Physics of Magnetic Flux Ropes

Title Page
......Page 5
Copyright
......Page 6
CONTENTS......Page 7
PREFACE......Page 13
1. Introduction......Page 16
2.1 Basic Solution......Page 19
2.2 Linear Force-Free Ropes......Page 21
2.4 Effect of Compressing or Expanding a Tube......Page 24
3.1 Expansion of a Section......Page 25
3.2 Thin Confined Untwisted Tube......Page 26
3.3 Thick Confined Force-Free Tubes......Page 27
4. Curved Tubes......Page 31
5. Effect of Gravity - the Solar Photosphere......Page 33
6. Solar Coronal Flux Tubes......Page 34
Questions and Answers......Page 36
References......Page 37
The Alfven Mode......Page 38
The Kink Mode......Page 40
Coronal Loops and Surface Waves......Page 41
Resonance Absorption......Page 42
Resonance Absorption and Velocity Shear......Page 44
References......Page 45
How do flares occur?......Page 47
Kinds of flares......Page 52
Morphology of the energy release......Page 53
Future directions of flare research......Page 54
References......Page 56
Equilibrium and linearized equations......Page 57
Stability properties......Page 59
Discussion......Page 62
References......Page 63
Introduction......Page 64
Resistive Instability of Two-Dimensional Equilibria......Page 67
Three-Dimensional Systems......Page 69
Flux Transfer Events......Page 70
Appendix......Page 72
References......Page 73
1. Introduction......Page 75
2. Definition......Page 77
3. Magnetic Field Annihilation Models......Page 78
4. Magnetic Field Reconnection Models......Page 80
6. Two Fluid Effects......Page 84
Questions and Answers......Page 85
References......Page 86
1.1 Magnetic field fragmentation of flux tubes insubphotospheric layers of the Sun......Page 88
1.5 Dispersion equation......Page 89
1.6 Particular cases......Page 90
2.2 The equation describing the behaviour of smallperturbations......Page 92
3. Magnetic tubes in the corona: force-free twisted loops......Page 93
REFERENCES......Page 95
Simulation Model......Page 96
Simulation Results......Page 97
References......Page 101
Model and Equations......Page 103
Diagnostic Diagram......Page 104
Umbral Oscillations......Page 105
References......Page 106
1. Introduction......Page 108
2. Flux tube with smooth radial profile of plasma parameters......Page 110
3. Longitudinal resonances in bending oscillations......Page 112
References......Page 114
1. Introduction......Page 115
3. The entropy constraint......Page 116
4.Thermodynamics of shocks of arbitrary strength......Page 117
5. Critique and further remarks......Page 118
Questions and Answers......Page 119
References......Page 120
1. Introduction......Page 121
b Density and pressure depletions......Page 123
c Temperature......Page 124
3. The Life and Times of a Tube......Page 125
4. The Geometrical Structure of a Thin Tube......Page 126
6. Waves in a Flux Tube......Page 128
7. Effects of Stratification: The Thin Tube Equations......Page 131
8. Sunspots......Page 134
Questions and Answers......Page 136
References......Page 137
Magnetic Flux Expulsion By Convective Eddies......Page 141
Convective Collapse of a Flux Tube......Page 142
References......Page 147
I. Introduction......Page 149
2. Expansion of the magnetohydrodynamicequations......Page 150
3. The zeroth-order thin flux tube approximation......Page 151
4. Linear waves in the second-order thin fluxtube approximation......Page 152
5. Equations of the magnetostatic structureof a twisted flux tube in a stratified atmosphere......Page 154
6. Discussion and final remarks......Page 155
References......Page 156
The Second-Order Set of Equations......Page 157
References......Page 159
Observational Data and Analysis......Page 160
Interpretation and Discussion......Page 162
References......Page 163
Model and Equations......Page 164
References......Page 166
Observations and Data Treatment......Page 167
Analysis of the Results......Page 168
Discussion......Page 169
References......Page 171
GENERATION OF CURRENTS IN THE SOLAR ATMOSPHERE BY ACOUSTIC WAVES......Page 172
