Microscopic Dynamics of Plasmas and Chaos

Some of the key intellectual foundations of plasma physics are in danger of becoming a lost art. Fortunately, however, this threat recedes with the publication of this valuable book. It renders accessible those aspects of theoretical plasma physics that are best approached from the perspectives of classical mechanics, in both its early nineteenth century and late twentieth century manifestations. Half a century has elapsed since the publication of seminal papers such as those by Bohm and Pines (1951), van Kampen (1955), and Bernstein, Greene and Kruskal (1957). These papers served to address a fundamental question of physics - namely the relation between degrees of freedom that exist at the individual particle level of description, and those that exist at the collective level - in the plasma context. The authors of the present book have played a major role in the investigation of this question from an N-body standpoint, which can be divided into two linked themes. First, those topics that can be illuminated by analytical methods that lie in the tradition of classical mechanics that stretches back to Lagrange, Legendre and Hamilton. Second, those topics that benefit from the insights developed following the redevelopment of classical mechanics in relation to chaos theory in the 1980s and subsequently. The working plasma physicist who wishes to dig more deeply in this field is faced at present with a number of challenges. These may include a perception that this subfield is of limited relevance to mission-oriented questions of plasma performance; a perception of the research literature as being self-contained and inaccessible; and, linked to this, unfamiliarity with the mathematical tools. The latter problem is particularly pressing, given the limited coverage of classical mechanics in many undergraduate physics courses. The book by Elskens and Escande meets many of the challenges outlined above. The rewards begin early, by the end of the second chapter, with beautiful derivations of the self-consistent Lagrangian for wave-particle interactions, followed by an equivalent Hamiltonian formulation in terms of action-angle variables. In the following two chapters, these and related techniques are used to explore the deepest topics of plasma dynamics and wave theory, often from a beam-plasma perspective. The book begins afresh at chapter 5, which is an ambitious attempt to summarise modern classical dynamics. This chapter begins well, with a nice introduction to action-angle variables (these have already been extensively exploited in the preceding chapters, however! ), but the account eventually became too compressed for the present reviewer. There follow two further chapters on both diffusion and the single-wave-particle system. Perhaps this book is best considered as a companion to the research literature (indeed there is a useful and extensive bibliography), rather than as a conventionally structured textbook. Certainly it is a book that should be read backwards and sideways, as well as forwards. Most readers, for example, will be more familiar with the Vlasov-Poisson system than with the N-body approach to particles and fields that is developed here: their natural starting point will perhaps be appendix G.4 of the present volume. Nor does the book provide a free-standing account of plasma dynamics from the chosen perspective. For example, prior familiarity with van Kampen modes in the Vlasov--Poisson description would greatly assist understanding of chapter 3. Challenging exercises are embedded in the text throughout (even in the otherwise excellent appendices), with answers not necessarily provided. Altogether, this book provides a wealth of theoretical information that is not easily accessible from any other source. It is a book with character, written from a definite viewpoint, but it also facilitates the development of the reader's own perspective by offering a clear path to the original research literature. R O Dendy