Table of contents

A characterization of the H-mode in Tokamak de Varennes (TdeV) is presented, combining results obtained from spectroscopic measurements with observations of global plasma parameters. Controlled L- and H-modes are obtained by applying an external bias on the divertor plate and/or by varying the plasma triangularity using similar steady-state discharges with electron cyclotron resonance heating (ECRH). A qualitative study of the impurity emission asymmetries is presented and discussed by proposing a simple model which considers that the emissivity has radial and poloidal components. The poloidal velocities are small with no significant variations with respect to the plate biasing, EC power and plasma triangularity. Toroidal rotation velocities show more consistent trends and have larger values in the H-modes with respect to the L-modes. No significant shear in the radial electric field is observed between the H- and L-modes. Differences in the electric field and in the E×B shear are observed for several discharges, but they are not consistent overall. A study on the impurity transport shows low diffusivity values in the plasma centre and high values in the edge during the H-mode. The energy confinement time decreases with the severity of the edge localized modes and, consequently, with the neutral fluxes. The presence of a toroidal torque which affects the particle transport inside the plasma plays an important role in the TdeV H-modes.

In this work it is demonstrated that robust burn control in long-pulse operations of subignited thermonuclear reactors can be achieved with radial basis neural networks (RBNNs) composed of Gaussian nodes in the hidden layer and sigmoidal units in the output layer. The results reported here correspond to a volume-averaged zero-dimensional nonlinear model of a subignited fusion reactor with design parameters corresponding to those of the ITER-EDA group. The control actions are implemented through the concurrent modulation of the D-T refuelling rate, a neutral ⁴He beam and an auxiliary heating power, constrained to lie below maximum allowable levels.

It is shown that the resulting network provides feedback stabilization over a wide range of energy confinement times for plasma density and temperature excursions significantly far from their nominal operating values. The results show that the RBNN feedback-controlled nonlinear system is stable regardless of any particular scaling law, as long as the confinement time lies within the scope of the training region. In addition, it also shows robustness with respect to noise in the energy confinement time value fed into the controller during simulated transients of a thermonuclear system using a particular ELMy scaling law, as well as with respect to the thermalization time of the alpha particles produced by fusion.

An analysis of the m = 0 magnetic perturbation in the vacuum region of an RFP device is carried out using toroidal flux and toroidal field measurements. This perturbation is associated to the locked-mode phenomenon which is a coherent superimposition of modes, mainly m = 0,1, locked in phase together. The m = 1 distortion of the magnetic surface is the dominant effect and was considered in a previous analysis. The purpose of this work is to study the m = 0 component using the same technique. The experimental data are elaborated with simple analytical expressions derived from the vacuum Maxwell equations and the general contravariant representation of the magnetic field in terms of the flux function. The m = 0 geometrical distortion of the magnetic surfaces is reconstructed. Its dependence on the plasma current and the impact on the plasma wall interaction are discussed.

It is computationally shown that quasi-axially symmetric finite-β stellarators can simultaneously exhibit good collisionless α-particle confinement and ballooning-stability properties.

A direct method to measure the localized magnetic shear stress and hence electromagnetic torque or force exerted on a wall by a fluctuating magnetic field is presented. A model of the wall is needed when the magnetic measurements do not include the normal component. Explicit formulae for thin and thick walls are given. Estimates of the force in illustrative Alcator C-Mod tokamak plasmas provide evidence against the theory that resistive magnetic drag determines mode locking.

For a simple two-dimensional nonlinear model of the collisional drift instability the relationship between mixing length and strong turbulence fluxes investigated. Calculation of the turbulent wavenumber spectrum within a strong turbulence model shows that the transport is dominated by an inertial range contribution; this yields a similar result for the fluxes to that from an improved mixing length theory. The nature of the spectrum in the dissipation region, where collisional viscosity dominates, provides an explanation of an apparent paradox that arises when transport fluxes are cast in a form proportional to viscosity (or the diffusion coefficient).

