Plasma Astrophysics, Part II (eBook)

Contents 7
About This Book 15
Acknowledgements 17
Plasma Astrophysics 18
Particles and Fields: Exact Self- Consistent Description 20
1.1 Interacting particles and Liouville’s theorem 20
1.2 Charged particles in the electromagnetic . eld 28
1.3 Gravitational systems 31
1.4 Practice: Exercises and Answers 32
Statistical Description of Interacting Particle Systems 36
2.1 The averaging of Liouville’s equation 36
2.2 A collisional integral and correlation functions 43
2.3 Equations for correlation functions 48
2.4 Practice: Exercises and Answers 50
Weakly-Coupled Systems with Binary Collisions 51
3.1 Approximations for binary collisions 51
3.2 Correlation function and Debye shielding 58
3.3 Gravitational systems 62
3.4 Comments on numerical simulations 63
3.5 Practice: Exercises and Answers 64
Propagation of Fast Particles in Plasma 70
4.1 Derivation of the basic kinetic equation 70
4.2 A kinetic equation at high speeds 73
4.3 The classical thick-target model 75
4.4 The role of angular di.usion 79
4.5 The reverse-current electric-.eld e.ect 82
4.6 Practice: Exercises and Answers 92
Motion of a Charged Particle in Given Fields 93
5.1 A particle in constant homogeneous .elds 93
5.2 Weakly inhomogeneous slowly changing .elds 100
5.3 Practice: Exercises and Answers 111
Adiabatic Invariants in Astrophysical Plasma 117
6.1 General de.nitions 117
6.2 Two main invariants 118
6.3 The .ux invariant 125
6.4 Approximation accuracy. Exact solutions 126
6.5 Practice: Exercises and Answers 127
Wave-Particle Interaction in Astrophysical Plasma 129
7.1 The basis of kinetic theory 129
7.2 Stochastic acceleration of particles by waves 136
7.3 The relativistic electron-positron plasma 141
7.4 Practice: Exercises and Answers 142
Coulomb Collisions in Astrophysical Plasma 147
8.1 Close and distant collisions 147
8.2 Debye shielding and plasma oscillations 153
8.3 Collisional relaxations in cosmic plasma 156
8.4 Dynamic friction in astrophysical plasma 165
8.5 Practice: Exercises and Answers 172
Macroscopic Description of Astrophysical Plasma 176
9.1 Summary of microscopic description 176
9.2 Transition to macroscopic description 177
9.3 Macroscopic transfer equations 178
9.4 General properties of transfer equations 186
9.5 Equation of state and transfer coe.cients 188
9.6 Gravitational systems 190
9.7 Practice: Exercises and Answers 191
Multi-Fluid Models of Astrophysical Plasma 195
10.1 Multi-.uid models in astrophysics 195
10.2 Langmuir waves 196
10.3 Electromagnetic waves in plasma 200
10.4 What do we miss? 202
10.5 Practice: Exercises and Answers 203
The Generalized Ohm’s Law in Plasma 205
11.1 The classic Ohm’s law 205
11.2 Derivation of basic equations 206
11.3 The general solution 208
11.4 The conductivity of magnetized plasma 209
11.5 Currents and charges in plasma 211
11.6 Practice: Exercises and Answers 215
Single-Fluid Models for Astrophysical Plasma 217
12.1 Derivation of the single-.uid equations 217
12.2 Basic assumptions and the MHD equations 221
12.3 Magnetic .ux conservation. Ideal MHD 228
12.4 Practice: Exercises and Answers 233
Magnetohydrodynamics in Astrophysics 235
13.1 The main approximations in ideal MHD 235
13.2 Accretion disks of stars 241
13.3 Astrophysical jets 246
13.4 Practice: Exercises and Answers 249
Plasma Flows in a Strong Magnetic Field 254
14.1 The general formulation of the problem 254
14.2 The formalism of two-dimensional problems 256
14.3 On the existence of continuous .ows 263
14.4 Flows in a time-dependent dipole .eld 264
14.5 Practice: Exercises and Answers 269
MHD Waves in Astrophysical Plasma 274
15.1 The dispersion equation in ideal MHD 274
15.2 Small-amplitude waves in ideal MHD 276
15.3 Dissipative waves in MHD 282
15.4 Practice: Exercises and Answers 285
Discontinuous Flows in a MHD Medium 287
16.1 Discontinuity surfaces in hydrodynamics 287
16.2 Magnetohydrodynamic discontinuities 291
16.3 Transitions between discontinuities 306
16.4 Shock waves in collisionless plasma 308
16.5 Practice: Exercises and Answers 309
Evolutionarity of MHD Discontinuities 314
17.1 Conditions for evolutionarity 314
17.2 Consequences of evolutionarity conditions 322
17.3 Dissipative e.ects in evolutionarity 324
17.4 Discontinuity structure and evolutionarity 328
17.5 Practice: Exercises and Answers 333
Particle Acceleration by Shock Waves 336
18.1 Two basic mechanisms 336
18.2 Shock di.usive acceleration 337
18.3 Shock drift acceleration 341
18.4 Practice: Exercises and Answers 349
Plasma Equilibrium in Magnetic Field 351
