Lectures on Solar and Planetary Dynamos (Publications of the Newton Institute, Series Number 2)

Dynamo theory is the study of the generation and maintenance of magnetic fields by fluid motion. It is important in many areas of physics, ranging from stellar and galactic dynamics, through solar physics and geomagnetism to reactor physics. This volume is the only modern introduction to the subject, and is comprised of the lectures given by leading specialists for an intensive course held at the Newton Institute in Cambridge, U.K. as part of a NATO Advanced Study Institute. Topics covered include planetary and solar dynamos, fast dynamos, and the use of symmetry principles to derive evolution equations. Each chapter starts with background material and goes right up to the forefront of current research. Detailed bibliographies are provided. This book will be welcome reading for graduate students in planetary and solar physics, plasma physics, and astrophysics. 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 CHAPTER 10. Maps and Dynamos......Page 0 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 Cambridge University Press Contents 5 Preface 9 Introduction 11 CHAPTER 1. Fundamentals of Dynamo Theory 15 1.1 Introduction 15 1.2 Basic Electromagnetic Theory 22 1.3 General Considerations 33 1.4 Working Dynamos 42 1.5 Mean Field Electrodynamics 54 CHAPTER 2. Solar and Stellar Dynamos 73 2.1 Introduction 73 2.2 Stellar Magnetic Activity 75 2.3 Solar Activity 79 2.4 The Origin of the Solar Cycle 85 2.5 Where is the Solar Dynamo? 87 2.6 Self-Consistent Nonlinear Dynamo Models 89 2.7 Mean Field Dynamos 91 2.8 Illustrative Models 94 2.9 Stellar Dynamos 99 CHAPTER 3. Convection and Magnetoconvection in a Rapidly Rotating Sphere 111 3.1 Introduction 111 3.2 Scaling, Geometry and Governing Equations 112 3.3 Non-magnetic Convection 113 3.4 Effects of a Weak Imposed Magnetic Field 117 3.5 Instability of Toroidal Fields in the Magnetostrophic Limit 119 3.6 Resistive and Diffusionless Instabilities 122 3.7 Instabilities of the Magnetic Field 124 3.8 Conclusions 126 CHAPTER 4. Solar Dynamos; Computational Background 131 4.1 Introduction 131 4.2 Small-scale and Large-scale Magnetic Fields 132 4.3 Convective versus Mean-Field Dynamos 137 4.4 Numerical Methods 139 4.5 Direct Simulation of a Dynamo 142 4.6 Turbulent Transport Coefficients 149 4.7 Mean field Dynamos 152 4.8 The Solar Dynamo and Differential Rotation 158 4.9 Future Simulations 163 CHAPTER 5. Energy Sources for Planetary Dynamos 175 5.1 Introduction 175 5.2 Tidal and Precessional Resonant Bifurcations 176 5.3 Application to the Planets 184 5.4 Convective Energy Sources for Planetary Dynamos 186 5.5 In Temporary Conclusion 190 CHAPTER 6. Fast Dynamos 195 6.1 Introduction 195 6.2 The Cauchy Solution and Reference Fields 197 6.3 Linear Flows 202 6.4 Slow Dynamos 209 6.5 Rope Dynamos 214 6.6 Spatially Periodic Dynamos 216 CHAPTER 7. Nonlinear Planetary Dynamos 233 7.1 Introduction 233 7.2 Taylor's Constraint and its Variations 236 7.3 Equilibration through the Geostrophic Flow 243 7.4 Hydrodynamic Dynamos 253 CHAPTER 8. The Chaotic Solar Cycle 259 8.1 Preface 259 8.2 The Solar Tachocline 261 8.3 The Solar Oscillator 264 8.4 On/Off Intermittency 267 8.5 Solar Activity Waves 270 8.6 Final Remarks 275 CHAPTER 9. The Nonlinear Dynamo and Model-Z 281 9.1 Introduction 281 9.2 Nonlinear Axisymmetric Geodynamo Models 282 9.3 Model-Z Geodynamo 294 9.4 Conclusion 314 CHAPTER 10. Maps and Dynamos -1 10.1 Brief Review of Dynamo Problems 319 10.2 Map-dynamo Models 323 10.3 Pulsed Beltrami Wave Dynamos 326 10.4 Essentially One-dimensional Map Dynamos 328 10.5 Analysis of Finn-Ott and SFS Models 336 10.6 Summary 341 CHAPTER 11. Bifurcations in Rotating Systems 345 11.1 Introduction 345 11.2 Origin of Precession 347 11.3 Mode Interactions in Rotating Systems 368 11.4 Discussion 381 Index 387 ISBN-10,/,ASIN:,0521467047,ISBN-13,/,EAN:,9780521467049 ISBN-10 / ASIN:,0521467047,ISBN-13 / EAN:,9780521467049 Dynamo Theory, The Study Of The Generation And Maintenance Of Magnetic Fields By Fluid Motions, Is Important In Many Areas Of Physics, Ranging From Stellar And Galactic Dynamics, Through Solar Physics And Geomagnetism, To Reactor Physics. This Volume Contains The Lectures Given By Leading Specialists, For An Intensive Course Held At The Newton Institute, As Part Of A Nato Advanced Study Institute. The Course Was Intended For Beginning Graduate Students, So Starts With Background Material, Before Leading On To Describe Areas Closer To Current Research. Topics Covered Include Planetary And Solar Dynamos, Fast Dynamos And The Use Of Symmetry Principles To Derive Evolution Equations. Detailed Bibliographies Are Provided. As The Only Modern Introduction To The Subject, This Will Be Welcome Reading For Students In Planetary And Solar Physics, Plasma Physics And Astrophysics. Fundamentals Of Dynamo Theory / Paul H. Roberts -- Solar And Stellar Dynamos / N.o. Weiss -- Convection And Magnetoconvection In A Rapidly Rotating Sphere / M.r.e. Proctor -- Solar Dynamos : Computational Background / Axel Brandenburg -- Energy Sources For Planetary Dynamos / W.v.r. Malkus -- Fast Dynamos / Andrew M. Soward -- Nonlinear Planetary Dynamos / D.r. Fearn -- The Chaotic Solar Cycle / E.a. Spiegel -- The Nonlinear Dynamo And Model-z / S.i. Braginsky -- Maps And Dynamos / B.j. Bayly -- Bifurcations In Rotating Systems / E. Knobloch. Edited By M.r.e. Proctor And A.d. Gilbert. Texts Of The Invited Lectures Presented At The Nato Advanced Study Institute 'theory Of Solar And Planetary Dynamos' Held At The Isaac Newton Institute For Mathematical Sciences In Cambridge From September 20 To October 2 1992--p. Ix. Includes Bibliographical References And Index.