Table of contents

The unlocking of static resistive tearing modes by rotating external magnetic perturbations such as those which may arise from the natural tokamak error field is discussed. A threshold error field current is shown to exist, below which the mode frequency will not lock to the error field frequency. The slowing down drag applied to the island by the resistive vessel of the tokamak and the unphased magnetic perturbation arising from the error field at the rational surface of the mode eventually set the island into an oscillatory motion around ω ≈ 0 Hz. An upper limit in the error field frequency exists above which the threshold current is insufficient for locking the mode frequency to the error field frequency. This limit depends on the island width, the local plasma density and the non-linear wall response to magnetic perturbations.

A new technique for wall conditioning that will be especially useful for future larger superconducting tokamaks, such as ITER, has been successfully developed and encouraging results have been obtained. Solid carborane powder, which is non-toxic and non-explosive, was used. Pulsed RF plasma was produced by a non-Faraday shielding RF antenna with RF power of 10 kW. The ion temperature was about 2 keV with a toroidal magnetic field of 1.8 T and a pressure of 3 × 10^-1 Pa. Energetic ions broke up the carborane molecules, and the resulting boron ions struck and were deposited on the first wall. In comparison with glow discharge cleaning boronization, the B/C coating film shows higher adhesion, more uniformity and longer lifetime during plasma discharges. The plasma performance was improved after ICRF boronization.

The first systematic study on the mass dependence of the L mode density limit is reported for JET hydrogen, deuterium and tritium divertor plasmas. The density limit, defined as the density at the onset of the X point MARFE, is found to scale inversely with the ion mass in vertical target configurations, while no isotope effect is found in horizontal target configurations. Two dimensional numerical simulations reproduce the observed mass dependence in vertical target discharges. The experiments indicate a coupling between the mass and the power dependence of the L mode density limit. The experimental results are compared with analytic models, which suggest that the ion-neutral transverse collisionality plays a role in the density limit.

Because of its large size, single null divertor and flexible magnetic geometry, JET is capable of producing the most reactor relevant plasmas of any present generation tokamak. In recent DT experiments, the fusion performance of these plasmas was tested for the first time. Over 4 MW of fusion power was produced in a high power, steady state pulse of 5 s, limited by the duration of the heating power. The fusion Q^E, defined simply as the fusion energy produced divided by the input energy over this 5 s interval, was 0.18. These DT ELMy H mode discharges performed up to expectations based on DD preparation pulses and thus establish a firm basis for extrapolating to a next step machine. Operation at low q₉₅ is possible in JET with no degradation in the confinement enhancement factor and provides an improved margin to ignition when extrapolated to ITER. Considerable uncertainties remain, nonetheless. In particular, access to high density, relative to the Greenwald limit, and operation in close proximity to the H mode threshold may both result in a degradation of the confinement in the next step machine.

In equatorial single null diverted discharges in TEXT-Upgrade, up-down asymmetries have been noted, the sign and magnitude of which depend on plasma conditions such as electron density and X point position. Geometrical effects do not play a role in these plasmas, which are topologically up-down symmetric, so the asymmetry must come from physical driving mechanisms. Several such mechanisms will be investigated, both computationally and experimentally, and compared with data from tokamak discharges. An analysis is included of the E × B , diamagnetic and ∇ T × B drifts as well as plasma rotation. The B2-EIRENE plasma simulation code is used to evaluate the respective influences of the ∇ T × B driving terms. Scans of the X point position relative to the divertor plates and of the electron density are performed. The X point is brought in all the way to the divertor plates so as to assess the importance of the private region in the drift flow patterns and to break the flow loops. The low recycling regime typical of TEXT-Upgrade single null plasmas allows separation and identification of the influence of individual flows. It is concluded that E × B drift is the dominant effect and that it qualitatively explains the reported behaviour.

The similar poloidal patterns of divertor erosion and redeposition of the ASDEX Upgrade, DIII-D and JET tokamaks are examined by comparing hydrogen isotope retention at the surfaces of divertor tiles. The outer divertor strike point undergoes net erosion. The inner divertor is a region of net redeposition, with deuterium co-deposition rates ∼20 μg m² s^-1 for all three devices; despite their differences in geometry, size and plasma facing materials. This extrapolates to an unacceptably high tritium retention rate in a DT burning steady state tokamak.

A new target option for energy applications of heavy ion inertial fusion is analysed. It has a spherical hohlraum and is irradiated by ion beams along the directions of the zeros of the fourth Legendre polynomial P₄. The target performance is simulated with a 1-D three temperature hydrodynamics code and with a 2-D view factor code. Its efficiency is shown to depend crucially on the structure of the hohlraum wall, which, simultaneously, plays the role of the X ray converter. For an optimized pulse power profile, a 1-D energy gain of G = 78 is calculated with an input energy of E_dr = 6.1 MJ in the form of 5 GeV ²⁰⁹Bi ions focused on the target sphere with an outer radius of R = 6.37 mm.