References......Page 175
Data Collection and Processing......Page 176
Comparison of Regions of Differing Magnetic Flux......Page 178
Observations of Bright Points......Page 179
References......Page 183
2.1. Summary of Hydrodynamics......Page 185
3.1. Zero-Crossing Wavelength......Page 186
3.3. Stokes V Asymmetry......Page 187
References......Page 188
2. Description of Model Flux Tube......Page 189
3. Results of Models with Flows Outside the Magnetic Elements Only......Page 190
4. Results of Models with Velocities Inside and Outsidethe Magnetic Elements......Page 191
References......Page 192
"Loops" And The Coronal Magnetic Field......Page 193
Loop Energetics......Page 194
So, Why Are There Loops Anyway?......Page 195
Questions and Answers......Page 196
References......Page 197
Introduction......Page 199
Formal Integration of theField Equations......Page 201
Discussion......Page 203
Questions and Answers......Page 204
References......Page 205
STRUCTURE AND FLOWS IN CORONAL LOOPS......Page 207
I. Introduction......Page 215
III. Numerical Results......Page 216
References......Page 221
Introduction......Page 223
The Equilibrium of a Twisted Loopin an External Field......Page 224
Coronal Heating in Twisted Loops......Page 226
Summary......Page 231
References......Page 232
Introduction......Page 233
Analysis......Page 234
Discussion......Page 236
References......Page 237
Equations Describing the Quasi-Static Evolution of a Force-Free Field......Page 239
Perturbation method......Page 240
Asymptotic Behaviour......Page 241
Questions and Answers......Page 242
REFERENCES......Page 243
THE QUASI-STATIC EVOLUTION OF MAGNETIC CONFIGURATIONSON THE SUN AND SOLAR FLARES......Page 244
References......Page 247
2.1 Assumptions......Page 248
2.3 General properties of OPSE......Page 249
3.1 Obtention of the OPSE : the shearingprofiler......Page 250
3.3 The Asymmetric Case......Page 251
4. Conclusion......Page 252
References......Page 253
2. Braided Loop Model......Page 254
4. Three or More Tubes......Page 255
5. The Topology of 3-Braids......Page 256
6. The Energy of a Tangled Field......Page 257
8. Conclusions......Page 258
1. Introduction......Page 260
2.2 Resistive MHD equations......Page 261
3. Results......Page 262
3.2 Equilibrium......Page 263
Questions and Answers......Page 264
References......Page 265
Theory......Page 266
Results......Page 267
References......Page 271
Introduction......Page 272
Toroidal Current Loops......Page 273
Current Loop Dynamics......Page 274
Quasi-Equilibrium Evolution......Page 276
Discussion......Page 277
Questions and Answers......Page 279
References......Page 280
1. Energy Accumulation in the Current Sheet......Page 281
2. Magnetic Field Reconstruction......Page 282
3. Field-aligned currents and particle acceleration......Page 284
References......Page 285
Is the Flare Energy Release Possiblein a Single Loop?......Page 286
The Evolution of Equilibriumof an Emerging Loop Arcade......Page 287
Cross-Interaction of Identical Magnetic Tubes......Page 288
References......Page 289
Coronal Loop Model......Page 290
Aligned Flow Equilibria......Page 291
Damping of Surface Waves via Phase Mixing......Page 292
References......Page 295
1.1 Historical Perspective......Page 296
2.1 Magnetic Field......Page 297
2.2 Support Models......Page 298
3.2 Disparition Brusque - Dynamic......Page 299
4.1 Radiative Loss Function......Page 300
4.2 Thermal Instability......Page 301
5.1 Energetics......Page 302
5.2 An Analytical Model......Page 303
Questions and Answers......Page 305
References......Page 306
2. Two-dimensional models......Page 308
3. Flux tube model......Page 310
4. Stability analysis......Page 311
5. Conclusions and outlook......Page 312
References......Page 313
FILAMENT COOLING AND CONDENSATIONIN A SHEARED MAGNETIC FIELD......Page 315
REFERENCES......Page 318
Model and Basic Equations......Page 320
Fibril Structure with No External Field......Page 321
Without an external field......Page 322
