Table of contents

A two dimensional magnetohydrodynamic plasma model is presented and coupled to an existing three dimensional eddy current code which computes the currents and forces induced in the plasma facing components of a tokamak. In order to simplify the coupling to the finite element based eddy current code for the electromagnetic part of the plasma model a finite element method is applied. The fluid dynamic part is solved with a volume of fluid (VOF) technique which was modified to account for the preservation of the toroidal magnetic flux. This technique allows an easy and accurate tracking of the plasma boundary, which is important for the detection of the plasma-wall contact. Furthermore, the scraping-off of the outmost plasma layer and the retarding effect of the toroidal halo currents on the plasma motion are modelled. With this coupled code, a given initial equilibrium state and a rough guess of the temperature profile and evolution, a representative ASDEX Upgrade disruption including a vertical disruption event (VDE) is simulated successfully. The computation time needed for this coupled analysis is comparatively short.

Studies and selection of plasma facing materials continue to be a concern for future fusion devices, and ongoing efforts are being made in the HL-1M tokamak. The advanced methods of wall modification adopted on HL-1M are surveyed. Significant improvements in tokamak plasma performance have been obtained by using boron, silicon or lithium containing substances as a material for wall coatings. The siliconization technique is highlighted. Lithiumization, as the newest technique, will be investigated further.

The mode structure of the disruption precursors in the TFTR enhanced reversed shear (ERS) parameters has been studied by using T_e fluctuation profiles and q profiles obtained from electron cyclotron emission (ECE) and motional Stark effect (MSE) measurements. The observed profiles of the radial displacement associated with the MHD modes were consistent with the displacement profiles expected from the ideal MHD external kink mode. The observed mode frequencies differ from the plasma toroidal rotation frequency measured with C VI charge exchange recombination light. The independence of the mode frequency from the plasma rotation frequency supports the ideal MHD hypothesis. Possible causes of the frequency difference are discussed.

The possibility of self-excitation in tokamaks of microislands (whose width is much smaller than the ion gyroradius and whose mode numbers m and n are large) by pumping energy from the plasma through the interaction of the ions with densely packed island chains has been suggested in recent years by Kadomtsev. A number of questions are addressed in this article in the context of this suggestion. The time dependent island evolution equations are analysed in the linear approximation in the presence of energy pumping and resistive damping. In the stationary case the non-linear partial differential equation describing the structure of the microislands is reformulated and solved numerically, elucidating how the topology of the islands is affected by non-linearity. The saturation conditions of self-excited microislands are discussed on the basis of the energy integral of the evolution equations, assuming that the pumping is balanced by damping arising from a resistive-like anomalous dissipation related to a resonant electron-island wave interaction. The saturated island width is expressed in terms of the physical and geometrical parameters of the tokamak. The consequences for plasma transport and the scaling of the energy confinement time with respect to these parameters are presented.

Two interesting features of runaway behaviour are observed in the startup phase of the very low q_a (VLQ) (1 < q_a < 2) discharges in the SINP tokamak. As q_a was reduced by lowering the toroidal field values, the hard X (HX) ray intensity (which indicates the presence of runaway electrons) fell considerably. The time at which the peak in the HX ray intensity occurs also shifts ahead in time, indicating premature dumping of the runaway electrons. This seems to aid the development of the rest of the discharge as exhibited by the diamagnetic loop signal.

Experiments in the DIII-D tokamak have measured the scaling of heat transport with beta (β) while all other dimensionless parameters are held constant for both H mode and L mode plasmas. Experimental results from the beta scaling of heat transport help to differentiate between various proposed mechanisms of turbulent transport. For L mode plasmas, the beta scaling of heat transport over the range 0.26 ⩽ β_N ⩽ 0.49 is close to zero, with the thermal confinement time scaling as Bτ_th ∝ β^-0.05±0.10 and the effective (or one fluid) thermal diffusivity scaling as χ_eff ∝ χ_Bβ^0.11±0.20. The beta scalings of the ion and electron thermal diffusivities are the same as the effective diffusivity to within the experimental errors. Higher values of beta are investigated in H mode plasmas, where a weak-to-moderate beta scaling of transport is observed over the range 0.8 ⩽ β_N ⩽ 1.7, with the thermal confinement time scaling as Bτ_th ∝ β^0.03±0.11 and the effective thermal diffusivity scaling as χ_eff ∝ χ_Bβ^-0.54±0.21. The ion channel is responsible for the favourable beta scaling of H mode plasmas; the electron channel has no measurable beta dependence. These beta scalings determined by dimensionless parameter scans are much weaker than the predicted beta scalings from the L mode and H mode confinement scaling expressions that are currently being used to predict the performance of ITER.

