This book is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids.

Magnetohydrodynamics, or MHD, is a theoretical way of describing the statics and dynamics of electrically conducting uids. The most important of these uids occurring in both nature and the laboratory are ionized gases, called plasmas. These have the simultaneous properties of conducting electricity and being electrically charge neutral on almost all length scales. The study of these gases is called plasma physics. MHD is the poor cousin of plasma physics. It is the simplest theory of plasma dynamics. In most introductory courses, it is usually afforded a short chapter or lecture at most: Alfven ́ waves, the kink mode, and that is it. (Now, on to Landau damping!) In advanced plasma courses, such as those dealing with waves or kinetic theory, it is given an even more cursory treatment, a brief mention on the way to things more profound and interesting. (It is just MHD! Besides, real plasma phy- cists do kinetic theory!) Nonetheless, MHD is an indispensable tool in all applications of plasma physics.

This book revises the evolution of ideas in various branches of magnetohydrodynamics (astrophysics, earth and solar dynamos, pinch, MHD turbulence and liquid metals) and reviews current trends and challenges. Uniquely, it contains the review articles on the development of the subject by pioneers in the field as well as leading experts, not just in one, but in various branches of magnetohydrodynamics, such as liquid metals, astrophysics, dynamo and pinch.

This textbook provides a modern and accessible introduction to magnetohydrodynamics (MHD). It describes the two main applications of plasma physics, laboratory research on thermo-nuclear fusion energy and plasma astrophysics of the solar system, stars and accretion disks, from the single viewpoint of MHD. This approach provides effective methods and insights for the interpretation of plasma phenomena on virtually all scales, from the laboratory to the universe. It equips the reader with the necessary tools to understand the complexities of plasma dynamics in extended magnetic structures. The classical MHD model is developed in detail without omitting steps in the derivations and problems are included at the end of each chapter. This text is ideal for senior-level undergraduate and graduate courses in plasma physics and astrophysics.

Following on from the companion volume Principles of Magnetohydrodynamics, this textbook analyzes the applications of plasma physics to thermonuclear fusion and plasma astrophysics from the single viewpoint of MHD. This approach turns out to be ever more powerful when applied to streaming plasmas (the vast majority of visible matter in the Universe), toroidal plasmas (the most promising approach to fusion energy), and nonlinear dynamics (where it all comes together with modern computational techniques and extreme transonic and relativistic plasma flows). The textbook interweaves theory and explicit calculations of waves and instabilities of streaming plasmas in complex magnetic geometries. It is ideally suited to advanced undergraduate and graduate courses in plasma physics and astrophysics.

Suitable for advanced undergraduates and graduate students in engineering, this text introduces the concepts of plasma physics and magnetohydrodynamics from a physical viewpoint. The first section of the three-part treatment deals mainly with the properties of ionized gases in magnetic and electric fields, essentially following the microscopic viewpoint. An introduction surveys the concepts of ionized gases and plasmas, together with a variety of magnetohydrodynamic regimes. A review of electromagnetic field theory follows, including motion of an individual charged particle and derivations of drift motions and adiabatic invariants. Additional topics include kinetic theory, derivation of electrical conductivity, development of statistical mechanics, radiation from plasma, and plasma wave motion. Part II addresses the macroscopic motion of electrically conducting compressible fluids: magnetohydrodynamic approximations; description of macroscopic fluid motions; magnetohydrodynamic channel flow; methods of estimating channel-flow behavior; and treatment of magnetohydrodynamic boundary layers. Part III draws upon the material developed in previous sections to explore applications of magnetohydrodynamics. The text concludes with a series of problems that reinforce the teachings of all three parts.

This advanced textbook reviews the complex interaction between the Sun's plasma atmosphere and its magnetic field.

2 The linearized ideal MHO equations. . . . . . . . . . . . 204 3 Spectral problems corresponding to evolutionary problems . . 211 4 Stability of equilibrium configurations and the Energy Principle 215 5 Alternative forms of the plasma potential energy 220 6 Minimization of the potential energy with respect to a parallel displacement . . . . . . . . . . . . . 222 7 Classification of ideal MHO instabilities . 224 8 The linearized non-ideal MHO equations . 226 Chapter 6. Homogeneous and discretely structured plasma oscillations 229 I Introduction . . . . . . . . . . . . . . . 229 2 Alfven waves in an incompressible ideal plasma 230 3 Cold ideal plasma oscillations. . . . 233 4 Compressible hot plasma oscillations 236 5 Finite resistivity effects . . . . . . . 239 6 Propagation of waves generated by a local source 240 7 Stratified plasma oscillations . . . . . . . . . 247 8 Oscillations of a plasma slab . . . . . . . . . 254 9 Instabilities of an ideal stratified gravitating plasma 256 10 Instabilities of a resistive stratified gravitating plasma. 262 Chapter 7. MHO oscillations of a gravitating plasma slab 265 I Introduction . . . . . . . . . . . . . . . 265 2 Gravitating slab equilibrium . . . . . . . . 266 3 Oscillations of a hot compressible plasma slab 267 4 Investigation of the slab stability via the Energy Principle 270 5 On the discrete spectrum of the operator Kk . . . . . . 274 6 On the essential spectrum of the operator Kk . . . . . . 279 7 On the discrete spectrum embedded in the essential spectrum 282 8 The eigenfunction expansion formula . . . . . . . . . . 285 9 Excitation of plasma oscillations by an external power source . 288 10 The linearized equations governing resistive gravitating plasma slab oscillations . . . . . . . . . . . . . . . . . . . . . 290 II Heuristic investigation of resistive instabilities. . . . . . . . . .

I have felt the need for a book on the theory of solar magnetic fields for some time now. Most books about the Sun are written by observers or by theorists from other branches of solar physics, whereas those on magnetohydrodynamics do not deal extensively with solar applications. I had thought of waiting a few decades before attempting to put pen to paper, but one summer Josip Kleczek encouraged an im mediate start 'while your ideas are still fresh'. The book grew out of a postgraduate lecture course at St Andrews, and the resulting period of gestation or 'being with monograph' has lasted several years. The Sun is an amazing object, which has continued to reveal completely unexpected features when observed in greater detail or at new wavelengths. What riches would be in store for us if we could view other stars with as much precision! Stellar physics itself is benefiting greatly from solar discoveries, but, in tum, our understanding of many solar phenomena (such as sunspots, sunspot cycles, the corona and the solar wind) will undoubtedly increase in the future due to their observation under different conditions in other stars. In the 'old days' the solar atmosphere was regarded as a static, plane-parallel structure, heated by the dissipation of sound waves and with its upper layer expanding in a spherically symmetric manner as the solar wind. Outside of sunspots the magnetic field was thOUght to be unimportant with a weak uniform value of a few gauss.