Lectures on Solar and planetary dynamos

Contents......Page 5
Preface......Page 9
Introduction......Page 11
1.1 Introduction......Page 15
1.2 Basic Electromagnetic Theory......Page 22
1.3 General Considerations......Page 33
1.4 Working Dynamos......Page 42
1.5 Mean Field Electrodynamics......Page 54
2.1 Introduction......Page 73
2.2 Stellar Magnetic Activity......Page 75
2.3 Solar Activity......Page 79
2.4 The Origin of the Solar Cycle......Page 85
2.5 Where is the Solar Dynamo?......Page 87
2.6 Self-Consistent Nonlinear Dynamo Models......Page 89
2.7 Mean Field Dynamos......Page 91
2.8 Illustrative Models......Page 94
2.9 Stellar Dynamos......Page 99
3.1 Introduction......Page 111
3.2 Scaling, Geometry and Governing Equations......Page 112
3.3 Non-magnetic Convection......Page 113
3.4 Effects of a Weak Imposed Magnetic Field......Page 117
3.5 Instability of Toroidal Fields in the Magnetostrophic Limit......Page 119
3.6 Resistive and Diffusionless Instabilities......Page 122
3.7 Instabilities of the Magnetic Field......Page 124
3.8 Conclusions......Page 126
4.1 Introduction......Page 131
4.2 Small-scale and Large-scale Magnetic Fields......Page 132
4.3 Convective versus Mean-Field Dynamos......Page 137
4.4 Numerical Methods......Page 139
4.5 Direct Simulation of a Dynamo......Page 142
4.6 Turbulent Transport Coefficients......Page 149
4.7 Mean field Dynamos......Page 152
4.8 The Solar Dynamo and Differential Rotation......Page 158
4.9 Future Simulations......Page 163
5.1 Introduction......Page 175
5.2 Tidal and Precessional Resonant Bifurcations......Page 176
5.3 Application to the Planets......Page 184
5.4 Convective Energy Sources for Planetary Dynamos......Page 186
5.5 In Temporary Conclusion......Page 190
6.1 Introduction......Page 195
6.2 The Cauchy Solution and Reference Fields......Page 197
6.3 Linear Flows......Page 202
6.4 Slow Dynamos......Page 209
6.5 Rope Dynamos......Page 214
6.6 Spatially Periodic Dynamos......Page 216
7.1 Introduction......Page 233
7.2 Taylor\'s Constraint and its Variations......Page 236
7.3 Equilibration through the Geostrophic Flow......Page 243
7.4 Hydrodynamic Dynamos......Page 253
8.1 Preface......Page 259
8.2 The Solar Tachocline......Page 261
8.3 The Solar Oscillator......Page 264
8.4 On/Off Intermittency......Page 267
8.5 Solar Activity Waves......Page 270
8.6 Final Remarks......Page 275
9.1 Introduction......Page 281
9.2 Nonlinear Axisymmetric Geodynamo Models......Page 282
9.3 Model-Z Geodynamo......Page 294
9.4 Conclusion......Page 314
10.1 Brief Review of Dynamo Problems......Page 319
10.2 Map-dynamo Models......Page 323
10.3 Pulsed Beltrami Wave Dynamos......Page 326
10.4 Essentially One-dimensional Map Dynamos......Page 328
10.5 Analysis of Finn-Ott and SFS Models......Page 336
10.6 Summary......Page 341
11.1 Introduction......Page 345
11.2 Origin of Precession......Page 347
11.3 Mode Interactions in Rotating Systems......Page 368
11.4 Discussion......Page 381
Index......Page 387