Cover

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Contents

Preface

Introduction

Fundamentals of Dynamo Theory

1.1 Introduction

1.2 Basic Electromagnetic Theory

1.3 General Considerations

1.4 Working Dynamos

1.5 Mean Field Electrodynamics

Solar and Stellar Dynamos

2.1 Introduction

2.2 Stellar Magnetic Activity

2.3 Solar Activity

2.4 The Origin of the Solar Cycle

2.5 Where is the Solar Dynamo?

2.6 Self-Consistent Nonlinear Dynamo Models

2.7 Mean Field Dynamos

2.8 Illustrative Models

2.9 Stellar Dynamos

Convection and Magnetoconvection in a Rapidly Rotating Sphere

3.1 Introduction

3.2 Scaling, Geometry and Governing Equations

3.3 Non-magnetic Convection

3.4 Effects of a Weak Imposed Magnetic Field

3.5 Instability of Toroidal Fields in the Magnetostrophic Limit

3.6 Resistive and Diffusionless Instabilities

3.7 Instabilities of the Magnetic Field

3.8 Conclusions

Solar Dynamos: Computational Background

4.1 Introduction

4.2 Small-scale and Large-scale Magnetic Fields

4.3 Convective versus Mean-Field Dynamos

4.4 Numerical Methods

4.5 Direct Simulation of a Dynamo

4.6 Turbulent Transport Coefficients

4.7 Mean-field Dynamos

4.8 The Solar Dynamo and Differential Rotation

4.9 Future Simulations

Energy Sources for Planetary Dynamos

5.1 Introduction

5.2 Tidal and Precessional Resonant Bifurcations

5.3 Application to the Planets

5.4 Convective Energy Sources for Planetary Dynamos

5.5 In Temporary Conclusion

Fast Dynamos

6.1 Introduction

6.2 The Cauchy Solution and Reference Fields

6.3 Linear Flows

6.4 Slow Dynamos

6.5 Rope Dynamos

6.6 Spatially Periodic Dynamos

Nonlinear Planetary Dynamos

7.1 Introduction

7.2 Taylor's Constraint and its Variations

7.3 Equilibration through the Geostrophic Flow

7.4 Hydrodynamic Dynamos

The Chaotic Solar Cycle

8.1 Preface

8.2 The Solar Tachocline

8.3 The Solar Oscillator

8.4 On/Off Intermittency

8.5 Solar Activity Waves

8.6 Final Remarks

The Nonlinear Dynamo and Model-Z

9.1 Introduction

9.2 Nonlinear Axisymmetric Geodynamo Models

9.3 Model-Z Geodynamo

9.4 Conclusion

Maps and Dynamos

10.1 Brief Review of Dynamo Problems

10.2 Map-dynamo Models

10.3 Pulsed Beltrami Wave Dynamos

10.4 Essentially One-dimensional Map Dynamos

10.5 Analysis of Finn-Ott and SFS Models

10.6 Summary

Bifurcations in Rotating Systems

11.1 Introduction

11.2 Origin of Precession

11.3 Mode Interactions in Rotating Systems

11.4 Discussion

Index