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Magnetohydrodynamics of the Sun
Magnetohydrodynamics of the Sun describes the subtle and complex interaction between the Sun’s plasma
atmosphere and its magnetic field, which is responsible for many fascinating dynamic phenomena. Chapters
cover the generation of the Sun’s magnetic field by dynamo action, magnetoconvection and the nature of
photospheric flux tubes such as sunspots, the heating of the outer atmosphere by waves or reconnection,
the structure of prominences, the nature of eruptive instability and magnetic reconnection in solar flares
and coronal mass ejections, and the acceleration of the solar wind by reconnection or wave-turbulence.
Developed for a graduate course at St Andrews University, this advanced textbook provides a detailed
account of our progress towards answering the key unsolved puzzles in solar physics. It is essential reading
for graduate students and researchers in solar physics and related fields of astronomy, plasma physics and
fluid dynamics. Problem sets and other resources are available at www.cambridge.org/9780521854719.
Eric Priest was elected Fellow of the Royal Society of Edinburgh in 1985, of the Norwegian Academy of
Sciences and Letters in 1994, of the Royal Society in 2002 and of the European Academy of Sciences in
2005. He has delivered many named lectures, including the James Arthur Prize Lecture at Harvard and
the Lindsay Memorial Lecture at the Goddard Space Flight Center. He was awarded the Hale Prize of the
American Astronomical Society, only the second time it has been awarded to a British scientist, and the
Gold Medal of the Royal Astronomical Society. Priest created and led an extremely active and successful
group at St Andrews, served three times on UK Research Assessment Panels and, as Co-Chair of the
PPARC Science Committee, he played an important role when the UK joined the European Southern
Observatory.
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MAGNETOHYDRODYNAMICS
OF THE SUN
Eric Priest
University of St Andrews
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Eric Priest
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32 Avenue of the Americas, New York, NY 10013-2473, USA
Cambridge University Press is part of the University of Cambridge.
It furthers the University’s mission by disseminating knowledge in the pursuit of
education, learning and research at the highest international levels of excellence.
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Information on this title: www.cambridge.org/9780521854719
c
Eric Priest 2014
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2014
Printed in the United States of America
A catalogue record for this publication is available from the British Library.
Library of Congress Cataloguing in Publication data
Priest, E. R. (Eric Ronald), 1943–
Magnetohydrodynamics of the Sun / Eric Priest.
pages cm
Includes bibliographical references and index.
ISBN 978-0-521-85471-9 (hardback)
1. Sun. 2. Solar activity. 3. Magnetohydrodynamics. 4. Solar magnetic fields.
5. Astrophysics. I. Title. II. Title: Magnetohydrodynamics of the Sun.
QB524.P75 2014
523.7
2–dc23 2013029372
ISBN 978-0-521-85471-9 Hardback
Additional resources for this publication at www.cambridge.org/9780521854719
Cambridge University Press has no responsibility for the persistence or accuracy of
URLs for external or third-party Internet Web sites referred to in this publication
and does not guarantee that any content on such Web sites is, or will remain,
accurate or appropriate.
