Table of contents

A two-dimensional wave propagation code, developed specifically to simulate correlation reflectometry in large-scale fusion plasmas, is described. The code makes use of separate computational methods in the vacuum, underdense and reflection regions of the plasma in order to obtain the high computational efficiency necessary for correlation analysis. Simulations of TFTR plasma with internal transport barriers are presented and compared with one-dimensional full-wave simulations. It is shown that the two-dimensional simulations are remarkably similar to the results of the one-dimensional full-wave analysis for a wide range of turbulent correlation lengths. Implications for the interpretation of correlation reflectometer measurements in fusion plasma are discussed.

The correlation between O- and X-mode reflectometer signals is studied with a one- and two-dimensional reflectometer model in order to explore its feasibilities as a q-profile diagnostic. It was found that two-dimensional effects and finite fluctuation levels both decrease the O-X correlation. At very low fluctuation levels, which are usually present in the plasma core, there is a good possibility of determining the local magnetic field strength and use that as a constraint for the equilibrium reconstruction.

The additional power absorbed by the plasma can be determined from the time derivative of the total plasma energy, which can be estimated from the diamagnetic flux of the plasma using a diamagnetic loop. The main difficulty in using diamagnetic measurements to estimate the kinetic energy is the compensation of the flux measurement sensitivity to poloidal magnetic fields, which is not always easy to adjust. A method based on the temporal variations of the diamagnetic flux of the plasma during modulated electron cyclotron heating (MECH) has been developed. Using MECH has the advantage that these poloidal fields are not significantly modulated and a good compensation of these fields is not necessary. However, a good compensation of the vessel poloidal image current is crucial to ensure a sufficiently large bandwidth. The application of this diagnostic to studies of the extraordinary mode (X-mode) absorption at the third electron cyclotron harmonic frequency (X3) has been performed on the TCV tokamak in plasmas pre-heated by the X-mode at the second harmonic (X2). A MECH frequency scan has allowed the determination of an optimum modulation frequency, situated at about 200-250 Hz. Based on this diagnostic, full single-pass absorption of the injected X3 power was measured with the X2 pre-heating in co-current drive. This high absorption is more than a factor of 2 higher than that predicted by the linear ray tracing code TORAY. Experimental evidence indicates that a large fraction of the X3 power is absorbed by electrons in an energetic tail created by the X2 pre-heating.

The mechanism of stochastization of particle motion in a spatially localized monochromatic lower hybrid wave of high amplitude is discussed. Such a model of interaction enables simple analytic formulation and numerical elaboration; the mechanism of the stochastization is caused by the nonintegrability of the corresponding Hamiltonian. Using this simple model, we discuss the effects connected with the anomalous interaction, namely the acceleration of electrons with velocities far from the phase velocity, the stochasticity threshold of the interaction, and the change of the distribution function of accelerated electrons. Statistical analysis of the particle dynamics shows the possibility of the generation of the bump-on-tail distribution function. This paper also discusses the conditions under which the presented model is relevant.

The DINA free-boundary equilibrium simulation code has been implemented for TCV, including the full TCV feedback and diagnostic systems. First results showed good agreement with control coil perturbations and correctly reproduced certain non-linear features in the experimental measurements. The latest DINA code simulations, presented in this paper, exploit discharges with different cross-sectional shapes and different vertical instability growth rates which were subjected to controlled vertical displacement events (VDEs), extending previous work with the DINA code on the DIII-D tokamak. The height of the TCV vessel allows observation of the non-linear evolution of the VDE growth rate as regions of different vertical field decay index are crossed. The vertical movement of the plasma is found to be well modelled. For most experiments, DINA reproduces the S-shape of the vertical displacement in TCV with excellent precision. This behaviour cannot be modelled using linear time-independent models because of the predominant exponential shape due to the unstable pole of any linear time-independent model. The other most common equilibrium parameters like the plasma current I_p, the elongation κ, the triangularity δ, the safety factor q, the ratio between the averaged plasma kinetic pressure and the pressure of the poloidal magnetic field at the edge of the plasma β_p, and the internal self inductance l_i also show acceptable agreement. The evolution of the growth rate γ is estimated and compared with the evolution of the closed-loop growth rate calculated with the RZIP linear model, confirming the origin of the observed behaviour.