The spectral profile of the deuterium Dα line (a common diagnostic of recycling particles in present tokamaks), emitted in front of an equatorial neutralizer plate in Ergodic Divertor Tore Supra plasmas, shows, in the presence of large helium contents, some features which have been interpreted as the contribution of the near-by hydrogen-like helium Brβ line intensity. In order to validate this interpretation, the intensities of several other He II lines have been measured, and their ratios compared to theoretical values calculated from a collisional-radiative model. These data have been used to estimate the brightness of the He II Brβ line. Although the effect of the He II Brβ line intensity on the Dα line profile shape is evaluated (and measured) to be non-negligible in these ad hoc plasmas (having a large helium content), it is concluded that it should be of no influence in usual fusion plasmas.

The ideal induction of vector fields in fluids and plasmas is presented as invariance under local convection, `freezing' into flowlines and transfer of potential. Related consequences are discussed, namely the conservation of local flux and total helicity and the force-free relaxation state. In the framework of single-fluid Hall-MHD plasma flow model, the magnetic field and vorticity (which are formally analogous and generally anti-correlated, but each not ideally inducted, i.e. perfectly `frozen-into' the flow) are shown to combine in a unified magneto-vorticity field, which is ideally inducted in perfectly-conducting, however even forced, non-isentropic and viscous plasmas. Relaxation plasma states of conserved or extreme helicity magneto-vorticity fields are derived and shown to be generalized force-free states, similar to those previously derived in the framework of Hall-MHD and the multi-component plasma model. The magneto-vorticity induction in visco-resistive plasmas is also discussed. Application of the magneto-vorticity field concept in the study of type I superconductors and the spontaneous generation of magnetic fields are reviewed. The Cowling `anti-dynamo' theorem for axisymmetric flows is extended in Hall-MHD and for arbitrary flows and is shown that, in principle, the resistive (ohmic) dissipation of the magnetic field can be balanced by non-isentropic heating and/or helical forcing effects.

The succinct title of this book belies a great breadth of discussion and detail regarding not only ionospheres themselves but all those physical and chemical processes upon which their characteristics, dynamics and energetics depend.

After a descriptive scene-setting first two chapters introducing solar system neutral and ionised atmospheres, it moves rapidly and comprehensively into the mathematics of the underlying mechanisms such as plasma distribution functions, collisional processes, 13-moment transport equations, diffusion and shocks. This requires the reader to have good graduate-level agility in mathematics and, although it is written in a logical and lucid fashion, this may deter readers with less experience. Conversely, it will be welcome reference material for those whose work is in plasma and space physics and for whom such material is essential and yet difficult to come by in a single publication. There follows, amongst many other things, an extensive discussion of influences.

Such is the authors' determination to provide a complete toolkit for understanding how ionospheres are formed, their energy sources and sinks and their coupling to the planetary atmosphere, that the first real mention of the layers of the Earth's ionosphere does not appear until over half-way through the book. It does not dwell on the Earth's ionosphere for a disproportionate time, however, but treats it with commensurate weight to the ionospheres of the other planets, of their satellites and of comets. Therefore, this is not, in my view, a book for those who are looking for a comprehensive treatise on the Earth's ionosphere and its phenomenology; there are several of those already in print. Instead, this publication stands apart as taking a generic look at ionospheres from first principles. In addition, whereas others often look at the Earth's ionosphere from a geocentric perspective, this work takes a more global view as if looking on the system from outside the planet. It should prove excellent both as a tutorial for postgraduate or specialist final-year students and as a reference book for atmospheric scientists and plasma physicists.

Its value for students is greatly enhanced by the problems set at the end of most chapters and by its extensive appendices which provide fundamental mathematical equations and model parameters, etc. The set problems, however, are predominantly numerical or formulaic derivations and are excluded from the more descriptive chapters (e.g. Space Environment, Measurement Techniques); therefore the student appears to be asked to test their mathematical ability more than their philosophical understanding. On the other hand, many of the mathematical problems would suit plasma physics students with little direct interest in ionospheres. The final chapter on ionospheric measurement techniques seems a little superfluous and patchy but the general references supplied should be able to satiate whetted appetites.