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To Clare,
our wonderful children
(Andrew, Matthew, David and Naomi),
my ever-helpful brother (Gerry) and sister (June)
and amazing 97-year-old mum (Olive)
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Contents
Preface page xvii
1 A Description of the Sun 1
1.1 Brief History 1
1.2 Overall Properties 4
1.2.1 The Structure of the Solar Interior 5
1.2.2 The Structure of the Solar Atmosphere 6
1.3 The Solar Interior 10
1.3.1 The Solar Core 10
1.3.2 A Model for the Solar Interior 10
1.3.3 Convection Zone 12
1.3.4 Helioseismology and 5-Minute Oscillations 15
1.4 The Photosphere 21
1.4.1 Granulation, Meso- and Super-Granulation 21
1.4.2 Magnetic Field 25
1.4.3 The VAL Model 30
1.5 The Chromosphere and Transition Region 31
1.5.1 Quiet (Internetwork Non-magnetic) Chromosphere 31
1.5.2 Magnetic (Network or Plage) Chromosphere 31
1.6 The Corona 34
1.6.1 The Structure of the Corona from Eclipses and X-ray
Images 36
1.6.2 Coronal Loops, X-ray Bright Points and X-ray Jets 37
1.6.3 Coronal Holes 38
1.6.4 Solar Wind 40
1.7 Active Regions, Sunspots and the Solar Cycle 44
1.7.1 Active Regions 45
1.7.2 Sunspots 47
1.7.3 Solar Cycle 53
1.8 Prominences 57
1.8.1 Introduction 57
1.8.2 Plasma and Magnetic Properties 57
1.8.3 Structure 59
1.8.4 Development 62
1.8.5 Eruption 62
vii
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viii Contents
1.9 Coronal Mass Ejections (CMEs) and Solar Flares 63
1.9.1 Coronal Mass Ejections 63
1.9.2 Solar Flares 65
2 The Basic Equations of Magnetohydrodynamics (MHD) 74
2.1 Electromagnetic Equations 74
2.1.1 Maxwell’s Equations 74
2.1.2 Ohm’s Law 76
2.1.3 Generalised Ohm’s Law 76
2.1.4 Induction Equation 78
2.1.5 Values for Electrical Conductivity and Magnetic Diffusivity 79
2.2 Plasma Equations 80
2.2.1 Mass Continuity 80
2.2.2 Equation of Motion 80
2.2.3 Perfect Gas Law 81
2.3 Energy Equations 82
2.3.1 Different Forms of the Heat Equation 82
2.3.2 Thermal (or Heat) Conduction 83
2.3.3 Radiation 84
2.3.4 Heating 85
2.3.5 Energetics 85
2.4 Summary of Equations 86
2.4.1 Dimensionless Equations 87
2.4.2 Assumptions 87
2.4.3 Reduced Forms of the Equations 88
2.5 Dimensionless Parameters 89
2.6 Consequences of the Induction Equation 91
2.6.1 Diffusive Limit (R
m
1) 91
2.6.2 Ideal Limit (R
m
1) 92
2.6.3 Non-ideal Flow 94
2.7 The Lorentz Force 96
2.8 Some Theorems 98
2.8.1 Alfv´en’s Frozen Flux Theorem 98
2.8.2 The Minimum-Energy Theorem for Potential Fields 98
2.8.3 The Minimum-Energy Theorem for Force-Free Fields 98
2.8.4 Woltjer’s Minimum-Energy Theorem 98
2.8.5 Cowling’s Anti-dynamo Theorem 99
2.8.6 Taylor-Proudman Theorem 99
2.8.7 Ferraro’s Law of Isorotation 99
2.8.8 Virial Theorem 99
2.9 Summary of Magnetic Flux Tube Behaviour 100
2.9.1 Definitions 100
2.9.2 General Properties 101
2.9.3 Flux Surfaces for Two-Dimensional or Axisymmetric Fields 103
2.9.4 Flux Tubes in the Solar Atmosphere 104
2.10 Summary of Current Sheet Behaviour 104
2.10.1 Processes of Formation 106
2.10.2 Properties 106
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Contents ix
3 Magnetohydrostatics 107
3.1 Introduction 107
3.1.1 Representation of the Magnetic Field 108
3.1.2 Pressure Scale-Height 108
3.1.3 Plasma Structure in a Given Magnetic Field 110
3.2 Structure of Magnetic Flux Tubes (Cylindrically Symmetric) 111
3.2.1 Purely Axial Field 112
3.2.2 Purely Azimuthal Field 112
3.2.3 One-Dimensional Force-Free Flux Tubes 113
3.2.4 One-Dimensional Magnetostatic Flux Tubes 116