19.1 The virial theorem in MHD 351
19.2 Force-free .elds and Shafranov’s theorem 358
19.3 Properties of equilibrium con.gurations 361
19.4 The Archimedean force in MHD 367
19.5 MHD equilibrium in the solar atmosphere 369
19.6 Practice: Exercises and Answers 371
Stationary Flows in a Magnetic Field 374
20.1 Ideal plasma .ows 374
20.2 Flows at small magnetic Reynolds numbers 381
20.3 The 386
dependent 386
force and vortex .ows 386
20.4 Large magnetic Reynolds numbers 393
20.5 Practice: Exercises and Answers 398
Appendix 1. Notation 399
Latin alphabet 399
Greek alphabet 402
Appendix 2 Useful Expressions 404
Appendix 3. Constants 407
Fundamental physical constants 407
Some useful constants and units 407
Some astrophysical constants 407
Bibliography 409
Index 430
Contents 446
Reconnection and Flares 453
Acknowledgements 456
Magnetic Reconnection 457
1.1 What is magnetic reconnection? 457
1.2 Acceleration in current layers, why and how? 465
1.3 Practice: Exercises and Answers 471
Reconnection in a Strong Magnetic Field 473
2.1 Small perturbations near a neutral line 473
2.2 Large perturbations near the neutral line 482
2.3 Dynamic dissipation of magnetic .eld 486
2.4 Nonstationary analytical models of RCL 490
Evidence of Reconnection in Solar Flares 499
3.1 The role of magnetic .elds 499
3.2 Three-dimensional reconnection in .ares 503
3.3 A current layer as the source of energy 515
3.4 Reconnection in action 520
The Bastille Day 2000 Flare 529
4.1 Main observational properties 529
4.2 Simpli.ed topological model 539
Electric Currents Related to Reconnection 551
5.1 Magnetic reconnection in the corona 551
5.2 Photospheric shear and coronal reconnection 559
5.3 Shear .ows and photospheric reconnection 566
5.4 Motions of the HXR footpoints in .ares 569
5.5 Open issues and some conclusions 577
Models of Reconnecting Current Layers 580
6.1 Magnetically neutral current layers 580
6.2 Magnetically non-neutral RCL 587
6.3 Basic physics of the SHTCL 590
6.4 Open issues of reconnection in .ares 600
6.5 Practice: Exercises and Answers 602
Reconnection and Collapsing Traps in Solar Flares 604
7.1 SHTCL in solar .ares 604
7.2 Coronal HXR sources in .ares 611
7.3 The collapsing trap e.ect in solar .ares 619
7.4 Acceleration mechanisms in traps 628
7.5 Final remarks 635
7.6 Practice: Exercises and Answers 636
Solar-type Flares in Laboratory and Space 643
8.1 Solar .ares in laboratory 643
8.2 Magnetospheric Physics Problems 650
8.3 Flares in accretion disk coronae 652
8.4 The giant .ares 658
Particle Acceleration in Current Layers 660
9.1 Magnetically non-neutral RCLs 660
9.2 Regular versus chaotic acceleration 668
9.3 Ion acceleration in current layers 675
9.4 How are solar particles accelerated? 681
9.5 Cosmic ray problem 685
Structural Instability of Reconnecting Current Layers 686
10.1 Some properties of current layers 686
10.2 Small perturbations outside the RCL 693
10.3 Perturbations inside the RCL 699
10.4 Solution on the boundary of the RCL 707
10.5 The criterion of evolutionarity 709
10.6 Practice: Exercises and Answers 715
Tearing Instability of Reconnecting Current Layers 717
11.1 The origin of the tearing instability 717
11.2 The simplest problem and its solution 720
11.3 Physical interpretation of the instability 727
11.4 The stabilizing e.ect of transversal .eld 730
11.5 Compressibility and a longitudinal .eld 733
11.6 The kinetic approach 736
Magnetic Reconnection and Turbulence 744
12.1 Reconnection and magnetic helicity 744
12.2 Coronal heating and .ares 751
12.3 Stochastic acceleration in solar .ares 754
12.4 Mechanisms of coronal heating 760
12.5 Practice: Exercises and Answers 764
Reconnection in Weakly- Ionized Plasma 766
13.1 Early observations and classical models 766
13.2 Model of reconnecting current layer 768
13.3 Reconnection in solar prominences 772
13.4 Element fractionation by reconnection 775
13.5 The photospheric dynamo 776
13.6 Practice: Exercises and Answers 781
Magnetic Reconnection of Electric Currents 785
14.1 Introductory comments 785
14.2 Flare energy storage and release 786
14.3 Current layer formation mechanisms 792
14.4 The shear and reconnection of currents 801
14.5 Potential and non-potential .elds 805
14.6 To the future observations by 808
Epilogue 810
Appendix 1. Acronyms 812
Appendix 2. Notation 813
Latin alphabet 813
Greek alphabet 814
Appendix 3 Useful Formulae 815
Appendix 4. Constants 819
Fundamental physical constants 819
Some useful constants and units 819
Some astrophysical constants 820
Bibliography 821
Index 851