Density profiles measured in RFX by a 13 chord mid-infrared (MIR) interferometer are found to be flat or hollow. Density gradients are large only in a region typically of the order of 2 to 4 cm from the edge. A detailed investigation of the form of the electron density profile during the current flat-top phase in different experimental conditions has been performed. The shape of the profile seems to depend only on the I/N (plasma current/line density) parameter, varying from flat or slightly peaked at high I/N to clearly hollow at low I/N. The systematic existence of stationary hollow density profiles implies the presence of an outward directed fluid velocity. A one dimensional (1-D) particle transport code has been used to simulate the profile behaviour in order to obtain quantitative information on the form of the diffusion coefficient and of the `anti-pinch' velocity. The results are compatible with a transport mechanism based on parallel transport along stochastic magnetic field lines in a large part of the plasma core region. In this framework, the apparent anti-pinch term would be driven by the temperature gradient.

On JT-60U, for the first time in negative shear plasmas, toroidicity induced Alfvén eigenmodes (TAEs) with frequencies in the range of 90 to 110 kHz and toroidal mode numbers n = 5-8 were observed after a broadening of the density profile due to sequential partial collapses during ion cyclotron range of frequency (ICRF) heating. TAEs are more stable in negative shear plasmas than plasmas with a monotonically increasing q profile. The TAE stability was analysed with the NOVA-K code. It was found that the stability is highly sensitive to the gap alignment just inside q_min and that the theoretical results are consistent with the experimental results. In a weak central magnetic shear discharge, modes with very rapid frequency chirping were observed during ICRF heating. The frequencies of these modes rapidly increased from ∼30 kHz up to ∼110 kHz in a period of ∼150 ms. The large frequency chirping is not well understood by the present theory.

A series of observations is presented concerning divertor heat flux, q_div, in the DIII-D tokamak, and it is shown that many features can be accounted for by assuming that the heat flux flows preferentially along field lines because τ_|| < τ_⊥ in the scrape-off layer (SOL). Exceptions to this agreement are pointed out and the discrepancies explained by means of two dimensional (2-D) effects. About 80% of the discharge input power can be accounted for. The power deposited on the target plate due to enhanced losses during edge localized modes (ELMs) is less than 10% of the total target power in most cases. X point height scans for lower single null (LSN) diverted discharges show that the peak heat flux variation is primarily due to flux expansion and secondarily due to transport of energy across the magnetic field in the divertor. At the outer strike point q_div,peak ∝ P_in(I_p - I_p,0)G(g_in)(1/B_t)^4/9(B_div/B_mp)f(L_divχ_⊥), where G is a linear function of the inner gap, g_in, over a specified range and f describes cross-field energy transport in the divertor. Evidence of radial in-out asymmetries (comparing the outer strike point with the inner strike point or centre-post) and toroidal asymmetries in q_div is presented and the heat flux peaking due to tile gaps and misalignment of tiles is examined. For magnetically balanced double null (DN) discharges with downward ∇B ion drift, it is found that q_div is inherently higher in the lower divertor than in the upper divertor, having a 3:1 downward bias. Examples of heat flux reduction by gas puffing deuterium or neon in LSN and DN discharges are given. At least a threefold reduction of the peak heat flux in both the upper and lower divertors of a DN discharge, using D₂ puffing, is reported.

Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas.

The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader.

In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers.

The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium equations of a plasma in a magnetic field (which will be used further in models of dynamic processes), approaches to the description of three dimensional (3-D) equilibrium are briefly discussed, and the basis of the theory of linear instabilities and the basic types of MHD instabilities, with account taken of ideal resistive modes, are considered. The value of the material of these chapters is that here in a brief form the results of numerous researches in this area are presented, and frequently with a fresh point of view of old results.

