Plasma Astrophysics, Part I: Fundamentals and Practice

Plasma Astrophysics, Part I: Fundamentals and Practice

by Boris V. Somov

Hardcover(2nd ed. 2012)

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Product Details

ISBN-13: 9781461442820
Publisher: Springer New York
Publication date: 08/31/2012
Series: Astrophysics and Space Science Library , #391
Edition description: 2nd ed. 2012
Pages: 498
Product dimensions: 6.10(w) x 9.25(h) x 0.05(d)

About the Author

Boris Somov is a professor at the Moscow State University, laureate of the State Prize of the former USSR (the Honor Prize of the USSR Government), and laureate of the IBC Award, “2000 Outstanding People of the 20th Century,” in honor of his contribution to space physics and astrophysics.

Five well-known monographs, “Physical Processes in Solar Flares,” “Fundamentals of Cosmic Electrodynamics,” “Cosmic Plasma Physics” and “Plasma Astrophysics, Parts I&II (First Edition)” by Boris Somov were published by Kluwer Academic Publishers and Springer in 1992, 1994, 2000 and 2006, respectively. He has contributed more than 280 articles to the scientific literature in solar physics and plasma astrophysics.

Table of Contents

About This Book xiii

Plasma Astrophysics: History and Neighbours 1

1 Particles and Fields: Exact Self-Consistent Description 3

1.1 Interacting particles and Liouville's theorem 3

1.1.1 Continuity in phase space 3

1.1.2 The character of particle interactions 5

1.1.3 The Lorentz force, gravity 7

1.1.4 Collisional friction in plasma 7

1.1.5 The exact distribution function 9

1.2 Charged particles in the electromagnetic field 11

1.2.1 General formulation of the problem 11

1.2.2 The continuity equation for electric charge 12

1.2.3 Initial equations and initial conditions 12

1.2.4 Astrophysical plasma applications 13

1.3 Gravitational systems 14

1.4 Practice: Exercises and Answers 15

2 Statistical Description of Interacting Particle Systems 19

2.1 The averaging of Liouville's equation 19

2.1.1 Averaging over phase space 19

2.1.2 Two statistical postulates 21

2.1.3 A statistical mechanism of mixing in phase space 22

2.1.4 The derivation of a general kinetic equation 24

2.2 A collisional integral and correlation functions 26

2.2.1 Binary interactions 26

2.2.2 Binary correlation 27

2.2.3 The collisional integral and binary correlation 29

2.3 Equations for correlation functions 31

2.4 Practice: Exercises and Answers 33

3 Weakly-Coupled Systems with Binary Collisions 35

3.1 Approximations for binary collisions 35

3.1.1 The small parameter of kinetic theory 35

3.1.2 The Vlasov kinetic equation 37

3.1.3 The Landau collisional integral 38

3.1.4 The Fokker-Planck equation 39

3.2 Correlation function and Debye shielding 42

3.2.1 The Maxwellian distribution function 42

3.2.2 The averaged force and electric neutrality42

3.2.3 Pair correlations and the Debye radius 43

3.3 Gravitational systems 46

3.4 Comments on numerical simulations 47

3.5 Practice: Exercises and Answers 48

4 Propagation of Fast Particles in Plasma 55

4.1 Derivation of the basic kinetic equation 55

4.1.1 Basic approximations 55

4.1.2 Dimensionless kinetic equation in energy space 57

4.2 A Kinetic equation at high speeds 58

4.3 The classical thick-target model 60

4.4 The role of angular diffusion 64

4.4.1 An approximate account of scattering 64

4.4.2 The thick-target model 65

4.5 The reverse-current electric-field effect 67

4.5.1 The necessity for a beam-neutralizing current 67

4.5.2 Formulation of a realistic kinetic problem 69

4.5.3 Dimensionless parameters of the problem 72

4.5.4 Coulomb losses of energy 73

4.5.5 New physical results 75

4.5.6 To the future models 76

4.6 Practice: Exercises and Answers 77

5 Motion of a Charged Particle in Given Fields 79

5.1 A particle in constant homogeneous fields 79

5.1.1 Relativistic equation of motion 79

5.1.2 Constant non-magnetic forces 80

5.1.3 Constant homogeneous magnetic fields 81

5.1.4 Non-magnetic force in a magnetic field 83

5.1.5 Electric and gravitational drifts 84

5.2 Weakly inhomogeneous slowly changing fields 86

5.2.1 Small parameters in the motion equation 86

5.2.2 Expansion in powers of m/e 87

5.2.3 The averaging over gyromotion 89

5.2.4 Spiral motion of the guiding center 91

5.2.5 Gradient and inertial drifts 92

5.3 Practice: Exercises and Answers 97

6 Adiabatic Invariants in Astrophysical Plasma 103

