Table of contents

Particle exhaust studies have been carried out with the pump limiter ALT-II in the TEXTOR tokamak, under ohmic conditions as well as with NBI and with ICRF auxiliary heating, and the pumping effectiveness is shown to meet the requirements for a fusion reactor. Quantitative measurements of Dα emission, made with a CCD camera, have been used to determine the particle efflux from the plasma. Roughly one third of the Dα emission occurs in a diffuse `halo' that surrounds the limiter belt. The particle confinement time is less than the energy confinement time by a factor of typically 4. Modelling in 2-D of plasma and neutral flows in the TEXTOR boundary has been performed. The source of D⁺ ions can be related to the Dα emission by a factor that is found to depend on the location of the emission and on the discharge density. The predicted total Dα emission agrees with the measurements within a factor of about 2. Pumping of ALT-II allows for density control; with NBI, the density can be increased well beyond the ohmic limit without the discharge ending in disruption. The plasma particle efflux and the pumped flux both increase with density as well as with heating power. The exhaust efficiency is typically ∼2%, with the highest values observed in high density NBI discharges. Higher exhaust rates are observed with NBI than with ICRF. Plasma and neutral flows in the ALT-II scoops have been simulated, making use of a simple plasma model. The scoop may be viewed as a non-linear amplifier of the plasma particle flux; the amplification is found to range from about 2 to 3 for most cases. Flow reversal in the scoop is found in some of the NBI cases and particularly in the highest density case.

Recently, various schemes for controlling the resistive wall mode have been proposed. Here, the problem of resistive wall mode feedback control is formulated utilizing concepts from electrical circuit theory. Each of the coupled elements (the perturbed plasma current, the poloidal passive shell system and the active coil system) is considered as lumped parameter electrical circuits obeying the usual laws of linear circuit theory. A dispersion relation is derived using different schemes for the feedback logic. The various schemes differ in the choice of sensor signal, which is determined by some combination of the three independent circuit currents. Feedback schemes are discussed which can, ideally, completely stabilize the kink mode. These schemes depend, for their success, on a suitable choice for the location of the sensors. A feedback scheme based on sensing the passive shell eddy current is discussed which seeks to drive the feedback system response to a point of marginal stability. For realizable feedback gain factors, this feedback system can suppress the kink mode amplitude for times that are very long compared with the L/R time-scale of the passive shell system. The circuit equation approach discussed provides a useful means for comparing various control strategies for n ⩾ 1 kink mode control, and allows useful analogies to be drawn between kink mode control and the control of n = 0 vertical position instabilities.

Metal impurity ions have been injected in Tore Supra discharges by laser blow-off. The ion transport is studied by means of an impurity ion transport code; the radial profiles of the diffusion coefficient D and of the inward convection velocity V are obtained by simulating soft X ray brightness and emissivity time evolutions. Three different experimental situations are considered: a discharge with sawteeth stabilized by LH heating, a high-n_e discharge with ICR heating and a strongly sawtoothing discharge with combined ICR and LH heating. In all cases, the simulations show the presence of two transport regions, the central core having reduced transport coefficients, and the outer region where there is the necessity to increase transiently the diffusion coefficient D during the first few milliseconds after the injection. It has been previously suggested that the shear s = 0.5 is the critical physical parameter governing the transition from low to high transport coefficients. The s = 0.5 criterion seems satisfied in the first two cases, whereas the closeness of the s = 0.5 and q = 1 surfaces does not allow a conclusion to be made in the combined heating case.

The DIVIMP/NIMBUS onion skin model (OSM) has been used to calculate 2-D plasma distributions of n_e, T_e and T_i in the JET edge, based on boundary conditions measured across the targets with built-in Langmuir probes. Ohmic, L mode and ELMy H mode discharges were analysed. From the calculated 2-D plasma profiles, values of χ_⊥^SOL(r) were extracted as a function of radial location within the SOL, showing that χ_⊥^SOL(r) increases with radius. At the separatrix χ_⊥^SOL(0) was in the range ∼0.05-1 m²·s^-1, with the lowest values occurring for H modes (between ELMs). It was found that χ_⊥^SOL(r) ∼[T_eu(r)]^-2, where T_eu is the electron temperature at the `upstream' end of the SOL flux tube. No clear correlation with the magnetic field, B_T, was found. The results are not consistent with Bohm (χ_⊥^SOL ∝ T_eu/B) scaling.

The performance of deuterium targets with small tritium seeding is analysed. The objective is to take advantage of the features of fusion reactivity ratios for very high burning temperatures in order to minimize tritium needs and to reduce the ignition temperature as much as possible. It is found theroretically and computationally that there is a regime for deuterium-tritium DT_x plasmas (with x ≈ 0.03) where the final content of tritium in the pellet debris is the same as the initial contents in the original pellet. No external blankets to breed tritium would thus be needed. Although energy gains are limited because of the small fusion yield of DD reactions, the energy gain of DT_x targets is higher than that of pure deuterium plasmas. The ignition temperature and the driver energy are lower than the corresponding values of DD pellets. This concept is also very useful to reduce the tritium inventory and to simplify the complexity of inertial fusion reactors which use stoichiometric DT.