With an external field......Page 323
References......Page 324
2. Model 1: equilibrium of a massivecurrent sheet in a constant-a force-freefield......Page 326
4. Model 3: equilibrium of an isothermalplasma......Page 327
5. Conclusion......Page 329
Introduction......Page 330
Specific Case of Filament Formation and Eruption......Page 331
Questions and Answers......Page 333
References......Page 334
2. Flux Cancellation in Sheared Fields......Page 335
3. Models for the Field Evolution......Page 336
4. Polar Crown Prominences......Page 337
Questions and Answers......Page 339
References......Page 340
Fast Coronal Mass Ejection Events and Shock Wave Disturbances in the Solar Wind......Page 341
Signatures of Coronal Mass Ejection Eventsin Interplanetary Space......Page 342
Origins of Counterstreaming Suprathermal Electron Events in Interplanetary Space......Page 343
Coronal Mass Ejection Events in the Solar Wind Lacking Large Internal Field Rotations......Page 344
Magnetic Clouds......Page 347
Occurrence Rates of Coronal Mass Ejection Eventsand Magnetic Clouds......Page 348
Other Coronal Mass Ejection Events With Large Internal Field Rotations......Page 350
Magnetic Clouds as Magnetic Flux Ropes......Page 353
Speed Gradients and the Radial Expansion of CMEs and Flux Ropes......Page 356
Discussion: A Suggested Originfor Interplanetary Flux Ropes......Page 358
Questions and Answers......Page 360
References......Page 361
Introduction......Page 363
Data and Interpretation......Page 364
References......Page 368
1. Introduction......Page 370
2. Observations......Page 371
References......Page 373
Introduction......Page 375
Results for Simulations of an Advected Plasma Parcel......Page 376
Simulations of Magnetically Driven CMEs......Page 377
Questions and Answers......Page 379
References......Page 380
Introduction......Page 381
Observations......Page 382
Questions and Answers......Page 386
References......Page 387
Magnetohydrodynamic Waves......Page 389
Interplanetary Manifestation of CME-Associated Shock Pairs......Page 391
References......Page 394
II. The Solar Wind Interaction with Venusat Solar Maximum......Page 396
III. The Solar Wind Interactionwith Mars and with Venus at Solar Minimum......Page 402
Questions and Answers......Page 404
References......Page 405
Modeling Flux Ropes......Page 407
Global Properties of Flux Ropes......Page 410
The Helical Kink Instability......Page 413
The Source Region of Venus Flux Ropes......Page 415
Questions and Answers......Page 416
References......Page 417
Introduction......Page 418
Observations......Page 419
Wave Analysis......Page 420
Discussion......Page 423
Concluding Remarks......Page 424
References......Page 425
Local Instability of Solar Wind Stream Flowing Around the lonopause......Page 426
The Influence of the Mass-Loading of Solar Wind Flowby Ionospheric Ions......Page 428
Summary and Conclusions......Page 429
References......Page 430
Introduction......Page 431
Early History......Page 433
Magnetopause Motion and Thickness......Page 435
Magnetopause Structure......Page 437
Flux Transfer Events......Page 439
Questions and Answers......Page 443
References......Page 444
Introduction......Page 446
Magnetic Field Signature......Page 447
Plasma and Particle Observations......Page 451
FTE Occurrence......Page 454
Transient Reconnection......Page 455
Multiple X-line Reconnection......Page 456
FTEs and Solar Wind Pressure Pulses......Page 457
Discussion......Page 458
Summary and Conclusions......Page 459
Questions and Answers......Page 460
References......Page 461
1. Introduction......Page 463
2. The Dynamics of the Drift Tearing Perturbationsat the Magnetic Surfaces within the Magnetopause Boundary Layer......Page 464
3. Stochastic Percolation Model......Page 466
4. Macroscopic Pictures of Magnetopause Reconnection......Page 470
Questions and Answers......Page 475
References......Page 476
IMBEDDED OPEN FLUX TUBES AND "VISCOUS INTERACTION"IN THE LOW LATITUDE BOUNDARY LAYER......Page 478
