Magnetohydrodynamics, or MHD, is the study of electrically conducting fluids, usually plasmas or liquid metals, in which the magnetic field plays a dynamical role. Hannes Alfvén’s Nobel Prize–winning research in the 1940s showed that in a highly conducting fluid, magnetic field lines impart elasticity to it through the Lorentz force. MHD has a wide range of applications in geophysics, planetary science, and astrophysics, and it is also of great importance for magnetic confinement fusion and metallurgy.
Sébastien Galtier’s textbook, Introduction to Modern Magnetohydrodynamics, offers a wide-ranging, general primer on MHD and its various applications. Derived from a graduate course taught by the author at the Université Paris–Saclay, the book is well suited for graduate students in physics, mathematics, and engineering. Many sections are accessible to advanced undergraduate students in those disciplines as well, but some topics in the second half of the book, and many of the exercises, are more suitable for graduate students.
Introduction to Modern Magnetohydrodynamics is divided into four parts, each of which is followed by a modest number of useful exercises with worked solutions. The book contains a generous helping of diagrams and graphs that illustrate the text’s concepts and results. A wealth of photographic images and snapshots from numerical simulations help to illuminate MHD’s historical background and its various applications.
In part 1, “Foundations,” Galtier introduces the physics of plasmas and derives the basic equations of MHD. He shows how those equations imply conservation laws for mass, momentum, energy, and helicity, and he discusses the consequences of the induction equation for the preservation of the flux and topology of the magnetic field. The Hall effect is included here because of its importance at length scales smaller than the ion inertial length.
Part 2, “Fundamental Processes,” begins with a discussion of linear magnetohydrodynamic waves. In addition to the classical Alfvén and magnetosonic waves, the author describes the whistler, ion-cyclotron, and kinetic Alfvén waves that emerge when the Hall effect is taken into account. Subsequent chapters provide brief but clear discussions of natural and experimental dynamos, discontinuities such as shocks and current sheets, and magnetic reconnection in which irreversible changes of magnetic topology occur. That material is well illustrated with descriptions of recent experiments on dynamos in liquid metals and reconnection in plasmas.
Part 3, “Instabilities and Magnetic Confinement,” presents the classical theory of the equilibrium and stability of magnetized configurations. It emphasizes the demanding requirements for the stable magnetic confinement of plasmas in controlled thermonuclear fusion; those requirements constrain the design of tokamaks such as ITER. Also included is an analysis of the magnetorotational instability in the accretion disks that orbit around stars or black holes, an emerging area of research in astrophysical MHD.
In part 4, “Turbulence,” Galtier introduces the theoretical study of turbulence in fluids and plasmas. He describes the phenomenology of hydrodynamic turbulence and outlines the few exact statistical results that can be mathematically derived. He then takes a similar approach to MHD turbulence, whose more complicated phenomenology exhibits changing properties in different physical contexts. The final chapter discusses such advanced topics as intermittency and weak turbulence, which are close to the author’s own field of research.
With an appealing combination of background material and carefully selected mathematics, Galtier succeeds in presenting the flavor of each topic. His approach manages to whet readers’ appetites without overwhelming them with lengthy derivations or excessive technicalities. The manageable level of detail and the modest length of the book make it suitable as an accompaniment to a graduate lecture course, which is indeed how the text originated. Particularly noteworthy is the inclusion of material on the Hall effect, which reflects a growing interest in that phenomenon in the context of MHD.
Introduction to Modern Magnetohydrodynamics is largely an English translation of Galtier’s 2013 French textbook Magnétohydrodynamique: Des plasmas de laboratoire à l’astrophysique with some new material. The English text contains occasional Gallicisms that may puzzle readers, such as surface instead of area and Ecin to denote kinetic energy. Although I did come across a small number of errors and typos in the equations, the quality of the text and mathematical notation is high.
Galtier’s attractive and concise volume joins several excellent modern introductory textbooks with somewhat different styles and emphases. They include Peter Davidson’s Introduction to Magnetohydrodynamics (2nd edition, 2017), Hans Goedbloed and Stefaan Poedts’s Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas (2004), and Eric Priest’s Magnetohydrodynamics of the Sun (2014). I would recommend Introduction to Modern Magnetohydrodynamics to students—especially graduate students—learning the basics of this exciting field.
Gordon Ogilvie is a professor of mathematical astrophysics at the University of Cambridge in the UK. His research is in theoretical astrophysical fluid dynamics and magnetohydrodynamics with applications to astrophysical disks and exoplanets.