3.3 Current-Free (or Potential) Magnetic Fields 117
3.3.1 Potential Minimum-Energy Theorem 117
3.3.2 General Current-Free Solutions 118
3.3.3 Coronal Magnetic Fields – Roughly Potential? 119
3.4 Force-Free Magnetic Fields 120
3.4.1 General Theorems for Force-Free Fields 121
3.4.2 Simple Linear (Constant-α) Solutions 124
3.4.3 General Linear (Constant-α) Solutions 126
3.4.4 Nonlinear (i.e., Non-constant-α) Solutions 129
3.4.5 Numerical Methods for Force-Free Fields 132
3.4.6 Diffusion of Force-Free Fields 134
3.5 Magnetohydrostatic Fields 135
3.5.1 Magnetostatic Fields 135
3.5.2 Effect of Gravity 138
3.5.3 Transforming to Incompressible Field-Aligned Flows 143
4Waves 144
4.1 Introduction 144
4.1.1 Fundamental Modes 144
4.1.2 Basic Equations 145
4.2 Sound Waves 147
4.3 Magnetically Driven Waves 147
4.3.1 Alfv´en Waves (i.e., Shear or Torsional Alfv´en
Waves) 149
4.3.2 Compressional Alfv´en (or Fast-Mode) Waves 151
4.4 Internal Gravity Waves 152
4.5 Inertial Waves 153
4.6 Magnetoacoustic Waves 155
4.7 Acoustic Gravity Waves 157
4.8 Summary of Magnetoacoustic Gravity Waves 158
4.9 Waves in a Non-uniform Medium 159
4.9.1 Waves in a Continuous Planar Magnetic Field 160
4.9.2 Surface Waves on a Magnetic Interface 161
4.9.3 Surface and Body Waves on a Magnetic Slab 162
4.9.4 Waves in a Continuous Twisted Flux Tube 164
4.9.5 Modes of a Uniform Untwisted Flux Tube 165
4.10 MHD Continua 167
4.10.1 Continuous Spectra 167
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x Contents
4.10.2 Initial-Value Problem 168
4.10.3 Quasi-Modes 170
4.11 Waves on the Sun 172
4.11.1 Waves in the Low Atmosphere 172
4.11.2 Coronal Seismology 172
5 Shock Waves 177
5.1 Introduction 177
5.1.1 Formation of a Hydrodynamic Shock 177
5.1.2 Effects of a Magnetic Field 179
5.2 Hydrodynamic Shocks 181
5.3 Perpendicular Shocks 182
5.4 Oblique Shocks 184
5.4.1 Jump Relations 184
5.4.2 Slow-Mode and Fast-Mode Shocks 186
5.4.3 Switch-Off and Switch-On Shocks 187
5.4.4 Intermediate Wave 188
6 Magnetic Reconnection 189
6.1 Introduction 189
6.1.1 Brief History 190
6.1.2 Overview of Reconnection Concepts 191
6.2 Two-Dimensional Null Points 193
6.2.1 2D Null Point Structure 193
6.2.2 Collapse of 2D Null Points 193
6.3 Current Sheet Formation 196
6.3.1 Planar Motion in 2D Potential Fields 197
6.3.2 Current Sheets in 3D and Non-potential Fields 199
6.3.3 Creation of Sheets at Separatrices by Shearing 202
6.3.4 Braiding by Random Footpoint Motions 203
6.4 Magnetic Annihilation 204
6.4.1 Equations for Steady Annihilation and 2D Reconnection 204
6.4.2 Diffusion and Advection of a 1D Current Sheet 204
6.4.3 Stagnation-Point Flow Model (Sonnerup-Priest 1975) 205
6.4.4 Reconnective Annihilation 207
6.5 Slow 2D Reconnection: The Sweet-Parker Mechanism 208
6.5.1 The Basic Sweet-Parker Model (1958) 208
6.5.2 Effect of Pressure Gradients and Compressibility 210
6.5.3 Energetics 211
6.6 Fast 2D Reconnection: Petschek’s Mechanism 211
6.6.1 Petschek’s Model (1964) 212
6.6.2 Non-steady Petschek Reconnection 214
6.7 Fast 2D Reconnection: Other Families 214
6.7.1 Almost-Uniform Non-potential Reconnection 215
6.7.2 Early MHD Numerical Experiments 218
6.7.3 Non-uniform Reconnection Theory 219
6.8 Unsteady 2D Reconnection by Resistive Instability 219
6.8.1 Tearing-Mode Instability (Furth et al. 1963) 221
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Contents xi
6.8.2 Extensions to the Basic Tearing-Mode Analysis 223
6.8.3 Nonlinear Development of Tearing 223