The results of an edge biasing experiment in RFX are reported. The particle balance has been interpreted by a zero-dimensional model which allows the particle confinement time to be adjusted in order to reproduce the experimental behaviour of the plasma density. It is found that, despite the substantial reduction of the electrostatic transport by a factor of three, the particle confinement time does not increase by more than 35%. This behaviour has been interpreted as an indication that another loss channel must be considered which is responsible for a particle flux twice as large as that carried by electrostatic fluctuations and it has been identified in the perturbation due to the locked mode.

Recent experiments in the Joint European Torus (JET) have provided evidence of sawtooth stabilization by fast ions arising from deuterium neutral beam injection (NBI). A possible theoretical basis for the interpretation of the observed sawtooth period behaviour is investigated and predictions are compared with experimental results, using a sawtooth period model developed to predict the sawtooth period in the International Thermonuclear Experimental Reactor (ITER). Unlike the case of ion cyclotron resonance heating, a detailed comparison between theory and experiment for NBI has not yet been made. In the model employed in this paper, a beam ion contribution to the internal kink potential energy has been incorporated, using a simple analytical expression valid in the limit of isotropic fast particles. This analytical expression has been found to compare well with detailed calculations performed with a hybrid kinetic/MHD code NOVA-K, using fast particle distribution functions computed with a plasma analysis code TRANSP. The beam ion contribution has been implemented in a transport code PRETOR and a few representative JET discharges have been analysed and modelled. The beam ion term is found to be sufficiently stabilizing to produce simulated sawtooth periods in agreement with the experimental results. Sawtooth periods computed without taking this term into account are much shorter than the measured periods. The model indicates that sawteeth are triggered in these JET discharges by excitation of the internal kink in the semi-collisional ion-kinetic regime: this was found by previous authors to be the sawtooth trigger most likely to be relevant to ITER. The role of beam ions in determining the sawtooth period in JET is thus found to be similar to the predicted role of α-particles in ITER.

The possibility of producing radiative collapses in pinches is studied using a 1/2D numerical model with pure bremsstrahlung as the source of radiation, including anomalous resistivities and axial mass losses. The results of the model show the existence of both a lower and an upper limit value of the pinch current to produce collapses. It is also shown that a minimum initial pinch radius (which depends on the initial particle density) is required in order to obtain radiative collapses. The inclusion of axial mass losses makes the production of the collapse more difficult, because it enhances the anomalous resistivity heating.

Pellet injection experiments have been performed on the RFX reversed field pinch (RFP). The main aim of the experimental campaign was the study of the target plasma response to get information both on the possibility of an efficient pellet fuelling of the discharge and on the associated transport modification. In this paper, we present an analysis of different experimental scenarios. The tool employed is a one-dimensional transport code coupled with an ablation calculation that yields the pellet particle source and trajectory. It is seen that, in standard plasmas, the pellets that reach the plasma centre trigger a phase of rapid profile flattening and poorer particle and energy confinement, and an increase of the transport coefficients is required to reproduce the post-pellet behaviour of the profiles. On the other hand, the slow pellets that suffer large deflection and miss the plasma centre do not have such a deleterious effect and, in this case, the unperturbed transport coefficients are able to reproduce the post-pellet evolution of the profiles. Finally, when the pellets are launched in combination with some method that induces an improved confinement, the transport degradation is less evident. In our case, pellet injection has been combined with pulsed poloidal current drive (PPCD), a technique that reduces magnetic field stochasticization and transport in the RFP core. When the effect of the PPCD is strong enough, a synergy between pellet injection and PPCD is observed and plasma fuelling without dramatic confinement reduction is possible.

Searching for ways of ³He isotope supply are one of the serious problems of ecologically attractive D-³He fusion. To solve the problem of ³He supply, cycles with ³He production are suggested. The concept of ³He self-sufficient D-³He cycles is developed. It is shown that, in such cycles, it is possible to achieve high power efficiency and low neutron yield.

A spectroscopic analysis of the deuterium Dα line (λ = 6561.0 Å) emitted in the edge of Tore-Supra just in front of the equatorial neutralizer plate of the ergodic divertor is presented. This analysis, which relies on a line shape modelling, is focused on asymmetric Dα spectra which are obtained in some diverted discharges. It will be shown that three populations of neutrals are necessary to interpret such spectra. A cold atoms population results from the dissociation of molecules desorbed from the surface, and a warm one from charge-exchange reactions with the plasma ions. The last population of neutrals is produced by normal reflection of plasma ions on the neutralizer V-shaped notches \mbox{(V-points)} and has an anisotropic velocity distribution function. The anisotropy of this velocity distribution function is due to its initial form and to its partial relaxation by neutral-ion elastic collisions. The analysis based on a line shape fitting program including a relaxation model allows one to estimate the relative contributions of the neutral populations of recycled deuterium to the Dα emission and their Doppler temperatures. Finally, the dependence of the ion and neutral temperatures deduced from the fits and the dominant molecular dissociation channels are discussed as a function of the edge electron density and temperature.

