Magnetohydrodynamics FLUID MECHANICS AND ITS APPLICATIONS Volume 80 Series Editor: R. MOREAU MADYLAM Ecole Nationale Supérieure d'Hydraulique de Grenoble Boîte Postale 95 38402 Saint Martin d'Hères Cedex, France Aims and Scope of the Series The purpose of this series is to focus on subjects in which fluid mechanics plays a fundamental role. As well as the more traditional applications of aeronautics, hydraulics, heat and mass transfer etc., books will be published dealing with topics which are currently in a state of rapid development, such as turbulence, suspensions and multiphase fluids, super and hypersonic flows and numerical modelling techniques. It is a widely held view that it is the interdisciplinary subjects that will receive intense scientific attention, bringing them to the forefront of technological advancement. Fluids have the ability to transport matter and its properties as well as transmit force, therefore fluid mechanics is a subject that is particulary open to cross fertilisation with other sciences and disciplines of engineering. The subject of fluid mechanics will be highly relevant in domains such as chemical, metallurgical, biological and ecological engineering. This series is particularly open to such new multidisciplinary domains. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of a field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity. For a list of related mechanics titles, see final pages. Magnetohydrodynamics Historical Evolution and Trends by S. MOLOKOV Coventry University UK R. MOREAU EPM-MADYLAM St Martin d’Hères France and H.K. MOFFATT University of Cambridge UK A C.I.P. 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Contents Part I Dynamo, Astrophysics, and Plasmas How MHD Transformed the Theory of Geomagnetism Paul Roberts .................................................... 3 Early Magnetohydrodynamic Research in Stockholm Bo Lehnert ...................................................... 27 Dynamo Experiments Agris Gailitis, Olgerts Lielausis, Gunter Gerbeth, and Frank Stefani .... 37 Mean-Field Dynamo Theory: Early Ideas and Today’s Problems Karl-Heinz Rädler ............................................... 55 Astrophysical MHD: The Early Years Leon Mestel ..................................................... 73 Turbulence and Magnetic Fields in Astrophysical Plasmas Alexander A Schekochihin and Steven C Cowley ..................... 85 Transient Pinched Plasmas and Strong Hydromagnetic Waves John E Allen ....................................................117 Part II High Magnetic Fields Early Years of MHD at Cambridge University Engineering Department Martin Cowley ..................................................131 vi Contents Julius Hartmann and His Followers: A Review on the Properties of the Hartmann Layer René Moreau and Sergei Molokov ..................................155 Liquid Metal Magnetohydrodynamics for Fusion Blankets Leo Bühler ......................................................171 Geostrophic Versus MHD Models Thierry Alboussière ..............................................195 Part III Turbulence The Birth and Adolescence of MHD Turbulence Keith Moffatt ....................................................213 How Analogous is Generation of Vorticity and Passive Vectors (Magnetic Fields)? Arkady Tsinober .................................................223 MHD Turbulence at Low Magnetic Reynolds Number: Present Understanding and Future Needs René Moreau, Andre Thess, and Arkady Tsinober ....................231 Modelling of MHD Turbulence Bernard Knaepen, Olivier Debliquy, and Daniele Carati ...............247 The Growth of Magnetohydrodynamics in Latvia and Israel Herman Branover ................................................263 Velocity Measurement Techniques for Liquid Metal Flows Sven Eckert, Andreas Cramer, and Gunter Gerbeth ...................275 Flow Control and Propulsion in Poor Conductors Tom Weier, Victor Shatrov, and Gunter Gerbeth .....................295 Part IV Electromagnetic Processing of Materials Overview of Electromagnetic Processing of Materials Shigeo Asai .....................................................315 Applications of High Magnetic Fields in Materials Processing Hideyuki Yasuda .................................................329 Effect of AC Magnetic Fields on Free Surfaces Yves Fautrelle, Alfred Sneyd, and Jacqueline Etay ....................345 Contents vii Numerical Modelling for Electromagnetic Processing of Materials Valdis Bojarevics and Koulis Pericleous .............................357 Magnetic Fields in Semiconductor Crystal Growth Hiroyuki Ozoe, Janusz S Szmyd, and Toshio Tagawa..................375 An Outline of Magnetoelectrochemistry Antoine Alemany and Jean-Paul Chopart ...........................391 Preface Magnetohydrodynamics (MHD) is concerned with the flow of electrically conducting fluids in the presence of magnetic fields, either externally applied or generated within the fluid by inductive action. Its origin dates back to pio- neering discoveries of Northrup, Hartmann, Alfvén, and others in the first half of the twentieth century. After 1950, the subject developed rapidly, and soon became well established as a field of scientific endeavour of great importance in various contexts: geomagnetism and planetary magnetism, astrophysics, nuclear fusion (plasma) physics, and liquid metal technology. This volume surveys both the historical evolution of the field and some of the current trends. It is based on a workshop on the History of MHD organ- ised at Coventry University, UK, 26–28 May 2004, by the working group on “High Magnetic Fields” within the European network “Magnetofluiddynamics” (COST Action P6). It contains contributions by the workshop participants, supplemented by several additional invited papers in order to provide more comprehensive coverage of the recent trends. It also includes reminiscences of scientists who worked during the period of pioneering discoveries in the field (1950s and 1960s), together with photos of at least some of the pioneers of the subject. Topics covered in this volume include dynamo theory and experiment, astrophysics, plasmas, high magnetic fields, turbulence, and electromagnetic processing of materials. Other topics such as magnetoconvection, magnetic reconnection, and tokamak plasmas are not included, simply because to do justice to these important topics would have required a book of unmanageable proportions. Judging by the vitality of the field as evidenced by this volume, we believe that MHD still poses challenges of great fundamental, as well as practical, importance, and that the prospects for its continuing vitality are bright. We gratefully acknowledge the willing cooperation of all participants of the workshop and contributors to this volume, the financial support of the European Cooperation in the field of Scientific and Technical Research (COST), the help of Svetlana Aleksandrova in organising the event, the advice xPreface of Leo Bühler on the sometimes painful process of conversion between various pieces of software, and last but by no means least, the patience and under- standing of the publishers (Springer). Coventry, Grenoble, Cambridge The Editors January 2006 Part I Dynamo, Astrophysics, and Plasmas How MHD Transformed the Theory of Geomagnetism Paul Roberts Department of Mathematics and Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, CA 90095, USA ([email protected]) Summary. The main magnetic field on the Earth is generated by, and has been maintained throughout Earth’s history by, a fluid dynamo operating in the Earth’s electrically conducting core. The author gives his personal view of how understand- ing of this ‘geodynamo’ grew during his lifetime, and he includes recollections of some of the scientists involved. The remarkable evolution of the subject from simple applications of electromagnetic theory to today’s sophisticated magnetohydrody- namic theory is outlined. The importance of Coriolis forces in core MHD is not fully appreciated even today, but it transforms MHD into an essentially different subject that is briefly reviewed here. Proposals are made to give it its own special name. 1Earlydays As this is a meeting about the history of magnetohydrodynamics (MHD), it seemed to me, when I was preparing my talk, that it might be appropriate to include some reminiscences1; I expected a fair number of people in the audience to be too young