Chapters 5 to 10 are devoted to the subject of the book, non-linear magnetohydrodynamics. In the introduction to Chapter 5 the author pays attention to the fact that long standing doubts about the feasibility of magnetic thermonuclear reactors because of inevitable instabilities of non-uniform plasmas have been overcome in the last two decades: the plasma in tokamaks is rather well confined, despite the presence of some instabilities. The latter, as a rule, result only in the redistribution of current and plasma pressure profiles and some increase of transport, but can also lead to extremely undesirable effects. In this connection in Chapter 5 the attention of the reader is directed to the physics of the most important plasma instabilities in tokamaks. Models of the development of external and internal kink modes in tokamaks are considered, including the `vacuum bubble' model in shearless plasmas, the evolution of the resistive tearing mode together with saturation of the magnetic islands arising at a tearing instability.

The rather long Chapter 6 is devoted to the fundamentals of the magnetic hydrodynamic dissipative process in the magnetic field line reconnection. This process of rapid dissipation of the energy of a magnetic field, having in the simplest case different directions in two adjacent volumes of plasma, underlies the theory of the phenomenon of powerful flares in the solar chromosphere, resulting in the well-known `magnetic storms' on the earth, and the theory of rather dangerous disruptive instabilities in tokamaks. After a discussion of the Sweet-Parker model of the diffusive current sheet, two models of the ideally conducting plasma flow generating such a sheet are considered in detail: the Petchek slow shock model (1964) and the Syrovatskii current sheet solution (1971). The first, introduced with a hypothesis about the geometry of the current sheet, has been dominant for more than two decades (at least, as the author writes, in the western hemisphere). It has been superseded by (accepted, mainly, in the eastern hemisphere) Syrovatskii's model with an external potential flow, compressing the hyperbolic branches of the magnetic field lines about an X point. This model quite naturally results in the necessity of introducing an extended singular current sheet, which is quite consistent with the later Biskamp numerical simulation (1986). In Chapter 6 the results are presented of 2-D simulations of the formation of a current sheet with details of the edge structure and with repeated generation of plasmoids at the edge, caused by tearing instability. Results on the coalescence of two identical magnetic islands, on the development of a kink island at a tearing instability of a primarily cylindrical plasma and on the generation of plasmoids in a model of the geomagnetic tail are described. At the end of Chapter 6 the topology of a 3-D configuration with a magnetic zero is briefly discussed. Finally, in the last section a way of explaning the explosive development of the reconnection process, based on the hypothesis of the growth of turbulent resistivity at an excess of the threshold value of current density is presented.

In Chapter 7 which covers MHD turbulence the classical spectral approach to the description of the turbulence of ideal non-dissipative systems is presented. The dynamically important invariants, which are quadratic in the magnetic and velocity fields, are introduced: the total energy, the magnetic helicity, the cross-helicity. Then it is shown how the corresponding spectral functions are deduced from the Gibbs distribution. The processes of self-organization are considered, which are connected with the selective dissipation rates of the ideal invariants. The best known example is the process of turbulent relaxation of energy at conservation of magnetic helicity, resulting in the alignment of the vectors j and B (j = μB, μ = const). Examples of numerical calculations of turbulence structure are presented. An important connection in dynamo theory (generation and maintenance of a magnetic field) between the electric field, generated along the basic magnetic field, with averaged helicity (α effect), and the Alfvén effect on turbulence (asymptotic approach of a velocity field to a field of Alfvén velocity; briefly, alignment of the vectors v and normalized B) is deduced. Furthermore, the spectra of uniform turbulence (the distribution of the energy on the wavenumbers), the Kolmogorov spectrum E_k ∝ k^-5/3 in the usual hydrodynamics and the Iroshnikov-Kraichnan spectrum E_k ∝ k^-3/2 in magnetic hydrodynamics are derived, and the turbulent dissipation scales and the intermittence, a property of the structure (the spottiness) of the fully developed turbulence when the dissipative processes are concentrated in narrow layers of complicated form, are considered. At the end of this chapter a picture of the turbulent convection of a weak magnetic field, when it is possible to neglect the Lorentz force, is presented.