Ionospheres is a book which I anticipate will appear as a standard on bookshelves both in research laboratories and university libraries. The combined sixty-five years of experience of the two authors at the cutting-edge of this topic area should certainly provide a sound and reliable knowledge-base for dedicated students and academics alike.

Dr M J Jarvis Geospace-Atmosphere Transfer Functions, British Antartic Survey, Madingly Road, Cambridge CB3 0ET

Writing a book on The Plasma Boundary of Magnetic Fusion Devices is a challenge and few others than Peter Stangeby would have been capable of such a task. Indeed, heat load control onto plasma facing components or helium ash removal can only be resolved by fully integrating all the physics of fusion. Furthermore, they are among the key issues that remain to be solved for the next step machine on the way to Nuclear Fusion with magnetic confinement.

As the Preface of the book rightly points out, this handbook is well suited for experimentalists or code scientists who wish to interpret their results and bring some common sense into a complex story. Part 1, which includes may problems, will also be appropriate to students and those plasma physicists who are not specialists of boundary physics but wish to capture the physics of this field of research. The very worthy choice of putting physics forward, backing at each step the modelling effort with experimental facts (and vice versa), is performed at the cost of a rigorous and mathematical analysis. The book also falls short of establishing the connection between the engineering issues, such as heat removal in the steady state, and the physics at hand, although the former are clearly the incentive for the present effort in the physics. Another weakness of the book is too short a section dedicated to turbulent plasma transport depited its importance in defining the boundary plasma itself and despite the fact that most of the available data are measured in the boundary plasma.

In a busy book of more than 700 pages, Peter Stangeby has covered many years of research, from pioneering work, for instance sheath physics by Tonk and Langmuir in the late 1920's, to areas that remain the subject of active investigation like drifts in the boundary plasma. The book is divided into 3 parts of very different footing. Part 1, An introduction to the subject of the plasma boundary, is the textbook of various courses given by Peter throughout the world. In this part, the reader is introduced to many of the concepts and facets of the physics of the boundary plasma. Part 2, Introduction to fluid modelling of the boundary plasma, is a review of the theoretical background and the modelling effort of the boundary plasma. Rather naturally, Part 3, Plasma boundary research, addresses several issues that are currently the scope of experimental, modelling and theoretical investigation. The text is further divided in numerous sections and subsections that organise this complex subject in a series of well-defined topics. The style is in the very spirit of Peter's talks, so lively that one can nearly hear him.

Part 1, written for the largest audience, is more than half of the book (about 380 pages). This part starts with the definitions of the Scrape Off Layer (SOL), i.e. that region of open field lines that surrounds the magnetically confined plasma and the sheath, namely the standing shock wave between the plasma and wall material. A third section is dedicated to the most important aspects of atomic physics in the SOL, such as ionization of incoming particles and erosion of wall material. The following sections are then dedicated to more and more sophisticated description of the SOL, a long section addressing the issue of impurity generation and subsequent transport. Part 2 of the book deals with modelling issues and is relatively short (80 pages). The issue of 1-D versus 2-D models as well as the intermediate so-called onion skin models are introduced. Most of this part assumes a fluid analysis although some kinetic aspects are also included. The most important sections in Part 3 are dedicated to currents and drifts in the SOL as well as divertor detachment.

Peter Stangeby thus offers the community of fusion physicists a very precious survey of boundary plasma physics. This effort is all the more welcomed since the previous reference book, the often quoted Physics of Plasma Wall Interactions in Controlled Fusion, edited by D E Post and R Behrisch (Nato ASI series, Plenum Press, N.Y. 1986), was written prior to the ITER internation project that definitely boosted this field of research.

Philippe Ghendrih Association Euratom-CEA sur la Fusion Contrôlée, CEA-Cadarache, F-13108 St-Paul-lez-Durance Cedex, France