6.9 3D Reconnection: Geometrical Structures 224
6.9.1 3D Null Points 225
6.9.2 Separatrices and Separators 226
6.9.3 Bifurcations 229
6.9.4 Topological Skeletons in the Solar Corona 229
6.9.5 Quasi-Skeletons 232
6.10 3D Reconnection: Magnetic Helicity 233
6.10.1 Equations for Magnetic Helicity 235
6.10.2 Time-Variation of Magnetic Helicity 235
6.10.3 Magnetic Helicity of Simple Structures 236
6.11 3D Reconnection: Flux and Field-Line Conservation 237
6.11.1 An Ideal Plasma 237
6.11.2 A Non-ideal Plasma 238
6.11.3 Topological Conservation Laws 240
6.12 3D Reconnection Concepts 240
6.12.1 Conditions for Reconnection 241
6.12.2 Reconnection in Two Dimensions (E · B = 0) 241
6.12.3 Failure of Concept of Flux Velocity in 3D (E ·B = 0) 241
6.12.4 Differences Between 2D and 3D Reconnection 242
6.12.5 Definition and Classification of Reconnection 243
6.12.6 Magnetic Helicity and 3D Reconnection 247
6.13 3D Reconnection Regimes 247
6.13.1 Ways to Model Reconnection at a Null Point 247
6.13.2 3D Null Regimes (Priest and Pontin, 2009) 250
6.13.3 Separator Reconnection 252
6.13.4 Quasi-Separator Reconnection (Priest-D´emoulin
1995) 254
7 Instability 256
7.1 Introduction 256
7.2 Linearised Equations 258
7.3 Normal-Mode Method 260
7.3.1 Example: Rayleigh-Taylor Instability 260
7.4 Energy (or Variational) Method 264
7.4.1 Example: Helical Kink Instability with Line-Tying 266
7.4.2 Use of the Energy (or Variational) Method 269
7.5 Summary of Instabilities 270
7.5.1 Interchange Instability 270
7.5.2 Rayleigh-Taylor Instability 271
7.5.3 Instability of a Cylindrical Tube 272
7.5.4 Hydrodynamic Instability 274
7.5.5 Resistive Instability 275
7.5.6 Convective Instability 278
7.5.7 Radiatively Driven Thermal Instability 279
7.5.8 Other Instabilities 280
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xii Contents
8DynamoTheory 281
8.1 Introduction 281
8.1.1 Observed Solar Magnetic Field Patterns 281
8.1.2 Preliminary Comments and Terminology 282
8.1.3 History of Dynamo Ideas 284
8.2 Cowling’s Anti-dynamo Theorem 287
8.3 Early Turbulent Dynamos 289
8.3.1 Parker’s 1955 Model 289
8.3.2 Mean-Field MHD Theory 291
8.4 Flux-Transport Dynamos 294
8.4.1 Babcock-Leighton Ideas 294
8.4.2 Flux-Transport Dynamo Model 294
8.5 Tachocline Dynamos 298
8.5.1 Overshoot Dynamo 298
8.5.2 Interface Dynamo (Parker 1993) 298
8.5.3 The Solar Tachocline 300
8.6 Other Approaches 301
8.6.1 Global Computations 301
8.6.2 Low-Order Models 302
8.6.3 Stellar Dynamos 303
8.7 Future Directions 304
9 Magnetoconvection and Sunspots 306
9.1 Magnetoconvection 306
9.1.1 Physical Effects 306
9.1.2 Linear Stability Analysis 308
9.1.3 Magnetic Flux Concentration and Expulsion 310
9.1.4 Cooling of Sunspots 312
9.2 Intense Flux Tubes 313
9.2.1 Equilibrium of a Thin Flux Tube 314
9.2.2 Dynamics of a Thin Flux Tube 315
9.2.3 Intensification of a Thin Flux Tube by Convective Collapse 315
9.2.4 Spicule Generation 316
9.3 Magnetic Buoyancy 317
9.3.1 Qualitative Effect 318
9.3.2 Magnetic Buoyancy Instability 318
9.3.3 The Emergence of Magnetic Flux 320
9.4 Overall Equilibrium Structure of Sunspots and Pores 322
9.4.1 Magnetohydrostatic Equilibrium 322
9.4.2 Sunspot Stability 324
9.5 Fine Structure of a Sunspot 325
9.5.1 Umbral Fine Structure 325
9.5.2 The Sunspot Penumbra 326
9.5.3 Oscillations 328
9.6 Evolution of a Sunspot 329
9.6.1 Formation 329
9.6.2 Decay 329
9.7 Unified Model 330
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Contents xiii
