This monograph on magnetohydrodynamic
(MHD) relaxation in plasmas by Ortolani and
Schnack occupies a fascinating niche in the plasma physics literature. It is rare in the
complex and often technically sophisticated subject of plasma physics to be able to isolate a
topic and deal with it comprehensively in a mere 180 pages. Furthermore, it brings a
refreshingly original and personal approach to the treatment of plasma relaxation,
synthesizing the experiences of the two authors to produce a very readable account of
phenomena appearing in such diverse situations as laboratory reversed field pinches (RFPs)
and the solar corona. Its novelty lies in that, while it does acknowledge the seminal Taylor
theory of relaxation as a general guide, it emphasizes the role of large scale numerical MHD
simulations in developing a picture for the relaxation phenomena observed in experiment and
nature. Nevertheless, the volume has some minor shortcomings: a tendency to repetitiveness and
some omissions that prevent it being entirely self-contained.
The monograph is divided into nine chapters, with the first a readable, `chatty', introduction
to the physics and phenomena of relaxation discussed in the later chapters. Chapter 2
develops the tools for describing relaxation processes, namely the resistive MHD model,
leading to a discussion of resistive instabilities and the stability properties of RFPs. This
chapter demonstrates the authors' confessed desire to avoid mathematical detail with a rather
simplified discussion of Δ' and magnetic islands; it also sets the stage for their own belief, or
thesis, that numerical simulation of the non-linear consequences of the MHD model is the
best approach to explaining the physics of relaxation. Nevertheless, in Chapter 3 they
provide a reasonably good account and critique of one analytic approach that is available, and
which is the commonly accepted picture for relaxation in pinches - the Taylor relaxation
theory based on the conservation of global magnetic helicity.
Some of the shortcomings of the Taylor theory in explaining details of real pinch experiments
are used by the authors as a justification for a more phenomenological approach, described in
detail in Chapter 4. They construct a `phenomenological model' that utilizes experimental
information and linear stability properties; this is described authoritatively, since the authors
have been very much involved in this work. The experimental evidence showing the
presence of large scale instabilities in RFPs is used to provide support for the main thrust of
the monograph, described in Chapter 5, namely that numerical computations of the non-linear
evolution of MHD modes is the key to understanding the dynamical processes
occurring in relaxation. These MHD processes give rise to a dynamo effect, analogous to that
generating magnetic fields in the earth or stars, which overcomes the natural consequences of
Spitzer resistivity and produces a reversed toroidal field. Chapter 5 begins with a general
discussion of dynamo models and then moves on to the pioneering work of Sykes and
Wesson on numerical simulation of relaxation, before launching into an authoritative
account of more detailed and advanced simulations in which the authors themselves have
played a major part. These calculations capture the basic features of relaxation in pinches
and provide a demonstration of Taylor's theory.
Chapters 6 and 7 describe some applications to RFPs of relaxation theory: the anomalous
loop voltage, improving their performance by helicity injection, as well as sawteeth and
thermal transport.
The penultimate Chapter 8 proposes applications of this computational approach to
relaxation, developed initially for laboratory pinches, to the solar corona. This is a
stimulating discussion, drawing analogues between the two very different situations, ideal for
broadening the perspectives of the fusion physicist. Specifically, the authors consider
modelling of the evolution of active magnetic arcades, associated with sunspots, and coronal
heating, both of which result from footprint motions in the photosphere.
The volume is completed with a summary chapter, which ends by posing a number of
outstanding questions and needs. Despite their thesis that numerical simulations are the key to
understanding relaxation, the authors wisely indicate limitations to this approach, recognizing
the need for an analytic theory, with more dynamical content than the Taylor theory, to
support the simulations.
In short, this is a readable, stimulating and reasonably self-contained volume that can be
recommended to those interested in the dynamics of plasma relaxation or, indeed, to those with
more general interests in the behaviour of plasmas in the laboratory or the sun.