Discrete kinetic shear Alfvén modes driven by ion temperature gradient (AITG) are investigated in the full gyrokinetic limit. It is shown that AITG instability may occur when the plasma pressure gradient is well below the threshold value for ideal MHD ballooning instabilities and that the critical magnetic shear required to completely stabilize the former is significantly higher than that for the latter. In addition, finite-β (=plasma pressure/magnetic pressure) effects on toroidal electrostatic ion temperature gradient (ITG) modes are studied, and the coexistence of AITG and ITG in a certain parameter regime is demonstrated. The effects of AITG instabilities on plasma confinement are discussed.

A variety of low density discharges in the DIII-D tokamak exhibit a prompt response (<10 ms) to neutral beam injection as evidenced by changes in the Doppler shift of the density fluctuations. This variation in the Doppler shift, attributed to a changing V_{θ,Er × B} velocity, which is in turn due to a rapidly changing radial electric field E_r, is observed from the deep core to the edge of these plasmas. The core changes are large and occur much more quickly than collisional beam equilibration times (⩾ 120 ms for the core) indicating a different momentum transfer mechanism. Towards the edge the Doppler shift times approach the collisional transfer times. Theoretical predictions of changes in the core E_r due to radial fast particle currents are not large enough to explain the observations. Although not yet understood this effect could lead to a tool for relatively fast feedback control of core electric fields in advanced confinement regimes.

Report on the Joint Meeting of the IAEA Technical Committee Meeting on Spherical Tori and the Fourth International Workshop on Spherical Tori held at the University of Tokyo, Tokyo, Japan 26-28 October 1998.

This is the only book with which I am familiar that attempts to cover both fluids and plasmas. It is true that these subjects are closely related, but the logic of attempting to survey both fields, each of which is very broad, in a single volume is not really clear. References between the two subjects are not so frequent and there are excellent readily available texts in fluid mechanics. I would have preferred to see a more extensive coverage of the plasma physics of interest and usefulness to astrophysical students.

The book is well written, covering quite a large number of topics in a clear and pleasant style which makes enjoyable reading. It familiarizes the student with a considerable number of interesting and important subjects. The student who reads this book will successfully gain a very good understanding of many, often referred to, astrophysical topics such as accretion discs, dynamos, astrophysical jets and magnetic reconnection.

As is clear from the title, the author first treats fluids or neutral gases in this broad survey. He starts from the microscopic point of view, deriving the Boltzmann equation and the H theorem. He then arrives at the ideal and Navier-Stokes fluid equations in a systematic manner by expanding in the small mean free path, a technique also applied in plasma physics.

He then discusses the basic properties of fluids that every physics student should know, such as Bernoulli's law, the conservation of circulation, the steepening of waves to form shocks and the jump conditions in a shock. He intersperses his derivations of these relations with helpful illustrations, such as aerodynamic lift and supernova blast waves. He then takes up convection in a compressible medium, and Raleigh-Bernard convection in sufficient detail to give the reader a sound appreciation of these important phenomena. At the end of the fluid section of the book he presents Kolmogoroff turbulence, and in a very useful chapter the physics of fluids in rotating systems. I found this last chapter very helpful, as well as entertaining.

The first part of the book is valuable, helping students to find their way through more formal fluid dynamics texts such as those of Landau and Lifshitz, Lamb and even Shu.

On the other hand, the second part of the book, on the more complicated field of plasmas, is actually shorter than the first part, 183 pages versus 200 pages devoted to fluids, and is not so well balanced.

In this part the author first treats the orbits of individual particles (Chapter 10). He then turns to collections of particles, starting with the rather difficult BBGKY formalism. This is in line with his goal of developing each subject from basic principles. However, only the Vlasov equation emerges from this chapter, and there is no really deep explanation of the more basic kinetic theory being presented. The author then presents the collisionless theory of plasma waves, including Landau damping. He does not go into Landau damping in any great physical detail, contenting himself with describing how one must modify the velocity contour to surround any poles, referring the student to other texts for the true explanation. Only a hazy idea of the significance of this process is given.

Chapter 14 concerns magnetohydrodynamics, and again the treatment is sketchy, but some quite interesting examples of magnetohydrodynamics in astrophysics are provided. Chapter 15 takes up magnetic reconnection and Taylor relaxation, while Chapter 16 sketches classical dynamo theory giving the famous Cowling theorem to motivate this theory. Chapter 17 is an epilogue, which touches on a number of topics not covered earlier.

