary

This well-illustrated monograph is devoted to classic fundamentals, current practice, and perspectives of modern plasma astrophysics. The first part of the book is unique in covering all the basic principles and practical tools required for understanding and work in plasma astrophysics. The second part represents the physics of magnetic reconnection and flares of electromagnetic origin in space plasmas in the solar system, single and double stars, relativistic objects, accretion disks, their coronae. The level of the book is designed mainly for professional researchers in astrophysics. The book will also be interesting and useful to graduate students in space sciences, geophysics, as well as to advanced students in applied physics and mathematics seeking a unified view of plasma physics and fluid mechanics.

Author Biography

Boris Somov is a professor at the Moscow State University, laureate of the State Prize of the former USSR (the Honour Prize of the USSR Government), and laureate of the IBC Award GÇÿ2000 Outstanding People of the 20th Century' in honour of his contribution to space physics. Three well-known monographs "Physical Processes in Solar Flares", "Fundamental of Cosmic Electrodynamics", and "Cosmic Plasma Physics" by Boris Somov were published by Kluwer Academic Publishers in 1992, 1994 and 2000. He has contributed more than 170 articles to the scientific literature in solar physics and plasma astrophysics.

Table of Contents

About This Book	xiii
Plasma Astrophysics: History and Neighbours	1	(182)
1 Particles and Fields: Exact Self-Consistent Description	3	(16)
1.1 Interacting particles and Liouville's theorem	3	(8)
1.1.1 Continuity in phase space	3	(2)
1.1.2 The character of particle interactions	5	(2)
1.1.3 The Lorentz force, gravity	7	(1)
1.1.4 Collisional friction in plasma	7	(2)
1.1.5 The exact distribution function	9	(2)
1.2 Charged particles in the electromagnetic field	11	(3)
1.2.1 General formulation of the problem	11	(1)
1.2.2 The continuity equation for electric charge	12	(1)
1.2.3 Initial equations and initial conditions	12	(1)
1.2.4 Astrophysical plasma applications	13	(1)
1.3 Gravitational systems	14	(1)
1.4 Practice: Exercises and Answers	15	(4)
2 Statistical Description of Interacting Particle Systems	19	(16)
2.1 The averaging of Liouville's equation	19	(7)
2.1.1 Averaging over phase space	19	(2)
2.1.2 Two statistical postulates	21	(1)
2.1.3 A statistical mechanism of mixing in phase space	22	(2)
2.1.4 The derivation of a general kinetic equation	24	(2)
2.2 A collisional integral and correlation functions	26	(5)
2.2.1 Binary interactions	26	(1)
2.2.2 Binary correlation	27	(2)
2.2.3 The collisional integral and binary correlation	29	(2)
2.3 Equations for correlation functions	31	(2)
2.4 Practice: Exercises and Answers	33	(2)
3 Weakly-Coupled Systems with Binary Collisions	35	(20)
3.1 Approximations for binary collisions	35	(7)
3.1.1 The small parameter of kinetic theory	35	(2)
3.1.2 The Vlasov kinetic equation	37	(1)
3.1.3 The Landau collisional integral	38	(1)
3.1.4 The Fokker-Planck equation	39	(3)
3.2 Correlation function and Debye shielding	42	(4)
3.2.1 The Maxwellian distribution function	42	(1)
3.2.2 The averaged force and electric neutrality	42	(1)
3.2.3 Pair correlations and the Debye radius	43	(3)
3.3 Gravitational systems	46	(1)
3.4 Comments on numerical simulations	47	(1)
3.5 Practice: Exercises and Answers	48	(7)
4 Propagation of Fast Particles in Plasma	55	(24)
4.1 Derivation of the basic kinetic equation	55	(3)
4.1.1 Basic approximations	55	(2)
4.1.2 Dimensionless kinetic equation in energy space	57	(1)