6.1 General definitions 103

6.2 Two main invariants 104

6.2.1 Motion in the Larmor plane 104

6.2.2 Magnetic mirrors and traps 105

6.2.3 Bounce motion 108

6.2.4 The Fermi acceleration 109

6.3 The flux invariant 111

6.4 Approximation accuracy. Exact solutions 112

6.5 Practice: Exercises and Answers 113

7 Wave-Particle Interaction in Astrophysical Plasma 115

7.1 The basis of kinetic theory 115

7.1.1 The linearized Vlasov equation 115

7.1.2 The Landau resonance and Landau damping 117

7.1.3 Gyroresonance 120

7.2 Stochastic acceleration of particles by waves 122

7.2.1 The principles of particle acceleration by waves 122

7.2.2 The Kolmogorov theory of turbulence 124

7.2.3 MHD turbulent cascading 126

7.3 The relativistic electron-positron plasma 127

7.4 Practice: Exercises and Answers 128

8 Coulomb Collisions in Astrophysical Plasma 133

8.1 Close and distant collisions 133

8.1.1 The collision parameters 133

8.1.2 The Rutherford formula 134

8.1.3 The test particle concept 135

8.1.4 Particles in a magnetic trap 136

8.1.5 The role of distant collisions 137

8.2 Debye shielding and plasma oscillations 139

8.2.1 Simple illustrations of the shielding effect 139

8.2.2 Charge neutrality and oscillations in plasma 141

8.3 Collisional relaxations in cosmic plasma 142

8.3.1 Some exact solutions 142

8.3.2 Two-temperature plasma in solar flares 144

8.3.3 An adiabatic model for two-temperature plasma 148

8.3.4 Two-temperature accretion flows 150

8.4 Dynamic friction in astrophysical plasma 151

8.4.1 The collisional drag force and energy losses 151

8.4.2 Electric runaway 155

8.4.3 Thermal runaway in astrophysical plasma 157

8.5 Practice: Exercises and Answers 158

9 Macroscopic Description of Astrophysical Plasma 163

9.1 Summary of microscopic description 163

9.2 Transition to macroscopic description 164

9.3 Macroscopic transfer equations 165

9.3.1 Equation for the zeroth moment 165

9.3.2 The momentum conservation law 166

9.3.3 The energy conservation law 169

9.4 General properties of transfer equations 173

9.4.1 Divergent and hydrodynamic forms 173

9.4.2 Status of conservation laws 174

9.5 Equation of state and transfer coefficients 175

9.6 Gravitational systems 177

9.7 Practice: Exercises and Answers 178

10 Multi-Fluid Models of Astrophysical Plasma 183

10.1 Multi-fluid models in astrophysics 183

10.2 Langmuir waves 184

10.2.1 Langmuir waves in a cold plasma 184

10.2.2 Langmuir waves in a warm plasma 186

10.2.3 Ion effects in Langmuir waves 187

10.3 Electromagnetic waves in plasma 188

10.4 What do we miss? 190

10.5 Practice: Exercises and Answers 191

11 The Generalized Ohm's Law in Plasma 193

11.1 The classic Ohm's law 193

11.2 Derivation of basic equations 194

11.3 The general solution 196

11.4 The conductivity of magnetized plasma 197

11.4.1 Two limiting cases 197

11.4.2 The physical interpretation 198

11.5 Currents and charges in plasma 199

11.5.1 Collisional and collisionless plasmas 199

11.5.2 Volume charge and quasi-neutrality 201

11.6 Practice: Exercises and Answers 203

12 Single-Fluid Models for Astrophysical Plasma 205

12.1 Derivation of the single-fluid equations 205

12.1.1 The continuity equation 205

12.1.2 The momentum conservation law in plasma 206

12.1.3 The energy conservation law 208

12.2 Basic assumptions and the MHD equations 209

12.2.1 Old and new simplifying assumptions 209

12.2.2 Non-relativistic magnetohydrodynamics 213

12.2.3 Relativistic magnetohydrodynamics 215

12.3 Magnetic flux conservation. Ideal MHD 216

12.3.1 Integral and differential forms of the law 216

12.3.2 The equations of ideal MHD 218

12.4 Practice: Exercises and Answers 221

13 Magnetohydrodynamics in Astrophysics 223

13.1 The main approximations in ideal MHD 223

13.1.1 Dimensionless equations 223

13.1.2 Weak magnetic fields in astrophysical plasma 225

13.1.3 Strong magnetic fields in plasma 226

13.2 Accretion disks of stars 229

13.2.1 Angular momentum transfer in binary stars 229

13.2.2 Magnetic accretion in cataclysmic variables 231

13.2.3 Accretion disks near black holes 231

13.2.4 Flares in accretion disk coronae 233

13.3 Astrophysical jets 234

13.3.1 Jets near black holes 234

13.3.2 Relativistic jets from disk coronae 236

13.4 Practice: Exercises and Answers 237

14 Plasma Flows in a Strong Magnetic Field 243

14.1 The general formulation of the problem 243