The subsequent three chapters of the book are devoted to the description of plasma dynamic processes in tokamaks, in reversed field pinches and in solar flares. This is a good opportunity for a detailed study of MHD processes in plasmas, as is described in detail in Chapter 8, for tokamaks. Here the three main dynamic phenomena observed in these installations are considered in detail: (a) Relaxation sawtooth oscillations of the electron temperature in the central region of the plasma column (internal disruptions), (b) The most dangerous major disruptions, (c) The edge localized mode (ELM). The author analyses in detail the Kadomtsev reconnection model of the sawtooth collapse, as a basis for understanding all the different relaxation processes in tokamaks. He pays attention to the explanation of the difference between the Kadomtsev reconnection model of sawtooth collapse and the observed partial reconnection with a non-flat final q(r) profile inside the magnetic surface q = 1. Considering major disruptions he gives a clear qualitative picture of this threatening phenomenon, beginning with the shrinking of the temperature and current density profiles, followed by the (m, n) = (2,1) tearing mode instability and ending with multihelicity tearing instabilities leading to stochastic field lines and small scale turbulent processes. In connection with the ELMs observed after the L-H transition, the author explains initially the nature of the improved `high confinement' regime (H mode) developed from the `low confinement' regime (L mode) when the input power exceeds a threshold level at appropriate boundary conditions. The ELMs are considered as `a relaxation of the steep pressure gradient at the plasma edge' due to ballooning instability. The characteristic features of the giant ELMs (type 1) occurring at high plasma heating power and of the faster type III ELMs, which were the first to be observed, are presented in lucid form. At the end of Chapter 8, in Table 8.1, the main MHD properties of the disruptive processes in tokamak plasmas are summarized.

In Chapter 9, the dynamical processes in toroidal pinches with stabilization of large scale perturbations by a weak (mainly internal) toroidal magnetic field, having the reverse direction to the current channel, are considered. In this system 3-D turbulence redistributes the total flux, conserved owing to the metallic wall in accordance with Taylor's theory, to satisfy the above mentioned alignment of the vectorsj and B. The details of this remarkable process are described.

The final chapter is devoted to solar flares, which are as the author says `probably, the most spectacular eruptive events in cosmic plasmas'. This chapter describes in detail the structure of the solar convection zone and the solar atmosphere, considers the formation of the rope-like structure of the magnetic field and the thick flux tubes displayed as sunspots, as well as the buoyancy of the flux tubes and different models of the MHD processes leading to solar flares.

In summary, the reviewed book is rich in content, reflecting the important issues of striking phenomena such as solar flares, the, quite dangerous for plasma confinement, major disruptions in tokamaks and the, conversely quite favourable for plasma confinement, non-linear process of L-H transition in tokamaks and continuous turbulent generation and maintenance of stabilizing toroidal magnetic fields in reversed field pinches, as well as other interesting MHD processes. The analysis of these very complicated phenomena is based on non-elementary mathematics. This could make it difficult for non-theoreticians to read some parts of the book. However, as for an explanation of the physics of the phenomena, the author achieves this in a rather simple manner: briefly, and with the minimal number of necessary formulas. This is done strictly without oversimplifications. This makes the book useful to both theoreticians and experimenters who wish to learn about non-linear processes such as disruptions and plasma self-organization.

This book gives a comprehensive treatment of plasma spectroscopy, the quantitative study of line and continuous radiation from high temperature plasmas. This highly interdisciplinary field combines elements of atomic, plasma and statistical physics, and has wide application to simulations and diagnostics of laboratory and astrophysical plasmas. Plasma spectroscopy is naturally intertwined with magnetic and inertial fusion energy science. Radiative processes in plasmas are important in the design of fusion facilities, and can be used to diagnose and control conditions in fusion plasmas. In turn, fusion scientists and facilities have played a central role in developing plasma spectroscopy theory and applications.

The book covers radiation from plasmas, spectral line broadening, atomic processes in plasmas and level kinetic models, radiative transfer and applications to spectroscopic plasma diagnostics. It is successful both as an introductory text and as a source book of theoretical and experimental research. The book presents a broad development of the theoretical foundations of these topics, and discusses the seminal papers and critical experiments. There is a strong emphasis on applications of plasma spectroscopy, primarily to plasma diagnostics and calculations of radiative cooling rates. Extensive references (current through the end of 1995) point readers to original material and detailed discussions of advanced topics. Of course, a single text cannot treat all aspects of plasma spectroscopy in depth. The strongest and most detailed section of the book is a long chapter on spectral line broadening. For me, the most significant omission is lack of a discussion of laser assisted transitions which can occur in plasmas produced by high intensity lasers.

