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

Most of the visible matter in the universe exists in the plasma state. Plasmas are of major importance for space physics, solar physics, and astrophysics. On Earth they are essential for magnetic controlled thermonuclear fusion. This textbook collects lecture notes from a one-semester course taught at the K.U. Leuven to advanced undergraduate students in applied mathematics and physics. A particular strength of this book is that it provides a low threshold introduction to plasmas with an emphasis on first principles and fundamental concepts and properties. The discussion of plasma models is to a large extent limited to Magnetohydrodynamics (MHD) with its merits and limitations clearly explained. MHD provides the students on their first encounter with plasmas, with a powerful plasma model that they can link to familiar classic fluid dynamics. The solar wind is studied as an example of hydrodynamics and MHD at work in solar physics and astrophysics.

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.

An introductory text on magnetohydrodynamics for advanced students, covering its broad range of applications in nature and in the laboratory.

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.

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.

A self-contained introduction to magnetohydrodynamics with emphasis on nonlinear processes.

This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.

This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate students and researchers working in turbulence theory, plasma physics and astrophysics.

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