A model for calculations of Charge eXchange Recombination (CXR) signals of impurity nuclei injected in a high-temperature plasma has been developed. The CXR signals for an Li tracer in Tracer Encapsulated Solid PELlet (TESPEL) experiments on LHD and CHS machines have been calculated. The difference of about two orders of magnitude found in the calculated signals is due to the difference both in the NBI neutral flux density and in the capture-radiation cross-sections, and explains the weak Li³⁺ CXR signals observed in the measurements on LHD.

Calculations of the CXR signals for various injected impurities have been performed for LHD conditions. The operational range of TESPEL diagnostics in the visible spectral range on LHD has been determined. For T_e = 1-2 keV (P_NBI = 3 MW) and N_e = (2-5)×10¹³ cm^-3, injection of F, Mg and Al as tracer materials ensures the largest CXR signals together with complete ionization times of the injected impurity which are much smaller than the impurity transport times.

This new release of Reviews of Plasma Physics is somewhat different from the previous volumes, as it actually contains two reviews. The first one, due to the late B B Kadomtsev, is a general presentation of `Cooperative Effects in Plasmas'. The second Review is a collective work by different authors, and deals with recent results on `Relativistic interactions of laser-pulses with plasmas'.

The first part of the book is based on B B Kadomtsev's written lectures for students of the Moscow Institute of Physics and Technology. Although it begins with very general aspects of basic effects in plasmas such as Landau damping, waves, plasma echoes, two fluid MHD, it contains the more specialised material necessary to grasp the physical subtleties of laser-plasma interaction: nonlinear waves, solitons, self-focusing, three-wave processes with Manley-Rowe relations, wave-particle interaction, etc.

In connection with the first part, the second review is an exhaustive presentation of recent works on the physics of laser-plasma interaction, and covers a wide range of nonlinear relativistic topics on plasmas interacting with high-intensity laser pulses. The various subjects are presented from a theoretical point of view, with special emphasis on the use of numerical simulations. The matter covered includes relativistically strong electromagnetic waves propagating in underdense plasmas, stimulated Raman scattering, filamentation and self-focusing, charged particle acceleration as well as photon acceleration. A special paragraph is devoted to the interaction of an ultra-short ultra-intense laser pulse with an overdense plasma.

Although the first part can be read with profit by students, or physicists unfamiliar with nonlinear plasma physics, the second one is significantly more specialised. It is a systematic review of several areas of current research, with a concise presentation of the main results and exhaustive bibliographical references, rather than a detailed study of a few selected topics. The plasma physicist should find in it a valuable contribution for an exhaustive overview of laser-plasma phenomena. Students and physicists from other disciplines may profit from a more elementary introduction before addressing the second part of this book.

Pierre Bertrand and Giovanni Manfredi

As mentioned in the preface, there is much potential for cross-fertilisation in plasma physics between the different application areas such as astrophysics and fusion plasma physics. The book by N F Cramer represents a good effort to facilitate this cross-fertilisation in the subject of Alfvén waves.

The emphasis of the book is on the influence of extended (i.e. non-ideal) MHD models, such as the Hall-MHD model, on the Alfvén wave spectrum and its applications. After a short introduction to the MHD models in the first chapter, the influence of non-ideal MHD effects (Hall effects, multiple ion species, collisions) on the dispersion relation is discussed for uniform (chapter 2) and non-uniform plasmas (chapter 3). Surface waves at the interface of plasmas, i.e. at a strong non-uniformity, are discussed in chapter 4. Instabilities of Alfvén waves and non-linear waves are the subject of chapter 5. The last three chapters describe the applications of Alfvén waves, using the models described in the earlier chapters. This part is a mix of an overview of published material and some examples that are worked out in some more detail. Applications in laboratory plasmas, restricted to fusion plasmas, are followed by applications in space and solar plasmas (chapter 7) and astrophysical plasmas (chapter 8). Many references are given throughout the book, which facilitates the study of a particular subject in more detail.

The book may not be suitable as a first introduction to Alfvén waves or magnetohydrodynamics: for this the introductory part of the book is too concentrated and the style is in general too compact. However, it is certainly very useful for the both starting and active researchers in the field of Alfvén waves.

G T A Huysmans