The book was intentionally written to be accessible to young researchers and graduate students. The level is roughly that of a graduate text. It assumes some familiarity with quantum mechanics and statistical thermodynamics, but develops most of the advanced concepts. Plasma spectroscopy is widely used by non-specialists, and the level and organization of the book are suited to use by researchers developing applications of plasma spectroscopic techniques. Finally, the specialist will profit from the comprehensive overview and excellent bibliography presented.

The author is highly qualified to write a general book on the spectroscopy of plasmas. Professor Griem has worked in the field of plasma spectroscopy for more than four decades. He is the author ofPlasma Spectroscopy (1964, McGraw-Hill), the first general, quantitative book on the subject of radiation from plasmas, as well as Spectral Line Broadening by Plasmas (1974, Academic Press). Both of these monographs were tremendously influential books. In addition to his long career at the University of Maryland, Professor Griem has worked extensively with numerous research groups in the United States of America and Europe. The depth and breadth of his experience is reflected in the book.

The present book is largely new, rather than an update of the 1964 monograph. The two books have a similar organization, especially in the chapters introducing the classical and quantum theories of radiation. The later chapters of the two books diverge strongly as the present text incorporates a vast amount of modern material. The nomenclature and formalism have been updated, and I find this book more accessible than Professor Griem's earlier texts. The other significant changes are that the present book omits the problems at the end of the chapters, many of the tables of numerical results, and the chapters on plasma sources and detectors. While the tables of atomic and line shape results contained in the original book were extremely useful, they have been updated and extended in more recent works.

I enthusiastically recommend this book to all scientists interested in the spectroscopy of hot plasmas. Early in his career, Professor Griem wrote the seminal book on plasma spectroscopy. It is gratifying that as a senior scientist he has written a comprehensive monograph incorporating the past three decades of development in the field he so strongly influenced. It is certain to become a coveted and classic book.

A question often posed upon publication of a summer school proceedings is whether the contents are of lasting value, or are only an archive or diary of the gathering. This issue is exacerbated by the year's delay (or more) that is all too customary between the school itself and publication; and of course the attendees have had the contents in note form all along. Only occasionally, in this reviewer's experience, are the contents worth the purchase price of the book; and even less often is the book a useful reference for course work in a teaching context. It is thus gratifying to report that the present volume should be of lasting value, and should be a useful reference for students in high power microwave physics and related fields to have and to hold during their formative years.

The editors, Professor Alan Cairns of the University of St Andrews, and Professor Alan Phelps of the University of Strathclyde, have assembled some 14 essays in the book on a range of topics on microwave source physics and the uses of high power microwaves for fusion plasma heating. Amongst the essays are several tutorials, including Alan Phelps' own 8 page introduction; Michael Petelin's elegant overview of a range of classical spontaneous and stimulated radiation processes for free electrons; Rodolfo Bonifacio's exposition on free electron waveguide lasers; James Eastwood's overview of computer modelling methods; Georges Faillon's review of klystrons; Alan Cairns's and Nat Fisch's lucid descriptions of the physical basis of plasma heating with intense microwaves; and Manfred Thumm's two thorough contributions on microwave mode converters and on applications.

The other essays are less tutorial, but more topical, with expositions on new results on gyro-amplifiers by Monica Blank; on vacuum microelectronics issues for microwave power amplifiers by Morag Garven and Robert Parker; John Vomvoridis's theory of cyclotron resonance interactions for generation of high power microwaves using a rectilinear electron beam; and for generation of high power microwaves using a rectilinear electron beam; and Marco Brambilla's and C. Gormezano's descriptions of methods and systems for ion cyclotron, lower hybrid and electron cyclotron heating of tokamak plasmas.

It would be difficult to imagine that a single author could assemble into a single volume the wealth and breadth of material presented here. Students and professionals in high power microwave physics should benefit markedly from a study of this volume. The editors deserve high marks for their efforts in assembling and editing this Proceedings.