Physics of Space Plasma Activity

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
1 Introduction......Page 17
Part I Setting the scene......Page 21
2.1 Geospace......Page 23
2.2 Solar atmosphere......Page 32
2.3 Other sites......Page 38
3 Plasma models......Page 41
3.1 Single particle motion......Page 42
3.2 Kinetic models......Page 45
3.3 Fluid models......Page 51
3.3.1 Momentum equations of two-fluid models......Page 52
3.3.2 Ideal magnetohydrodynamics......Page 53
3.3.3 Resistive magnetohydrodynamics......Page 54
3.4 Chew–Goldberger–Low momentum equation......Page 55
3.5 On the validity of MHD models for space plasmas......Page 56
3.6 Electron magnetohydrodynamics, Hall current......Page 57
3.8.1 Conservation of mass and energy in ideal MHD......Page 58
3.8.2 Magnetic flux, line and topology conservation......Page 59
3.8.3 Conservation of magnetic helicity......Page 63
3.9 Discontinuities......Page 64
Part II Quiescence......Page 71
4 Introduction......Page 73
5.1.1 Basic equations......Page 77
5.1.2 Euler potentials......Page 80
5.1.3 Boundary conditions and a variational principle......Page 83
5.1.4 Field-aligned currents and current closure......Page 85
5.1.5 Force-free fields......Page 87
5.1.7 Virial theorem and generalizations......Page 88
5.2 Symmetric MHS states......Page 92
5.2.1 MHS systems with translational invariance......Page 93
5.2.2 Liouville’s solutions......Page 96
5.2.3 Rotational invariance......Page 97
5.2.4 General invariance......Page 98
5.3 Examples of exact solutions......Page 101
Rotating field......Page 102
5.3.2 Harris sheet......Page 103
5.3.3 Cylindrical configurations, Bennett pinch......Page 104
Kelvin’s cat’s eyes......Page 105
Two-dimensional magnetosphere model......Page 106
5.3.5 A linear two-dimensional solution......Page 108
5.4 Asymptotic expansions......Page 109
5.4.1 Systems with translational invariance......Page 111
An example......Page 114
5.4.2 A boundary value problem of two-dimensional MHS......Page 115
5.4.3 Birn’s asymptotic solutions of three-dimensional MHS......Page 117
5.4.4 On nonequilibrium theorems and their limitations......Page 120
6.1 General properties......Page 123
6.2 Systems with translational invariance......Page 124
6.2.1 The equations for A and script phi......Page 125
6.2.2 Quasi-neutral systems and local Maxwellians......Page 128
6.3 Adiabatic particle motion......Page 130
6.4 Regular and chaotic particle motion......Page 132
7 A unified theory of steady states......Page 139
7.1 Steady states without gravity......Page 140
Magnetohydrostatics with isotropic pressure......Page 141
Steady state with isotropic pressure and parallel flow......Page 142
7.2 Inclusion of the gravity force......Page 143
MHD with parallel flow and gravity......Page 144
7.3 Symmetric states......Page 145
7.3.1 Gravity supported sheets revisited......Page 146
7.3.2 A case with a perpendicular flow component......Page 147
8.1 Introduction......Page 149
8.2 Perturbed Harris sheet......Page 151
Example......Page 153
8.3.1 Model and procedure......Page 156
8.3.2 Selfsimilar solutions......Page 160
8.3.3 Steady state and pressure crisis......Page 162
8.3.4 Role of flux tube volume for TCS formation......Page 164
Example......Page 165
8.4.1 The model......Page 167
8.4.2 An example with loss of equilibrium......Page 169
8.5 Vlasov approach to quasi-static evolution......Page 172
Outline of the procedure......Page 173
The invariant......Page 174
The distribution function......Page 176
Recovering the fluid approach for…......Page 177
8.5.2 A kinetic snapshot containing a thin current sheet......Page 179
8.6.1 Potential fields......Page 184
8.6.2 Current sheets at separatrices......Page 188
8.6.3 Quasi-static formation of tangential discontinuities?......Page 191
8.6.4 Weak singularities......Page 192
8.6.5 Three-dimensional systems......Page 194
Part III Dynamics......Page 197
9.1 Generalized Ohm’s law......Page 201
9.2 Resistivity......Page 203
9.3 Microturbulence......Page 206
9.3.1 Microinstabilities......Page 207
9.3.2 Collective transport......Page 210
9.3.3 LHD turbulence......Page 215
9.4 Non-turbulent kinetic effects......Page 216
10.1 Stability concepts......Page 219
10.2.1 The energy principle......Page 220
10.2.2 Properties and specializations......Page 226
Significance of the steady state potential T for stability......Page 228
3D perturbations of 2D equilibrium......Page 229
3D perturbations of 1D equilibrium......Page 230
Remark on the significance of the constraint (10.50)......Page 233
The case By = 0......Page 234
10.2.3 Rayleigh–Taylor instability......Page 235
10.2.4 Kink instability of plasma columns......Page 236
10.2.5 The ballooning limit......Page 237
Ballooning of 3D equilibria......Page 238
Rotational invariance......Page 239
Interchange mode......Page 240
Translational invariance......Page 241
MHD stability of magnetotail equilibria......Page 242
10.3 The resistive tearing instability......Page 251
