Preface

Magnetohydrodynamics, or MHD, is a theoretical way of describing the statics and dynamics of electrically conducting fluids. The most important of these fluids 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: Alfvén 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 physicists do kinetic theory!) Nonetheless, MHD is an indispensable tool in all applications of plasma physics. Even the simplest experiment will not be built unless it has first passed muster with MHD. The reason is that MHD deals with fundamental force balance and deviation from it, concepts that are surprisingly subtle and complex. MHD also provides the machinery for understanding the basic properties of global structure of magnetized plasmas, how they can sustain themselves, and why they share a small number of global properties. In this course we will look at many of these important issues in what I hope is sufficient detail as to reveal some of the elegance that underlies this immensely useful theory, and gain some appreciation for the skill of the pioneers of the field. While MHD is the simplest mathematical model of a plasma, it is difficult to justify as a valid description of any interesting plasma. Surely plasmas know that they are made of individual ions and electrons (or at a minimum of separate ion and electron fluids) and that they are so hot that collisions between particles are relatively rare events! MHD completely ignores both of these issues. Nonetheless, it is a fact that MHD provides a remarkably accurate description of the low-frequency, long-wavelength dynamics of real plasmas. MHD seems to work (even when it shouldn’t)!