An Introduction to Magnetohydrodynamics , Peter A. Davidson Cambridge U. Press, New York, 2001. $110.00, $39.95 paper (531 pp.). ISBN 0-521-79149-9, ISBN 0-521-79487-0 paper
Peter A. Davidson’s An Introduction to Magnetohydrodynamics is one of the newest texts in the Cambridge Texts in Applied Mathematics series, founded by David Crighton, who edited the series until his death in April 2000. As was Crighton, Davidson is associated with the department of applied mathematics and theoretical physics at Cambridge University. Like other books in the series, Davidson’s is intended as an introductory text for advanced undergraduate and beginning graduate students in physics, applied mathematics, and engineering.
The first part—two thirds of the book—covers the fundamentals of magnetohydrodynamics (MHD), heavily weighted towards incompressible flows (correctly, in my opinion; the aerodynamic, compressible applications have largely not panned out) and terrestrial applications. In this part, in a pleasing, colloquial style that is appropriately rigorous, as called for by the material, the author presents a remarkably comprehensive treatment of the basics. His achievement is all the more remarkable because he presupposes little or no background on the part of the reader in either fluid mechanics or electromagnetism!
Interspersed with the usual topics one would expect in such a text, Hartmann boundary layers and Alfvén waves, for example, one will find some fairly sophisticated topics, among them buoyant flows and their stability and an extensive discussion of elements of geo-dynamo theory. Solar MHD topics are discussed—the structure of sunspots, the solar dynamo, and solar flares—as is stability theory in both plasma physics and plasma containment.
The author’s discussion of MHD turbulence begins with a succinct review of such relevant non-MHD turbulence theory as Kolmogorov theory. Here, as elsewhere in the book, Davidson presents excellent scaling arguments to justify his equations and to give the reader deeper insight into the subject.
The second and remaining part of the book gives an extensive discussion of various metallurgical applications of MHD. This part is different in tone, being more of a research monograph intended for professional researchers in industry and academia.
Problems are presented at the end of each of the book’s 12 chapters. Interesting historical interpolations appear as well, particularly in the first part of the book. Like other texts in the series, the typography is easy on the eyes and the price easy on the purse. All in all, a wonderful introduction to the subject and more!