10 Heating of the Upper Atmosphere 334
10.1 Introduction 334
10.1.1 Complex Nature of Chromospheric and Coronal Magnetic
Field 337
10.2 Chromospheric and Coronal Loops 339
10.2.1 Observations from Space 340
10.2.2 Physical Properties of Coronal-Loop Models 343
10.2.3 Static Energy-Balance Models for Coronal Loops 344
10.2.4 Dynamic Models for Chromospheric and Coronal Loops 349
10.2.5 Deducing the Form of Heating in Coronal Loops 352
10.2.6 Numerical Experiments on Active-Region Heating 355
10.3 Heating by MHD Waves 356
10.3.1 Propagation of Magnetic Waves 357
10.3.2 Chromospheric and Coronal Heating by Resonant Absorption 358
10.3.3 Chromospheric and Coronal Heating by Phase Mixing 361
10.3.4 Wave Heating of Chromospheric and Coronal Loops 363
10.4 Heating by Magnetic Reconnection 364
10.4.1 Formation of Current Sheets 366
10.4.2 Evidence from Space for Reconnection 367
10.4.3 X-ray Bright Points: The Converging Flux Model 369
10.4.4 Current-Sheet Formation by Parker Braiding 370
10.4.5 Flux-Tube Tectonics: Separator, Separatrix and QSL
Heating 374
10.5 Heating by Turbulence 386
10.5.1 Relaxation by MHD Turbulence 386
10.5.2 Avalanches: A Nonlinear Driven Dissipative Process 389
10.6 Conclusion 390
11 Prominences 391
11.1 Summary of Quiescent Prominence Properties 391
11.2 Basic Magnetic Structure (Current Sheet in a Flux Rope) 393
11.2.1 Kippenhahn-Schl¨uter Model for Prominence Sheet 393
11.2.2 2.5D Magnetic Flux-Rope Models of Inverse Polarity 396
11.2.3 Coronal Cavities 399
11.3 Global Nature of a Filament Channel and Chirality 399
11.4 Three-Dimensional Structure: Barbs (or Feet) 402
11.4.1 3D Aulanier-D´emoulin (1998) Flux-Rope Model 402
11.4.2 Numerical Flux-Rope Modelling 404
11.5 Threads 407
11.5.1 Local Structure 407
11.5.2 van Ballegooijen–Cranmer Model for Tangled Fields 408
11.6 Formation of Thermal Structure 409
11.6.1 Injection from Below (Surges) 409
11.6.2 Magnetic Levitation of Cool Plasma 411
11.6.3 Radiative Instability or Non-equilibrium 411
11.6.4 Magnetic Rayleigh-Taylor Instability 415
11.7 Conclusion 415
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12 Solar Flares and Coronal Mass Ejections 416
12.1 Introduction 416
12.1.1 Overview 416
12.2 Eruption by Non-equilibrium, Instability or Breakout 418
12.2.1 Non-equilibrium or Catastrophe in 2D 420
12.2.2 The Hoop Force of a Slender Toroidal Flux Rope 424
12.2.3 Non-equilibrium and Torus Instability in 3D 427
12.2.4 Titov-D´emoulin Model: An Active-Region Toroidal
Flux Rope 431
12.2.5 Helical Kink Instability 433
12.2.6 Resistive Kink Instability 434
12.2.7 Breakout 435
12.2.8 Emerging (or Evolving) Flux Model 437
12.2.9 Other Numerical Experiments on Initiation of Eruption 438
12.3 Reconnection and the Creation of Flare Loops 439
12.3.1 Standard (CSHKP) 2D Reconnection Model 439
12.3.2 3D Modifications to the Standard Model 442
12.4 Concluding Comment 450
13 The Solar Wind 451
13.1 Introduction 451
13.2 Chapman’s (1957) Static Corona 452
13.3 Parker’s Isothermal Solution 453
13.4 Breeze, Wind or Accretion? 455
13.4.1 Stability of Breeze Solutions 455
13.4.2 Dependence of Solutions on p
∞
and History 456
13.5 More General Models for a Spherical Expansion 457
13.5.1 Polytropic Solar Wind 457
13.5.2 Energy Equation 458
13.6 Effect of Rotation and a Magnetic Field 460
13.6.1 Rotating Wind 460
13.6.2 Magnetic Field 461
13.6.3 Early 1D Coronal-Hole Models 464
13.7 Fast Solar Wind: Self-Consistent Wave-Turbulence Models 466