In summary, the author is quite successful in bringing many interesting and important plasma astrophysical phenomena to the attention of students, but only in a semiquantitative way. Thus, the more able graduate student cannot really master the subject from this text without also supplementing it with more technical books such as those of Shu, Krall and Trivelpiece and Montgomery and Tidman. In this sense the plasma physics section is more appropriate to an undergraduate course than to a graduate course as the author recommends.

Furthermore, there are a number of quite important topics not covered in the book that are essential to any really basic understanding of plasma astrophysics. Examples of such topics are: the fact that thermal conductivity is strongly suppressed across even a weak magnetic field, the interaction caused by plasma instabilities of energetic particles, such as cosmic rays, with the background plasma, the buildup of a small scale magnetic field in turbulence by field line stretching, the Biermann battery mechanism, the Braginski equations for a two fluid plasma with transport coefficients, runaway electrons and the shock acceleration of cosmic rays. It is true there is an attempt to cover some of these topics through the excellent sets of problems for the student at the end of each chapter. However, I am not sure that the student will be able to gain any real understanding in this way, or even be able to solve some of them.

In summary, the author has done a really excellent job in qualitatively imparting knowledge of an impressive number of phenomena to the student in an effective and pleasant manner. However, because of the self-imposed constraint to cover two large topics, fluids and plasmas, he has not succeeded in rigorously training the student in the practice of plasma astrophysics.

Duncan Bryant is a retired space plasma physicist who spent most of his career at the Rutherford-Appleton Laboratory in Oxfordshire, England. For many years he has been challenging a widely accepted theory, that auroral electrons are accelerated by double layers, on the grounds that it contains a fundamental error (allegedly, an implicit assumption that charged particles can gain energy from conservative fields). It is, of course, right that models of particle acceleration in natural plasmas should be scrutinized carefully in terms of their consistency with basic physical principles, and I believe that Dr Bryant has performed a valuable service by highlighting this issue. He maintains that auroral electron acceleration by double layers is fundamentally untenable, and that acceleration takes place instead via resonant interactions with lower hybrid waves. In successive chapters, he asserts that essentially the same process can account for electron acceleration observed at the Earth's bow shock, in the neighbourhood of an `artificial comet' produced as part of the Active Magnetospheric Particle Explorers (AMPTE) space mission in 1984/85, in the solar wind, at the Earth's magnetopause, and in the Earth's magneto- sphere. The evidence for this is not always convincing: waves with frequencies of the order of the lower hybrid resonance are often observed in these plasma environments, but in general it is difficult to identify clearly which wave mode is being observed (whistlers, for example, have frequencies in approximately the same range as lower hybrid waves). Moreover, it is not at all clear that the waves which are observed, even if they were of the appropriate type, would have sufficient intensity to accelerate electrons to the extent observed. The author makes a persuasive case, however, that acceleration in the aurora, and in other plasma environments accessible to in situ measurements, involves some form of wave turbulence.

In Chapter 2 it is pointed out that the Debye number (the number of particles in a sphere of radius equal to the Debye length) is actually rather higher in the solar wind and the Earth's magnetosphere than it is in any laboratory plasma: in this sense space plasmas are more `ideal' than laboratory ones. Changes in magnetic field topology occur in both the magnetosphere and tokamaks, but in the former case the term `magnetic reconnection' tends to be used only in a steady state context: temporary or sporadic changes in field topology at the magneto- sphere/magnetosheath boundary, for example, are described instead as `flux transfer events'. Reconnection in tokamaks, on the other hand, is generally regarded as an intrinsically time dependent process. Such subtle distinctions in terminology should be borne in mind by any fusion researchers reading this book.

Dr Bryant's writing style is informal and often entertaining. A good example of this, from Chapter 3, is the following: ``Auroral arcs can be bright enough to use as a reading lamp, although it would be something of a waste to use it as such, since the aurora is vastly more interesting than any document (even this one).'' Chapter 3, indeed, is the best part of the book, covering as it does the author's principal area of expertise, namely the aurora. The author gives a very clear account of auroral phenomenology, in particular observations of auroral electrons, before considering the merits of rival acceleration mechanisms.

