Magnetic Helicity in Space and Laboratory Plasmas

Geophysical Monograph Series......Page 1
Magnetic Helicity in Spaceand Laboratory Plasmas......Page 3
CONTENTS......Page 5
PREFACE......Page 8
1. GAUSS AND ASTEROID TRACKING INTHE EARLY 19TH CENTURY......Page 9
2. HELICITY INTEGRALS......Page 10
4. SELF HELICITY AND MUTUAL HELICITY......Page 11
5. RELAXATION AND DISSIPATION......Page 12
6.1. Hellcity Integrals iv General......Page 13
6.2. Magnetic Helicity in an Open Volume......Page 14
7. HELICITY TRANSPORT......Page 15
REFERENCES......Page 16
2. CONSERVATION PROPERTIES......Page 18
3. IMPLICATIONS FOR DYNAMOS......Page 19
A. CONSTANCY OF jll/B......Page 20
B. FRACTAL NATURE OF jli/B......Page 21
C. FORMATION OF RUNAWAYS......Page 22
REFERENCES......Page 23
2. HELlCITY AND WRITHING NUMBER......Page 24
5. MAGNETIC FIELDS AND HELICITY......Page 25
8. SPECTRAL METHODS......Page 26
10. EXPLICIT COMPUTATION OFENERGY-MINIMIZING VECTOR FIELDS......Page 27
13. CONSTRAINTS ON ANY OPTIMAL DOMAIN......Page 28
1.1. How Domain Topology Influences Vector Calculus......Page 29
1.2. The Hodge Decomposition Theorem......Page 30
REFERENCES......Page 31
2. TAYLOR RELAXATION......Page 32
3. ERGODIC LINES OF FORCE......Page 33
4. ANCHORED MAGNETIC FIELDS......Page 34
5. OPEN DOMAINS......Page 35
7. SOLAR CORONAL MASS EJECTIONS......Page 36
REFERENCES......Page 38
1. INTRODUCTION......Page 40
2. CONSERVATION OF Hm; SPATIAL PERIODICITY......Page 42
3. FINITE BOUNDED GEOMETRIES; MHD "RELAXATION" PROCESSES......Page 46
4. DISCUSSION AND SUMMARY......Page 50
REFERENCES......Page 51
1. INTRODUCTION......Page 54
2.1. Fundamentals......Page 55
2.2. The Mean-Field Approach......Page 56
2.4 Models beyond the Mean-field Approach......Page 57
3.1.a-effect and Kinematic Hellcity......Page 58
3.2. Current Helicity......Page 59
3.3. Kinematic and Current Hellcity in a Saturnian Dynamo Model......Page 60
REFERENCES......Page 61
1. INTRODUCTION......Page 62
2. HELICITY-CONSERVING RELAXATION IN THELABORATORY......Page 63
3. DYNAMICS OF RELAXATION......Page 65
4. EXPERIMENTAL MEASUREMENTS OF THE MHDDYNAMO......Page 66
6. DYNAMO EFFECTS BEYOND THE STANDARDMODEL......Page 67
7. ACTIVE CONTROL OF RELAXATION......Page 68
REFERENCES......Page 69
1. INTRODUCTION......Page 71
2. DYNAMOS FROM OVERSHOOTING CONVECTION WITH SHEAR......Page 72
4. THE RELATION BETWEENALPHA-EFFECT AND HELICITY......Page 74
5. THE INVERSE CASCADE EFFECT INISOTROPICALLY FORCED SYSTEMS......Page 75
7. CONCLUSIONS......Page 77
REFERENCES......Page 78
1. SOME THOUGHTS ON TWIST AND HELICITY......Page 80
2.1. Mean Field Dynamo Equations......Page 81
2.3. Predicted Butterfly Diagrams and Twist forVarious Dynamos......Page 82
2.4. Conclusions about Twist from Mean FieldDynamos......Page 85
3, CHARACTERISTICS OF MOTIONS THATLEAD TO TWIST......Page 86
REFERENCES......Page 87
1. HELIOSEISMIC MEASUREMENTS OFSOLAR ROTATION AND FLOWS......Page 88
2.1. Tachocline......Page 90
2.3. Polar Vortex......Page 91
2.6. Supergranulation......Page 93
3. CONCLUSION......Page 94
REFERENCES......Page 95
1. FLUX TUBES......Page 97
3. EFFECTS OF TWIST: THEORY......Page 98
3.2. Instability......Page 99
4. A MODEL FOR THIN TWISTED FLUX TUBES......Page 100
5.2. Differential rotation......Page 101