13.8 Slow Solar Wind: Reconnection Models 468
13.9 2D and 3D Models: Streamers and Coronal Holes 469
13.9.1 2D Helmet-Streamer Model (Pneuman-Kopp) 470
13.9.2 Two-Dimensional Separable Solution for a Rotating
Wind 471
13.9.3 3D Topology of Pseudo Coronal Streamers and Coronal Holes 471
13.9.4 Global Three-Dimensional Modelling 474
13.10 Large- and Small-Scale Time-Dependence 475
13.11 Going Beyond a Single-Fluid Picture 475
13.11.1 Two-Fluid Model 476
13.11.2 Kinetic Effects 478
13.12 Conclusion 480
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Contents xv
Appendix 1 Units 483
Appendix 2 Useful Values and Expressions 487
References 493
Index 543
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Preface
I finished writing a book entitled Solar Magnetohydrodynamics back in 1981, which grew out of a post-
graduate lecture course at St Andrews. Since then, the whole field has been completely transformed by
spectacular new observations from spacecraft and ground-based telescopes which have spawned entirely
new theoretical concepts. Rather than tinker with that book, I have therefore completely rewritten it from
scratch and have given it a new title, Magnetohydrodynamics of the Sun.
Magnetohydrodynamics (or MHD for short) is the study of the interaction between a plasma (or elec-
trically conducting fluid) and a magnetic field. A magnetic field affects a plasma in several ways. It exerts
a force which is able, for instance, to support material in a prominence against gravity or propel it away
from the Sun at high speeds. It provides thermal insulation, and so allows cool plasma to exist alongside
hotter material, as in prominences or spicules. It also stores energy, which may be released violently as a
solar flare or sporadically to heat the corona.
Solar MHD has now blossomed to become a central part of solar physics, since the key role of the
magnetic field in producing many dynamic processes on the Sun has been recognised, and in turn solar
physics has become one of the most vibrant parts of astronomy. The Sun influences the Earth’s climate
and space weather and plays a crucial role as a key for unlocking the secrets of many cosmical plasma
phenomena. It provides a natural route for learning at close hand about fundamental cosmic processes
at work in the Universe, such as magnetic turbulence, dynamos, spots, cycles, coronae, winds, flares and
particle acceleration. What riches would be in store for us if we could view more distant objects with as
much precision!
Solar MHD has three strands with important complementary insights, namely, sophisticated analytical
theory guided by physical principles, observation from space and ground, and state-of-the-art computational
experiments. Often, the greatest progress comes when there is good communication between them and when
they work closely together.
The Sun is an amazing object, which has continued to reveal completely unexpected features when
observed in greater detail or at new wavelengths. Huge progress on the main questions in solar MHD has
been made. The questions have been greatly refined and remain hot topics of investigation, but none has
yet been conclusively answered:
* How is the magnetic field generated by dynamo action to create the solar cycle?
* What is the nature of flux emergence and how are sunspots created?
* How is the corona heated and the solar wind accelerated?
* How are prominences formed?
* How do solar flares and coronal mass ejections occur?