4.2 A kinetic equation at high speeds	58	(2)
4.3 The classical thick-target model	60	(4)
4.4 The role of angular diffusion	64	(3)
4.4.1 An approximate account of scattering	64	(1)
4.4.2 The thick-target model	65	(2)
4.5 The reverse-current electric-field effect	67	(10)
4.5.1 The necessity for a beam-neutralizing current	67	(2)
4.5.2 Formulation of a realistic kinetic problem	69	(3)
4.5.3 Dimensionless parameters of the problem	72	(1)
4.5.4 Coulomb losses of energy	73	(2)
4.5.5 New physical results	75	(1)
4.5.6 To the future models	76	(1)
4.6 Practice: Exercises and Answers	77	(2)
5 Motion of a Charged Particle in Given Fields	79	(24)
5.1 A particle in constant homogeneous fields	79	(7)
5.1.1 Relativistic equation of motion	79	(1)
5.1.2 Constant non-magnetic forces	80	(1)
5.1.3 Constant homogeneous magnetic fields	81	(2)
5.1.4 Non-magnetic force in a magnetic field	83	(1)
5.1.5 Electric and gravitational drifts	84	(2)
5.2 Weakly inhomogeneous slowly changing fields	86	(11)
5.2.1 Small parameters in the motion equation	86	(1)
5.2.2 Expansion in powers of m/e	87	(2)
5.2.3 The averaging over gyromotion	89	(2)
5.2.4 Spiral motion of the guiding center	91	(1)
5.2.5 Gradient and inertial drifts	92	(5)
5.3 Practice: Exercises and Answers	97	(6)
6 Adiabatic Invariants in Astrophysical Plasma	103	(12)
6.1 General definitions	103	(1)
6.2 Two main invariants	104	(7)
6.2.1 Motion in the Larmor plane	104	(1)
6.2.2 Magnetic mirrors and traps	105	(3)
6.2.3 Bounce motion	108	(1)
6.2.4 The Fermi acceleration	109	(2)
6.3 The flux invariant	111	(1)
6.4 Approximation accuracy. Exact solutions	112	(1)
6.5 Practice: Exercises and Answers	113	(2)
7 Wave-Particle Interaction in Astrophysical Plasma	115	(18)
7.1 The basis of kinetic theory	115	(7)
7.1.1 The linearized Vlasov equation	115	(2)
7.1.2 The Landau resonance and Landau damping	117	(3)
7.1.3 Gyroresonance	120	(2)
7.2 Stochastic acceleration of particles by waves	122	(5)
7.2.1 The principles of particle acceleration by waves	122	(2)
7.2.2 The Kolmogorov theory of turbulence	124	(2)
7.2.3 MHD turbulent cascading	126	(1)
7.3 The relativistic electron-positron plasma	127	(1)
7.4 Practice: Exercises and Answers	128	(5)
8 Coulomb Collisions in Astrophysical Plasma	133	(30)
8.1 Close and distant collisions	133	(6)
8.1.1 The collision parameters	133	(1)
8.1.2 The Rutherford formula	134	(1)
8.1.3 The test particle concept	135	(1)
8.1.4 Particles in a magnetic trap	136	(1)
8.1.5 The role of distant collisions	137	(2)
8.2 Debye shielding and plasma oscillations	139	(3)
8.2.1 Simple illustrations of the shielding effect	139	(2)
8.2.2 Charge neutrality and oscillations in plasma	141	(1)
8.3 Collisional relaxations in cosmic plasma	142	(9)
8.3.1 Some exact solutions	142	(2)
8.3.2 Two-temperature plasma in solar flares	144	(4)
8.3.3 An adiabatic model for two-temperature plasma	148	(2)
8.3.4 Two-temperature accretion flows	150	(1)
8.4 Dynamic friction in astrophysical plasma	151	(7)
8.4.1 The collisional drag force and energy losses	151	(4)
8.4.2 Electric runaway	155	(2)
8.4.3 Thermal runaway in astrophysical plasma	157	(1)
8.5 Practice: Exercises and Answers	158	(5)
9 Macroscopic Description of Astrophysical Plasma	163	(20)
9.1 Summary of microscopic description	163	(1)
9.2 Transition to macroscopic description	164	(1)
9.3 Macroscopic transfer equations	165	(8)
9.3.1 Equation for the zeroth moment	165	(1)
9.3.2 The momentum conservation law	166	(3)
9.3.3 The energy conservation law	169	(4)
9.4 General properties of transfer equations	173	(2)
9.4.1 Divergent and hydrodynamic forms	173	(1)