The radial profiles of the ion temperature as well as the flow velocity have been measured by using rotatable symmetric and asymmetric double probes in the boundary plasma of the JFT-2M tokamak. It has been found that the ion temperature is higher than the electron temperature by a factor of about 10, and the flow velocity is 0.2-0.3 of the ion sound velocity in the SOL for both ohmic and NB injection heating. These data can help to determine the cross-field thermal diffusivity in tokamak boundary plasma.

The soft X ray diagnostic at JET views the plasma from six directions with a total of 215 lines of sight. The good coverage of the plasma makes it possible to make detailed tomographic reconstructions of the soft X ray emission during various conditions. One of the tomography methods applied at JET is discussed: a grid based constrained optimization method that uses anisotropic smoothness on flux surfaces as regularization. This method has made it possible to study in detail the transport of heavy trace impurities injected into the plasma by laser blow-off. Impurity injection experiments in hot ion H mode and optimized shear plasmas are presented and discussed. The addition of a number of features to the algorithm, notably a non-negativity constraint, has made it possible to reconstruct very localized soft X ray emission from the wall during edge localized modes (ELMs). The detectors suffer damage from the neutrons produced in deuterium-deuterium (DD) fusion reactions. This damage influences the sensitivity of the detectors, which makes it necessary to cross-calibrate the cameras. A method based on tomographic reconstructions has been developed to achieve the cross-calibration.

The onset condition of a thermoelectric instability in divertor tokamaks has been studied analytically and numerically by using a five point model based on SOL and divertor plasmas. The SOL current due to the thermoelectric effect causes the thermoelectric instability and destabilizes the symmetric equilibrium of the SOL and divertor plasmas below a critical divertor plasma temperature. The critical temperature of the thermoelectric instability is equal to or higher than that of the thermal instability due to the divertor radiation, and depends on the midplane SOL plasma temperature and the divertor radiation loss. Below the critical temperature, stable asymmetric equilibria are obtained. As the degree of the asymmetry in the divertor plasma temperature increases, the SOL current has no effect on the instability, or even stabilizes the equilibrium. The SOL current generates spontaneously the divertor asymmetry through the thermoelectric instability.

The avalanche of runaway electrons in an ohmic tokamak plasma triggered by knock-on collisions of traces of energetic electrons with the bulk electrons is simulated by the bounce averaged Fokker-Planck code, CQL3D. It is shown that even when the electric field is small for the production of Dreicer runaways, the knock-on collisions can produce significant runaway electrons in a fraction of a second at typical reactor parameters. The energy spectrum of these knock-on runaways has a characteristic temperature. The growth rate and temperature of the runaway distribution are determined and compared with theory. In simulations of pellet injection into high temperature plasmas, it is shown that a burst of Dreicer runaways may also occur depending on the cooling rate due to the pellet injection. Implications of these phenomena on disruption control in reactor plasmas are discussed.

The first three moments of the energy distributions of products from fusion reactions in thermonuclear plasmas with Maxwellian ion velocity distributions are determined analytically. Relativistic kinematics is used allowing the desired accuracy to be reached, which is 2 to 3 orders of magnitude better than previous analytical results. In particular, neutron spectra of the reactions D(d,n)³He and D(t,n)α for plasma ion temperatures 0 < T_i < 100 keV are studied for which the results are also given in tabulated form with interpolation formulas for the purpose of practical use. The neutron energy distributions are also calculated with numerical methods, in order to assess the analytical results. High accuracy calculations are motivated by the crucial role that neutron measurements are envisaged to play in the next step fusion experiments on burning plasmas, which are also discussed.

The linear theory of plasma waves in homogeneous plasma is arguably the most mature and best understood branch of plasma physics. Given the recently revised version of Stix's excellent Waves in Plasmas (1992), one might ask whether another book on this subject is necessary only a few years later. The answer lies in the scope of this volume; it is somewhat more detailed in certain topics than, and complementary in many fusion research relevant areas to, Stix's book. (I am restricting these comments to the homogeneous plasma theory only, since the author promises a second volume on wave propagation in inhomogeneous plasmas.) This book is also much more of a theorist's approach to waves in plasmas, with the aim of developing the subject within the logical framework of kinetic theory. This may indeed be pleasing to the expert and to the specialist, but may be too difficult to the graduate student as an `introduction' to the subject (which the author explicitly states in the Preface). On the other hand, it may be entirely appropriate for a second course on plasma waves, after the student has mastered fluid theory and an introductory kinetic treatment of waves in a hot magnetized `Vlasov' plasma. For teaching purposes, my personal preference is to review the cold plasma wave treatment using the unified Stix formalism and notation (which the author wisely adopts in the present book, but only in Chapter 5). Such an approach allows one to deal with CMA diagrams early on, as well as to provide a framework to discuss electromagnetic wave propagation and accessibility in inhomogeneous plasmas (for which the cold plasma wave treatment is perfectly adequate). Such an approach does lack some of the rigour, however, that the author achieves with the present approach. As the author correctly shows, the fluid theory treatment of waves follows logically from kinetic theory in the cold plasma limit. I only question the pedagogical value of this approach. Otherwise, I welcome this addition to the literature, for it gives the teacher of the subject a valuable reference where the inquisitive student will be able to read up on and satisfy himself about the practicality and reliability of the Vlasov theory in a hot magnetized and collisionless plasma. The book has excellent treatments of several new topics not included in previous textbooks, for example, the relativistic theory of plasma wave propagation, so important in electron cyclotron heating of magnetically confined fusion plasmas, a discussion of current drive theory and there is a welcome introduction to parametric instabilities in the final chapter.