This book follows a similar pattern to Solar Magnetohydrodynamics. It first describes in detail new
observations of the Sun and the basic equations of MHD. Then follow chapters on the different aspects
of MHD, namely, equilibria, waves, shocks, and instabilities, which have been greatly extended in the
xvii
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xviii Preface
light of new research, such as on waves in non-uniform media. Next comes a substantial new chapter on
the fundamental topic of magnetic reconnection, which is dear to my heart. The subsequent chapters on
the applications of MHD to solar phenomena are completely different from the original book in view of
the enormous changes in understanding. Chapter 10 deals with the theory of chromospheric and coronal
loops and mechanisms for heating them by waves, reconnection or turbulence. Chapter 11 discusses flux-
rope models for prominences and their fine-scale structure, namely, barbs and threads. Chapter 12 describes
mechanisms for the eruption of a coronal flux rope to give an eruptive flare or coronal mass ejection, together
with the latest models for energy release by reconnection. The final chapter summarises classical theories
for the solar wind. It also describes wave turbulence models for the fast wind and reconnection models for
the slow wind. Appendices describe units, useful values and expressions. Problem examples are referred
to at various points in each chapter. They, together with their solutions and an appendix on ground- and
space-based instruments, can be found on the Web page www.cambridge.org/9780521854719. The book
ends with a comprehensive reference list and a detailed index.
The aim of mathematical modelling is not to account for all observational details of a particular phe-
nomenon, or simply to produce an image that resembles an observation, but rather to focus on the key
physical mechanisms at work. The full nonlinear equations of MHD are so complex that they often need
to be approximated drastically by focusing on a particular mechanism. One begins with a simple model,
and then extra effects are added in an attempt to make the model more realistic. Thus, simple analytical
models and complex numerical computations can play complementary roles in enhancing understanding.
Computational experiments are in many respects similar to laboratory experiments and can be so sophis-
ticated that the underlying processes are far from transparent. When modelling is undertaken successfully,
it is possible to predict behaviour with different parameter values and to give deep physical understanding
of a phenomenon. However, in order to decide what are the important observations and physical processes,
it is invariably crucial to listen carefully to insights from observers.
Single-fluid MHD is a remarkably successful model for describing solar plasma at large scales, even when
it is collisionless, for reasons described in Chapter 2. However, it will be important to develop MHD in
future to include multi-fluid effects, as well as kinetic models for the internal structure of non-ideal regions
in reconnection, shock waves and wave dissipation structures.
Trying to summarise the advances of the past thirty years and the current state of solar MHD has
been a formidable task. Although I have done my best, there are bound to be omissions and mistakes in
understanding, for which I apologise.
The notations adopted for cylindrical and spherical polars are (R, φ, z)and(r, θ, φ), respectively. All
quantities are measured in rationalised mks units, with the magnetic field in tesla (T) in most formulae.
In the text, however, magnetic field strengths are commonly quoted in gauss (G), such that 1 G = 10
−4
T,
while energy is sometimes given in erg instead of joules (J), such that 1 erg = 10
−7
J, since these are much
better known in the community. Lengths in formulae are usually measured in metres (m), although in the
text they are often quoted in megametres (Mm) such that 1 Mm = 10
6
m, since typical small observed
structures in the photosphere and corona are about 1 Mm across.
Figures 1.8, 1.13, 1.18, 1.41, 3.10, 3.11, 3.14–3.16, 9.4, 9.12, 9.16, 9.17, 10.8b, 10.14–10.16, 10.23, 10.24,
10.27, 10.28, 10.30–10.32 and 13.8 appeared in the Astrophysical Journal and are reproduced by permission
of the American Astronomical Society. Figure 9.11b appeared in Monthly Notices of the Royal Astronomical
Society and is reproduced by permission of Oxford University Press on behalf of the Royal Astronomical
Society.