14.2 The formalism of two-dimensional problems 245

14.2.1 The first type of problems 245

14.2.2 The second type of MHD problems 247

14.3 On the existence of continuous flows 252

14.4 Flows in a time-dependent dipole field 253

14.4.1 Plane magnetic dipole fields 253

14.4.2 Axisymmetric dipole fields in plasma 256

14.5 Practice: Exercises and Answers 258

15 MHD Waves in Astrophysical Plasma 263

15.1 The dispersion equation in ideal MHD 263

15.2 Small-amplitude waves in ideal MHD 265

15.2.1 Entropy waves 265

15.2.2 Alfven waves 267

15.2.3 Magnetoacoustic waves 268

15.2.4 The phase velocity diagram 269

15.3 Dissipative waves in MHD 271

15.3.1 Small damping of Alfven waves 271

15.3.2 Slightly damped MHD waves 273

15.4 Practice: Exercises and Answers 274

16 Discontinuous Flows in a MHD Medium 277

16.1 Discontinuity surfaces in hydrodynamics 277

16.1.1 The origin of shocks in ordinary hydrodynamics 277

16.1.2 Boundary conditions and classification 278

16.1.3 Dissipative processes and entropy 280

16.2 Magnetohydrodynamic discontinuities 281

16.2.1 Boundary conditions at a discontinuity surface 281

16.2.2 Discontinuities without plasma flows across them 284

16.2.3 Perpendicular shock wave 286

16.2.4 Oblique shock waves 288

16.2.5 Peculiar shock waves 293

16.2.6 The Alfven discontinuity 294

16.3 Transitions between discontinuities 296

16.4 Shock waves in collisionless plasma 298

16.5 Practice: Exercises and Answers 299

17 Evolutionarity of MHD Discontinuities 305

17.1 Conditions for evolutionarity 305

17.1.1 The physical meaning and definition 305

17.1.2 Linearized boundary conditions 307

17.1.3 The number of small-amplitude waves 309

17.1.4 Domains of evolutionarity 311

17.2 Consequences of evolutionarity conditions 313

17.2.1 The order of wave propagation 313

17.2.2 Continuous transitions between discontinuities 315

17.3 Dissipative effects in evolutionarity 315

17.4 Discontinuity structure and evolutionarity 319

17.4.1 Perpendicular shock waves 319

17.4.2 Discontinuities with penetrating magnetic field 323

17.5 Practice: Exercises and Answers 324

18 Practicle Acceleration by Shock Waves 327

18.1 Two basic mechanisms 327

18.2 Shock diffusive acceleration 328

18.2.1 The canonical model of diffusive mechanism 328

18.2.2 Some properties of diffusive mechanism 331

18.2.3 Nonlinear effects in diffusive acceleration 332

18.3 Shock drift acceleration 332

18.3.1 Perpendicular shock waves 333

18.3.2 Quasi-perpendicular shock waves 335

18.3.3 Oblique shock waves 339

18.4 Practice: Exercises and Answers 340

19 Plasma Equilibrium in Magnetic Field 343

19.1 The virial theorem in MHD 343

19.1.1 A brief pre-history 343

19.1.2 Deduction of the scalar virial theorem 344

19.1.3 Some astrophysical applications 347

19.2 Force-free fields and Shafranov's theorem 350

19.2.1 The simplest examples of force-free fields 350

19.2.2 The energy of a force-free fields 350

19.3 Properties of equilibrium configurations 353

19.3.1 Magnetic surfaces 353

19.3.2 The specific volume of a magnetic tube 355

19.3.3 The flute or convective instability 357

19.3.4 Stability of an equilibrium configuration 358

19.4 The Archimedean force in MHD 359

19.4.1 A general formulation of the problem 359

19.4.2 A simplified consideration of the effect 360

19.5 MHD equilibrium in the solar atmosphere 361

19.6 Practice: Exercises and Answers 363

20 Stationary Flows in a Magnetic Field 367

20.1 Ideal plasma flows 367

20.1.1 Incompressible medium 368

20.1.2 Compressible medium 369

20.1.3 Astrophysical collimated streams (jets) 369

20.1.4 MHD waves of arbitrary amplitude 370

20.1.5 Differential rotation and isorotation 371

20.2 Flows at small magnetic Reynolds numbers 374

20.2.1 Stationary flows inside a duct 374

20.2.2 The MHD generator or pump 376

20.2.3 Weakly-ionized plasma in astrophysics 378

20.3 The σ-dependent force and vortex flows 379

20.3.1 Simplifications and problem formulation 379

20.3.2 The solution for a spherical ball 381

20.3.3 Forces and flows near a spherical ball 382

20.4 Large magnetic Reynolds numbers 386

20.4.1 The general formula for the σ-dependent force 387

20.4.2 The σ-dependent force in solar prominences 389

20.5 Practice: Exercises and Answers 391

Appendix 1 Notation 393

Appendix 2 Useful Expressions 399

Appendix 3 Constants 403

Bibliography 405

Index 427

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