10.3.1 The model equations......Page 252
10.3.3 Internal solution......Page 255
10.3.4 The dispersion relation......Page 257
10.3.5 E.ect of an embedded thin current sheet......Page 260
10.3.6 Further generalizations......Page 262
10.3.7 Nonlinear tearing......Page 263
10.4.1 Harris sheet with equal masses......Page 265
10.4.2 Realistic particle masses......Page 269
10.5.1 Formulation......Page 270
No constraints......Page 272
Phase space condition and quasi-neutrality......Page 273
10.5.2 The limit of small electron mass......Page 276
10.5.3 A lower bound of W......Page 277
10.5.4 Complex perturbations......Page 278
10.5.5 Effect of a normal magnetic field component in the Earth’s magnetotail......Page 279
10.5.6 Ion tearing......Page 282
10.5.7 Remarks on boundary conditions and validity......Page 283
11.1 Introduction......Page 285
11.2.1 Basic configuration and properties......Page 287
11.2.2 Exact solutions: Magnetic annihilation......Page 293
11.2.3 Simplified picture of reconnection......Page 296
11.2.4 Sweet–Parker and Petschek models......Page 297
11.2.5 Modifications......Page 299
11.2.6 Non-symmetric configurations......Page 302
11.2.7 Reconnection with a guide field......Page 304
11.2.8 Energy conversion......Page 305
11.2.9 Layers of parallel flow......Page 306
11.2.10 Time-dependent energy release via tearing and plasmoid formation......Page 308
11.3 Kinetic reconnection in 2D collisionless plasmas......Page 313
11.3.1 The Hall zone......Page 315
11.3.2 The electron region......Page 317
11.3.3 Comparative simulation studies......Page 319
11.4 Inclusion of the third dimension......Page 321
11.4.1 Role of microinstabilities......Page 322
11.4.3 Flux linkage......Page 325
11.5 Kinematics of 3D reconnection......Page 327
Basic aspects of the approach......Page 331
Reconnection rate......Page 334
Remarks on the choice of gauge......Page 338
11.5.2 Reconnection based on magnetic nulls......Page 339
The magnetic field near a null point......Page 340
Reconnection in fields with null points......Page 343
A global kinematic model of null point reconnection......Page 345
From general magnetic reconnection to magnetic reconnection......Page 348
11.5.3 Approximate conservation of helicity......Page 353
11.6 Remark on relativistic covariance......Page 356
12.1 Bifurcation......Page 359
12.1.1 Bifurcation properties of Grad–Shafranov theory......Page 362
Convex currents......Page 363
Harris sheet: Loss of equilibrium......Page 365
Low’s solution......Page 368
Marginal states......Page 370
12.2 A statistical mechanics approach to 2D current sheet bifurcation......Page 371
12.2.1 Brief outline of the model......Page 372
12.2.2 Bifurcations of the Harris sheet......Page 374
12.3 Role of perturbations......Page 377
12.5 Low-dimensional modelling......Page 380
Part IV Applications......Page 383
13.1 Interaction between the solar wind and the magnetosphere......Page 387
13.1.1 Open versus closed magnetosphere......Page 388
13.1.2 Observation of magnetopause reconnection......Page 390
13.1.3 Alternative processes opening the magnetopause......Page 392
13.1.4 Flux transfer......Page 393
13.2.1 Convection......Page 394
Test assumptions......Page 395
The pressure crisis and its consequences......Page 396
13.2.2 Bursty bulk flows......Page 398
13.2.3 Near-Earth reconnection......Page 400
13.3.1 Growth phase......Page 401
13.3.2 Expansion phase......Page 403
13.3.3 Recovery phase......Page 405
13.3.4 Extended simulations......Page 406
13.3.5 Observations......Page 411
13.4.1 Quasi-steady convection......Page 414
13.4.3 Spontaneous versus directly driven processes......Page 415
13.5.1 Statistical mechanics with constraint......Page 416
13.5.2 Low-dimensional modelling......Page 417
13.5.3 Self-organized criticality......Page 418
13.6 Discussion......Page 419
14.1 General aspects......Page 423
14.1.1 Aspects of loading......Page 425
14.1.2 Aspects of release......Page 426
14.2.1 Constraints......Page 428
14.2.2 Boundary conditions for quasi-static evolution......Page 430
Energy supply......Page 432
Loss of equilibrium and stability......Page 433
Zwingmann’s model......Page 434
14.3.2 Dynamic arcade models......Page 437
14.4 Coronal mass ejections......Page 440
14.5.1 Particle acceleration......Page 447
14.5.2 Sun–Earth connection......Page 448
15.1 The reconnection problem......Page 449
15.2 A general eruption scheme......Page 454
The momentum equation......Page 457
The steady state potential and the field equations......Page 458
Variational principle......Page 460
Examples......Page 462
Symmetric states......Page 464
Appendix 2 Variational principle for collisionless plasmas......Page 467
No constraints......Page 470
Phase space condition and quasi-neutrality......Page 471
The limit…for two-species plasmas......Page 474
A lower bound on W......Page 477
Symbols......Page 481
Fundamental constants......Page 483
References......Page 485
Index......Page 519