9.4.2 Status of conservation laws	174	(1)
9.5 Equation of state and transfer coefficients	175	(2)
9.6 Gravitational systems	177	(1)
9.7 Practice: Exercises and Answers	178	(5)
10 Multi-Fluid Models of Astrophysical Plasma	183	(10)
10.1 Multi-fluid models in astrophysics	183	(1)
10.2 Langmuir waves	184	(4)
10.2.1 Langmuir waves in a cold plasma	184	(2)
10.2.2 Langmuir waves in a warm plasma	186	(1)
10.2.3 Ion effects in Langmuir waves	187	(1)
10.3 Electromagnetic waves in plasma	188	(2)
10.4 What do we miss?	190	(1)
10.5 Practice: Exercises and Answers	191	(2)
11 The Generalized Ohm's Law in Plasma	193	(12)
11.1 The classic Ohm's law	193	(1)
11.2 Derivation of basic equations	194	(2)
11.3 The general solution	196	(1)
11.4 The conductivity of magnetized plasma	197	(2)
11.4.1 Two limiting cases	197	(1)
11.4.2 The physical interpretation	198	(1)
11.5 Currents and charges in plasma	199	(4)
11.5.1 Collisional and collisionless plasmas	199	(2)
11.5.2 Volume charge and quasi-neutrality	201	(2)
11.6 Practice: Exercises and Answers	203	(2)
12 Single-Fluid Models for Astrophysical Plasma	205	(18)
12.1 Derivation of the single-fluid equations	205	(4)
12.1.1 The continuity equation	205	(1)
12.1.2 The momentum conservation law in plasma	206	(2)
12.1.3 The energy conservation law	208	(1)
12.2 Basic assumptions and the MHD equations	209	(7)
12.2.1 Old and new simplifying assumptions	209	(4)
12.2.2 Non-relativistic magnetohydrodynarnics	213	(2)
12.2.3 Relativistic magnetohydrodynamics	215	(1)
12.3 Magnetic flux conservation. Ideal MHD	216	(5)
12.3.1 Integral and differential forms of the law	216	(2)
12.3.2 The equations of ideal MHD	218	(3)
12.4 Practice: Exercises and Answers	221	(2)
13 Magnetohydrodynamics in Astrophysics	223	(20)
13.1 The main approximations in ideal MHD	223	(6)
13.1.1 Dimensionless equations	223	(2)
13.1.2 Weak magnetic fields in astrophysical plasma	225	(1)
13.1.3 Strong magnetic fields in plasma	226	(3)
13.2 Accretion disks of stars	229	(5)
13.2.1 Angular momentum transfer in binary stars	229	(2)
13.2.2 Magnetic accretion in cataclysmic variables	231	(1)
13.2.3 Accretion disks near black holes	231	(2)
13.2.4 Flares in accretion disk coronae	233	(1)
13.3 Astrophysical jets	234	(3)
13.3.1 Jets near black holes	234	(2)
13.3.2 Relativistic jets from disk coronae	236	(1)
13.4 Practice: Exercises and Answers	237	(6)
14 Plasma Flows in a Strong Magnetic Field	243	(20)
14.1 The general formulation of the problem	243	(2)
14.2 The formalism of two-dimensional problems	245	(7)
14.2.1 The first type of problems	245	(2)
14.2.2 The second type of MHD problems	247	(5)
14.3 On the existence of continuous flows	252	(1)
14.4 Flows in a time-dependent dipole field	253	(5)
14.4.1 Plane magnetic dipole fields	253	(3)
14.4.2 Axisymmetric dipole fields in plasma	256	(2)
14.5 Practice: Exercises and Answers	258	(5)
15 MHD Waves in Astrophysical Plasma	263	(14)
15.1 The dispersion equation in ideal MHD	263	(2)
15.2 Small-amplitude waves in ideal MHD	265	(6)
15.2.1 Entropy waves	265	(2)
15.2.2 Alfvén waves	267	(1)
15.2.3 Magnetoacoustic waves	268	(1)
15.2.4 The phase velocity diagram	269	(2)
15.3 Dissipative waves in MHD	271	(3)
15.3.1 Small damping of Alfvén waves	271	(2)
15.3.2 Slightly damped MHD waves	273	(1)
15.4 Practice: Exercises and Answers	274	(3)
16 Discontinuous Flows in a MHD Medium	277	(28)
16.1 Discontinuity surfaces in hydrodynamics	277	(4)
16.1.1 The origin of shocks in ordinary hydrodynamics	277	(1)
16.1.2 Boundary conditions and classification	278	(2)
16.1.3 Dissipative processes and entropy	280	(1)