The approach is largely non-mathematical, with few equations: those that do appear are not numbered (it would have been better if they had been). It has to be said that the author is not always rigorous or consistent. For example, acceleration a is first defined `in its most general sense' to be rate of change of speed, rather than velocity: thus, according to this definition, a = 0 in a static magnetic field. A few pages later, the same symbol is used to denote the modulus of the rate of change of velocity: this, of course, is finite in a static magnetic field. Such elementary distinctions matter, because in order to address the issue of whether or not electrons are `accelerated' in static or quasi-static fields, one must first define unambiguously what `acceleration' means. It is stated in Chapter 2 that the Larmor radius of a particle is proportional to its magnetic rigidity divided by the magnetic field component normal to the particle trajectory. This, of course, is incorrect: it is the particle's momentum component normal to the field which defines the Larmor radius. The book contains a number of statements which are either misleading or demonstrably incorrect. For example, at the end of Chapter 3, and again at the end of Chapter 4, neutral beam injection (NBI) in tokamaks is invoked as a precedent for lower hybrid wave excitation by cross-field drifts. Although it is true that lower hybrid waves can couple to energetic ions in a tokamak, and could in principle be amplified by fusion alpha particles [see N.J. Fisch, J.-M. Rax, Phys. Rev. Lett. 69 (1992) 612], NBI has not, to the best of my knowledge, been used as a source of such waves. In Chapter 9, referring to solar flares, the author states that ``characteristic products of the accelerated electrons are X rays generated by synchrotron radiation in the remaining magnetic fields''. In fact, flare accelerated electrons produce X rays via bremsstrahlung, the magnetic field and particle energies being such that synchrotron radiation occurs at microwave frequencies instead (the more general term `gyrosynchrotron radiation' tends to be used by solar flare researchers, in recognition of the fact that the electrons producing the bulk of the emission are only mildly relativistic). Indeed, bremsstrahlung X rays and gyrosynchrotron microwaves provide important sources of information on the distribution function of flare accelerated electrons, but the author makes only a brief mention of such observations, preferring to concentrate on direct measurements of flare accelerated electrons at the Earth's orbit, despite acknowledging that uncertainties in propagation effects make it very difficult to reconstruct conditions at the Sun from such measurements.

Similar remarks apply to the final chapter, on acceleration of cosmic ray electrons. Again, attention is focused almost exclusively on measurements of particles rather than the radiation signature of those particles, in this case synchrotron radiation by ultrarelativistic electrons. No mention is made of radio and X ray data, indicating that electrons with energies of up to around 10¹⁴eV are being accelerated at shocks associated with shell type supernova remnants. Interestingly, resonant acceleration of electrons by lower hybrid waves has been invoked by A.A. Galeev [Sov. Phys.-JETP 59 (1984) 965] as a mechanism for the production of cosmic ray electrons: although Galeev's paper is not cited in this book, the process he describes is very similar to that proposed by Dr Bryant for electron acceleration in the aurora and other near Earth plasma environments.

The book contains a number of physics errors. For example, on page 17 the time derivative of a magnetic field is equated to an induced electric field, rather than the curl of one. On page 21, the author invokes Larmor's formula for the power radiated by a non-relativistic charged particle, and then combines it with the relativistic relation between acceleration and energy to estimate the maximum acceleration rate. The book has also been badly proofread. For example, Figure 1.15 appears twice: where it is first used, on page 8, it is clear that the accompanying caption and text refer to a different figure. I found several errors in the reference list (one of my own publications is cited as two separate papers, with both citations containing inaccuracies). Having said that, the reference list is impressively comprehensive and eclectic. It includes, for example, Swift's `Gulliver's Travels': a spacecraft in the magnetosphere is compared to Gulliver in Brobdingnag, the magnetosphere being, in some respects, a vastly scaled-up version of a laboratory plasma. The author measures particle momentum in units of 10^-21 Ns ≡ 1 zNs - not, I suspect, a unit used often by nuclear fusion researchers. There are many typographical errors (in addition to the physics errors noted above).

At the end of the book listings are provided of three programs, written in QBasic (a PC compatible version of BASIC), which illustrate simple models of particle distribution evolution under various conditions, and in particular the formation of a bump-on-tail distribution when particles undergo random energy exchanges with waves. These are instructive and illuminating, although it would have been more useful if diskettes had been provided with the book rather than hard copy listings. Questions and exercises are also included, again with the purpose of illustrating the author's heterodox ideas regarding particle acceleration. He asks, for example, what the accelerator of Newton's apple was: according to Dr Bryant, the obvious answer (`the Earth') is incorrect, since it was radiation from the Sun which raised the apple's material against the force of gravity in the first place. The answer to the question depends, of course, on what one means by `acceleration': as I have discussed, the author is not wholly consistent in his definition of this term.

This book will, inevitably, be of more interest to space plasma physicists than to fusion researchers, although proponents of lower hybrid current drive in tokamaks may be gratified to see evidence of a similar process playing an important role in such a wide range of natural plasma environments. Despite some errors, omissions and inconsistencies, there is no doubt that the book provides a useful record of Dr Bryant's valuable contributions to the study of electron acceleration in the aurora and elsewhere.