5.4. Initial twist......Page 102
REFERENCES......Page 103
2. MEASURES OF HELICITY......Page 106
3.1. Vector Magnetographs......Page 107
4.1. Hemispheric Helicity Rule......Page 108
4.2. Tilt-Twist Correlation......Page 109
6.2. Large-Scale Helicity Areas......Page 110
7. DISCUSSION......Page 111
REFERENCES......Page 112
1. INTRODUCTION......Page 114
2. PRODUCTION OF MAGNETIC HELICITY BY AMEAN-FIELD DYNAMO......Page 115
3. ENCAPTURE OF MAGNETIC HELICITY AT THESUN DUE TO EJECTIONS......Page 117
4. FLUX OF MAGNETIC HELICITY THROUGH THESOLAR SURFACE......Page 118
4.2. Helicity of the Differentially Rotating Sun:Overwinding the Parker Spiral......Page 119
REFERENCES......Page 120
2. MAGNETIC HELICITY, K......Page 122
3. RELATIVE HELICITY, Kret......Page 123
4. CONSERVATION EQUATION FORRELATIVE HELICITY; INJECTION......Page 125
5. RELAXATION IN SYSTEMS WITH OPENFIELD LINES......Page 126
6. DISCUSSION OF y......Page 127
7. EVOLUTION OF THE RELAXED STATE......Page 128
8. RELAXED STATES, THE MHD ENERGY PRINCIPLE, AND STATIONARY STATES......Page 130
REFERENCES......Page 131
1. INTRODUCTION......Page 132
2. MAGNETIC HELlCITY AND TAYLOR'SMINIMUM ENERGY STATE......Page 133
3.1 Formation of RFP Plasmas......Page 134
3.2. Sawtooth Relaxation in RFP plasmas......Page 135
4.1 Spheromak Configuration......Page 136
4. 3 Verification of a Taylor State in Spheromaks......Page 137
4.4 Helicity Injection and Sustainment of SpheromakPlasma by Coaxial Gun......Page 138
4.5 Plasma Relaxation DuringSpheromakP lasmas......Page 139
5. EVOLUTION OF MAGNETIC FLUXES ANDHELICITIES DURING PLASMA MERGING......Page 140
7. SUMMARY......Page 141
REFERENCES......Page 142
1.1. The Solar Corona......Page 144
1.2. The Building Blocks of Coronal Magnetic Fields......Page 145
2.2. Coronal Relaxation......Page 147
3. THE ROLE OF MAGNETIC HELICITY INTHE EVOLUTION AND DYNAMICS OF THESOLAR CORONA......Page 148
3.1. Coronal Heating......Page 149
REFERENCES......Page 150
1. INTRODUCTION......Page 152
2. LINEAR FORCE FREE FIELD......Page 153
3.2. Energy Relaxation......Page 154
4.2. Numerical Model......Page 155
4.3. Results and Discussions......Page 156
REFERENCES......Page 158
1. INTRODUCTION......Page 160
2. A KINEMATIC DESCRIPTION OF THE RECONNECTION PROCESS......Page 161
3. THE EVOLUTION OF HELICITY......Page 165
3.1. Reconnection with E. B = 0......Page 166
3.2. Reconnection with E. B = 0......Page 167
REFERENCES......Page 168
1. INTRODUCTION......Page 169
2.2. Effects of Hellcity Content on Reconnection......Page 170
2.3. Effects of Reconnection on Heticity Conservation......Page 171
3.2. Helicity Conservation During Dynamo Action......Page 175
3.3. Helicity in Mean and Turbulent Fields......Page 176
4. CONCLUSIONS......Page 177
REFERENCES......Page 178
2. EXPERIMENTAL ARRANGEMENT......Page 180
3.1. Properties of Linear Whistler Vortices......Page 181
3.3. Collisions and Reflections of Vortices......Page 182
3. d. EMHD Fields with Magnetic Null Points......Page 184
REFERENCES......Page 187
1. INTRODUCTION......Page 188
2. SIMULATIONS OF BIPOLAR FIELDS......Page 190
3. SIMULATIONS OF MULTI-POLAR FIELDS......Page 191
REFERENCES......Page 197
1. INTRODUCTION......Page 198
2. HEMISPHERIC CHIRALITY PREFERENCE......Page 199