16.2 Magnetohydrodynamic discontinuities	281	(15)
16.2.1 Boundary conditions at a discontinuity surface	281	(3)
16.2.2 Discontinuities without plasma flows across them	284	(2)
16.2.3 Perpendicular shock wave	286	(2)
16.2.4 Oblique shock waves	288	(5)
16.2.5 Peculiar shock waves	293	(1)
16.2.6 The Alfvén discontinuity	294	(2)
16.3 Transitions between discontinuities	296	(2)
16.4 Shock waves in collisionless plasma	298	(1)
16.5 Practice: Exercises and Answers	299	(6)
17 Evolutionarity of MHD Discontinuities	305	(22)
17.1 Conditions for evolutionarity	305	(8)
17.1.1 The physical meaning and definition	305	(2)
17.1.2 Linearized boundary conditions	307	(2)
17.1.3 The number of small-amplitude waves	309	(2)
17.1.4 Domains of evolutionarity	311	(2)
17.2 Consequences of evolutionarity conditions	313	(2)
17.2.1 The order of wave propagation	313	(2)
17.2.2 Continuous transitions between discontinuities	315	(1)
17.3 Dissipative effects in evolutionarity	315	(4)
17.4 Discontinuity structure and evolutionarity	319	(5)
17.4.1 Perpendicular shock waves	319	(4)
17.4.2 Discontinuities with penetrating magnetic field	323	(1)
17.5 Practice: Exercises and Answers	324	(3)
18 Particle Acceleration by Shock Waves	327	(16)
18.1 Two basic mechanisms	327	(1)
18.2 Shock diffusive acceleration	328	(4)
18.2.1 The canonical model of diffusive mechanism	328	(3)
18.2.2 Some properties of diffusive mechanism	331	(1)
18.2.3 Nonlinear effects in diffusive acceleration	332	(1)
18.3 Shock drift acceleration	332	(8)
18.3.1 Perpendicular shock waves	333	(2)
18.3.2 Quasi-perpendicular shock waves	335	(4)
18.3.3 Oblique shock waves	339	(1)
18.4 Practice: Exercises and Answers	340	(3)
19 Plasma Equilibrium in Magnetic Field	343	(24)
19.1 The virial theorem in MHD	343	(7)
19.1.1 A brief pre-history	343	(1)
19.1.2 Deduction of the scalar virial theorem	344	(3)
19.1.3 Some astrophysical applications	347	(3)
19.2 Force-free fields and Shafranov's theorem	350	(3)
19.2.1 The simplest examples of force-free fields	350	(2)
19.2.2 The energy of a force-free field	352	(1)
19.3 Properties of equilibrium configurations	353	(6)
19.3.1 Magnetic surfaces	353	(2)
19.3.2 The specific volume of a magnetic tube	355	(2)
19.3.3 The flute or convective instability	357	(1)
19.3.4 Stability of an equilibrium configuration	358	(1)
19.4 The Archimedean force in MHD	359	(2)
19.4.1 A general formulation of the problem	359	(1)
19.4.2 A simplified consideration of the effect	360	(1)
19.5 MHD equilibrium in the solar atmosphere	361	(2)
19.6 Practice: Exercises and Answers	363	(4)
20 Stationary Flows in a Magnetic Field	367	(26)
20.1 Ideal plasma flows	367	(7)
20.1.1 Incompressible medium	368	(1)
20.1.2 Compressible medium	369	(1)
20.1.3 Astrophysical collimated streams (jets)	369	(1)
20.1.4 MHD waves of arbitrary amplitude	370	(1)
20.1.5 Differential rotation and isorotation	371	(3)
20.2 Flows at small magnetic Reynolds numbers	374	(5)
20.2.1 Stationary flows inside a duct	374	(2)
20.2.2 The MHD generator or pump	376	(2)
20.2.3 Weakly-ionized plasma in astrophysics	378	(1)
20.3 The σ-dependent force and vortex flows	379	(7)
20.3.1 Simplifications and problem formulation	379	(2)
20.3.2 The solution for a spherical ball	381	(1)
20.3.3 Forces and flows near a spherical ball	382	(4)
20.4 Large magnetic Reynolds numbers	386	(5)
20.4.1 The general formula for the σ-dependent force	387	(2)
20.4.2 The σ-dependent force in solar prominences	389	(2)
20.5 Practice: Exercises and Answers	391	(2)
Appendix 1. Notation	393	(6)
Appendix 2. Useful Expressions	399	(4)
Appendix 3. Constants	403	(2)
Bibliography	405	(22)
Index	427