REFERENCES......Page 480
I. Introduction......Page 482
III. Simulation Results......Page 483
IV. Discussion......Page 485
References......Page 486
Assumptions......Page 488
III. Simulation Results......Page 489
IV. Discussion......Page 490
References......Page 493
1. Introduction......Page 495
3. Simulation Results......Page 496
4. Discussion......Page 499
References......Page 500
Simulation Model......Page 502
I. Formation of Magnetic Flux Tubes......Page 503
3. Topology of Magnetic Field Lines......Page 504
References......Page 506
1. Introduction......Page 507
4. Boundary Motions......Page 508
References......Page 510
Introduction......Page 511
Magnetic helicity conservation and reconnection......Page 512
Basic dynamics of the magnetopause reconnection region......Page 514
Discussion......Page 516
References......Page 517
1 Introduction......Page 519
2 The Dynamo Effect of 3-D Magnetic Reconnection......Page 520
Average Input of Electromagnetic Energy theDynamo Effect......Page 521
4 Discussion......Page 522
References......Page 523
1. Concepts of Magnetospheric Current Systems......Page 525
2.1. Sources......Page 527
2.2. Propagation......Page 529
2.3. Reflection......Page 530
2.4. Closure......Page 532
2.5. Kinetic Effects......Page 533
2.6. Instability......Page 535
Questions and Answers......Page 537
References......Page 538
Introduction......Page 540
References......Page 548
Introduction......Page 550
Observations......Page 552
Discussion......Page 554
REFERENCES......Page 557
Analysis Technique......Page 559
Method for the evaluation of the divergenceand vorticity fields......Page 560
Results......Page 561
Discussion and Conclusion......Page 563
References......Page 564
INTRODUCTION......Page 565
THEORY......Page 566
OBSERVATIONS......Page 569
DISCUSSION......Page 571
CONCLUSION......Page 572
REFERENCES......Page 574
Introduction......Page 575
DE-1/2 Observations......Page 576
Discussion......Page 580
References......Page 581
Introduction......Page 583
Model Outline......Page 584
FTE's in an Otherwise Closed Magnetosphere......Page 585
Discussion and Conclusion......Page 586
References......Page 587
Introduction......Page 588
Ionospheric traveling convection vortices......Page 589
Mapping to the magnetosphere......Page 590
Summary and discussion......Page 591
REFERENCES......Page 592
Introduction......Page 594
Data Overview and Analysis......Page 595
Discussion and Conclusion......Page 598
References......Page 600
Introduction......Page 602
The Model......Page 603
Summary......Page 605
References......Page 607
2. Definitions......Page 609
3. Key Features of the Unloading Process......Page 610
4. The Near-Earth Neutral Line Model......Page 611
5. Flux Rope Structures in Substorms......Page 613
References......Page 615
Predictions......Page 618
Near-Earth Magnetotail......Page 620
Middle Magnetotail......Page 621
Distant Magnetotail......Page 623
Conclusions......Page 624
References......Page 625
Overview of the Substorm......Page 628
Tail-like Magnetic Field Prior to the Expansion Onset......Page 629
Expansion Onset and Streaming of Energetic Particles......Page 630
Observations of Magnetic Islands......Page 632
Discussion......Page 633
References......Page 635
Initial Configuration and Numerical Procedure......Page 636
Field Evolution and Magnetic Topology......Page 637
Summary......Page 640
Questions and Answers......Page 641
References......Page 642
Introduction......Page 643
Flux Rope Orientation......Page 645
Comparison to ISEE Observations......Page 646
Conclusions......Page 647
References......Page 648
1. Introduction......Page 649
2. The Simulation Model......Page 650
Dayside Reconnection......Page 651
Magneto tail Reconnection......Page 652
4. Discussion and Conclusions......Page 655
References......Page 657
2. Enhancements of Parallel Electric Fields......Page 659
3. Particle Acceleration......Page 661
4. Electron Injection Patterns......Page 662
References......Page 665