Figures 1.16, 1.20cd, 1.29a, 1.35b and 1.36 were produced by instruments on Hinode, which is a Japanese
space mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and
STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC
(Norway). Figures 1.3, 1.15, and 1.37b come from SDO and are courtesy of NASA/SDO and the AIA
or HMI science teams. Figures 1.12, 1.27 and 1.38 are courtesy of the MDI, LASCO and EIT consortia
www.cambridge.org
© in this web service Cambridge University Press
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978-0-521-85471-9 - Magnetohydrodynamics of the Sun
Eric Priest
Frontmatter
More information
Preface xix
on SOHO, which is a project of international cooperation between ESA and NASA. Figures 1.13, 1.14a,
1.20ab, 1.28, 1.29b, 1.35a, 9.7 and 11.14c are from the Swedish 1-m Solar Telescope (SST) on La Palma
(in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof´ısica de Canarias);
this is operated by the Institute for Solar Physics, which was managed by the Royal Swedish Academy of
Sciences until 1 January 2013 and since then by Stockholm University. Figures 1.22, 1.41 and 10.25 are
from TRACE, which was a NASA Small Explorer (SMEX) mission. Figures 1.21c and 10.14a are from
Yohkoh, which was a Japanese solar mission, developed and launched by ISAS/JAXA, Japan, with NASA
and SERC/PPARC (UK) as international partners. Credits to the other figures appear in the captions.
It has been a privilege to be James Gregory Professor at St Andrews University. Many of James Gregory’s
discoveries are invaluable in modern solar physics. He was one of the inventors of calculus (with Newton and
Leibniz), he invented the gregorian telescope and he discovered the diffraction grating by shining a light
through a seagull’s feather. He was appointed the first Regius Professor of Mathematics in the University
in 1668 at the age of 30 and sadly died at the age of 37.
Many people have generously helped with advice and suggestions, for which I am extremely grateful,
but they cannot be blamed for any inadequacy in treatment.
St Andrews and Dundee colleagues have given more support than they know and have provided a
kindly and highly stimulating environment, including: Vasilis Archontis, Peter Cargill, Ineke De Moortel,
Andrew Haynes, Alan Hood, Gunnar Hornig, Duncan Mackay, Julie McCormick, Karen Meyer, Thomas
Neukirch, Paolo Pagano, Clare Parnell, David Pascoe, Sarah Platten, David Pontin, Laurel Rachmeler,
Bernie Roberts, James Threlfall and Antonia Wilmot-Smith.
Many friends from over the world have also helped in countless ways, such as: Ernest Amouzou, Guil-
laume Aulanier, Tony Arber, Hubert Baty, Mitch Berger, Tom Berger, V´eronique Bommier, Sean Brannon,
Philippa Browning, Nic Brummell, Sacha Brun, Paul Cally, Robert Cameron, Dick Canfield, Mats Carlsson,
Arnab Choudhuri, Steve Cranmer, Len Culhane, Pascal D´emoulin, Bart De Pontieu, Mausumi Dikpati,
George Doschek, Alec Engell, Oddbjørn Engvold, Robert Erdelyi, Lyndsay Fletcher, Terry Forbes, Laurent
Gizon, Nat Gopalswamy, Mandy Hagenaar, Joanna Haigh, Louise Harra, Richard Harrison, Jack Harvey,
David Hathaway, Jean Heyvaerts, Kiyoshi Ichimoto, Elena Khomenko, Bernhard Kliem, Sam Krucker,
Jun Lin, Dana Longcope, Jean-Marie Malherbe, Eckart Marsch, Piet Martens, Marian Martinez Gonzalez,
Valentin Martinez Pillet, Sarah Matthews, Scott McIntosh, David McKenzie, Nicole Meyer-Vernet, Fer-
nando Moreno Insertis, Valera Nakariakov, Matthew Owens, Susi Parenti, Alex Pevtsov, Joseph Plowman,
Jiong Qiu, Matthias Rempel, Alex Russell, G¨oran Scharmer, Rolf Schlichenmaier, Brigitte Schmieder, Karel
Schrijver, Manfred Sch¨ussler, Roger Scott, Kazunari Shibata, Lara Silvers, Sami Solanki, Henk Spruit, Bob
Stein, Jack Thomas, Slava Titov, Steve Tobias, Juri Toomre, Javier Trujillo Bueno, Saku Tsuneta, Aad
Van Ballegooijen, Luc Rouppe Van Der Voort, Lidia van Driel-Gesztelyi, Marco Velli, Harry Warren, Nigel
Weiss, Thomas Wiegelmann, Anthony Yeates and Takaaki Yokoyama.
www.cambridge.org
© in this web service Cambridge University Press
Cambridge University Press
978-0-521-85471-9 - Magnetohydrodynamics of the Sun
Eric Priest
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