There are some things that make the readability of the book somewhat difficult. In the early parts, certain advanced concepts are introduced without much motivation or explanation, although the author is trying to be helpful by providing a list of relevant references at the end of each chapter. Here the teacher's role will be critical. Again, a certain amount of previous knowledge of the subject would prove to be invaluable to the student.

The main content of the book is included in 11 chapters. Use is made of CGS Gaussian units, a favourite of plasma theorists. As the author states, these are still widely used in advanced plasma theory, and the student is well advised to become familiar with this system of units (as well as the SI system for applications). To help the reader in the Introduction, the author defines various expressions often used in plasma physics in practical units (frequencies in hertz, lengths in centimetres, temperatures in kiloelectronvolts and magnetic fields in teslas). Chapter 2 is entitled `Plasma Electrodynamics' and it introduces the Maxwell-Vlasov set of equations, as well as the important fundamentals of wave propagation, such as polarization, dispersion and the dielectric tensor, and energy relations. In Chapter 3, `Elementary Plasma Kinetic Theory', the author derives the Vlasov equation and the Fokker-Planck equation from the BBGKY hierarchy. This is a somewhat unusual chapter in a book on plasma waves, but I welcome it since it demonstrates the author's desire to be complete and rigorous in justifying the use of the collisionless Vlasov equation for `high frequency' wave propagation phenomena. Incidentally, it is interesting that while the author derives the Fokker-Planck equation at great length, it is used only to derive the fluid and MHD equations, but not for estimating Coulomb collisional damping of specific waves in later chapters.

Chapter 4 gives the derivation of the hot plasma dielectric tensor. There is an extensive and excellent discussion of the relativistic formulation of the dielectric tensor, which is of fundamental importance to practising fusion physicists (for example) involved in ECR heating of high temperature plasmas. Various temperature limits are taken in Chapters 5, 6 and 7, and the author discusses the infinite number of waves in the cold plasma limit (Chapter 5), in the hot plasma limit (Chapter 6) and in the electrostatic limit (Chapter 7). In my opinion, these chapters represent the `meat' of the book. Chapter 7 includes a detailed treatment of electrostatic waves in a hot plasma, including Bernstein waves and their damping at high harmonics. This is a difficult topic, and the extensive treatment presented here is hard to find in other texts. The author also includes a discussion of two stream instabilities here, together with the Nyquist-Penrose criterion for instability.

Chapter 8 discusses linear wave-particle interactions, including damping of electromagnetic waves, RF current drive and RF heating. Chapter 9 is called `Collisionless Stochasticity' and institutes an introduction to the subject as well as applications to the heating of ions by high harmonic, lower hybrid waves. Chapter 10 is another key part of the book, on the quasilinear theory of heating and current drive. It deals with the practical aspects of RF heating and current drive in magnetically confined fusion plasmas, and is a `must read' for researchers dealing with RF heating and related transport. Chapter 11 attempts to deal with non-linear effects in the presence of high power RF waves in plasmas. First, the author deals with the difficult subject of mode coupling theory, but, owing to its complexity, the formulation is never reduced to practical applications. Only the `dipole approximation' section can be used to make practical estimates of non-linear effects during RF heating.

There are some shortcomings of this book that need to be mentioned here. There are some typographical errors, including spelling errors. The labelling on the figures is often hard to read due to their poor quality and small size. The figures themselves are often too small and are overloaded with curves (e.g., Figs 18.1, 18.2, 21.3, 28.13). The author must have spent a significant effort in producing these curves, and they deserve a better presentation, especially if they are to be used by students. Ease of readability is important for a textbook intended for students and researchers alike. It is hoped that such shortcomings will be improved in future editions, as well as in Volume II, which is to follow.

To summarize, this book presents an up to date major contribution to the field of plasma waves and is a `must' on the shelves of active researchers as well as advanced graduate students. Under the guidance of a knowledgeable teacher, the book may be used as a text, with appropriate omissions of certain sections for a one semester course in plasma waves. Alternatively for those who have mastered the fundamentals of wave propagation in plasmas, the book could be used as a basis for an advanced seminar course.

I am looking forward with anticipation to Volume II, Waves in Inhomogeneous Plasmas, by Marco Brambilla, one of the eminent plasma wave theorists of our generation.