3. ROLE OF CURRENTS IN MAGNETIC RECONNECTION......Page 200
4. TWIST AND RECONNECTION INPRE-ERUPTIVE STRUCTURES......Page 202
REFERENCES......Page 204
INFERRING MAGNETIC TOPOLOGIESIN THE SOLAR WIND......Page 206
MAGNETIC FLUX ROPES IN THE SOLAR WIND......Page 207
SUGGESTED ORIGINS OF FLUX ROPE CMES......Page 208
FLUX ROPES ORIGINATINGFROM 3-DIMENSIONAL RECONNECTION......Page 210
FIELD TOPOLOGIES RESULTING FROMSUSTAINED MAGNETIC RECONNECTION......Page 211
REFERENCES......Page 212
1. INTRODUCTION......Page 214
2. MAGNETIC FIELD MODEL......Page 216
3. SUMMARY......Page 219
REFERENCES......Page 220
2. EVIDENCE FOR MAGNETIC HELICITY INFILAMENTS......Page 222
3. ORIGIN OF MAGNETIC HELICITY INFILAMENTS......Page 226
REFERENCES......Page 227
1. INTRODUCTION......Page 229
2.2. X-ray Plasmoid Ejections from Impulsive Flares......Page 230
2.3. Plasmoid-Induced-Reconnection Model......Page 231
3.1. X-ray Jets......Page 232
3.3. Emerging Flux Model......Page 233
3.4. Generationo f Alfven Wavesa nd HelicalJ etsb yMagnetic Reconnection......Page 234
4.1. Unification of Emerging Flux Model and CSHKP Model......Page 235
4.2. Emergence of Twisted Flux Tube......Page 236
REFERENCES......Page 237
1. INTRODUCTION......Page 239
2. METHOD......Page 240
4. INERTIAL RANGE......Page 241
5.1. Net Helicity......Page 242
5.2. Correlation Functions......Page 243
REFERENCES......Page 244
1. INTRODUCTION......Page 246
2. HELICITY AND SPATIALLY HOMOGENEOUS FLUCTUATIONS......Page 247
3.1. Transport and Scale Ezpansions......Page 248
4.3. Pre-MHD Two Scale Ezpansion......Page 249
5.2. Inverse Cascade......Page 251
5.5. Hellcity in the Solar Wind......Page 252
REFERENCES......Page 253
2. PITCH ANGLE SCATTERING......Page 255
3. SPATIAL DIFFUSION AND CONVECTION......Page 257
4. MAGNETIC HELICITY AND SOLARMODULATION......Page 258
5.1. The Steady-State Anisotropy......Page 259
5.2. Charge Sign Dependent Modulation......Page 261
REFERENCES......Page 263
2.1. Dayside Reconnection......Page 265
2. 2. Nightside Reconnection......Page 269
3. DYNAMICAL CONSIDERATIONS......Page 271
5. CONCLUSION......Page 272
REFERENCES......Page 273
1. MAGNETOTAIL, PLASMA SHEET ANDSUBSTORMS--A BRIEF INTRODUCTION......Page 275
2.1 Coarse-Grained Helicity......Page 276
3. MERGING OF COHE?NT FLUX TUBES......Page 277
4. SELF-ORGANIZED CRITICALITY......Page 278
5. MULTIFRACTAL SPECTRA......Page 279
6. SYNOPSIS AND THE NEW MILLENNIUM MAGNETOTAIL......Page 280
REFERENCES......Page 281
1. CONTEXT......Page 283
2. CLUES AND CONSTRAINTS......Page 284
3. LOCAL MAGNETOHYDRODYNAMICINSTABILITIES IN DISKS......Page 285
5.1. Conventional a - m Dynamos......Page 286
5.2. Incoherent and Chaotic Dynamos......Page 287
6.1. Accretion Disks......Page 288
REFERENCES......Page 289
1. INTRODUCTION......Page 291
2. PROPERTIES OF STEADYAXISYMMETRIC MHD FLOW......Page 292
3. ACCRETION AVALANCHES AND THE JET FORMATION......Page 293
4. MASS OUTFLOWS DRIVEN BY TWISTINJECTION INTO CLOSED MAGNETICL OOPS......Page 294
5. GLOBAL 3D MHD SIMULATIONS OF ATORUS THREADED BY VERTICAL MAGNETIC FIELDS......Page 295
6. SUMMARY......Page 296
REFERENCES......Page 298
2. GAUGE INVARIANT DEFINITIONS OF HELICITY......Page 299
3. HELICITY CONSERVATION IN THE SUN......Page 300
6. HELICITY IN LABORATORY PLASMAS......Page 301