Table of contents

In the framework of adding new information to the reversed field pinch (RFP) confinement database, the radiation emitted by RFX plasmas has been investigated using an eight chord bolometric camera, whose detectors have been calibrated absolutely. From the experimental data the emissivity profiles have been reconstructed by means of a generalized tomography reconstruction algorithm. This analysis confirms that the radiation emitted in RFX is systematically concentrated at the edge. The dependence of the emitted power on the plasma density shows that the radiation increases approaching the high density regime, but it rarely goes beyond 30% of the input power for stationary discharges. This behaviour is strongly dependent on the concentration of impurities but, in any case, in RFX there is no evidence of disruptions. A simple local energy balance allows a preliminary evaluation of the radial heat flux profile to be obtained. These measurements indicate that an active impurity screening mechanism is acting in the edge and that transport is the major energy loss mechanism in RFX.

Experimental and theoretical investigations of lower hybrid (LH) turbulence in the W7-AS stellarator are presented. The turbulence is excited by an ion beam, which is generated by a weak neutral hydrogen beam injected transversely to the confining magnetic field. The instability is detected by collective Thomson scattering of powerful gyrotron radiation. From the measured density dependence of the frequency it was identified as an LH type of instability. The spectrum is characterized by a narrow bandwidth in spite of the inherently poor radial resolution of the backscattering geometry. The theoretical model of an LH instability driven by a transverse fast ion component under the double resonance condition (coincidence of the LH frequency with a high cyclotron harmonic of the fast ions) is developed. The instability growth rate is derived. The stabilizing effect of high bulk ion temperatures was observed experimentally, in accordance with theoretical modelling. An instability saturation mechanism similar to the well known stochastic ion heating is proposed.

The phenomenon of ion induced sputtering is integral to many applications. In magnetically confined fusion, this sputtering is important for both the lifetime of the plasma facing components and the contamination of the plasma. A method has been developed to obtain both the angular distribution and the total sputtering yield. The total yield is determined by collecting the sputtered material on a quartz crystal microbalance. The sputtered material is also collected on a pyrolytic graphite collector plate. By mapping the concentrations of the sputtered material on this plate, both the polar and the azimuthal angular distribution can be determined. Utilizing this set-up, data have been obtained for 10 to 700 eV D⁺ on beryllium at a 45° angle of incidence to the normal. Subthreshold sputtering (0.004 ± 0.003 at 10 eV) has been observed. These data are some of the first to become available, especially at the lower energies.

The basic roles of several of the principal modulations of plasma boundary shape on MHD equilibria are investigated. The appropriate combination of the principal helical modulations for elimination of the bumpy field component in the realization of the quasi-axisymmetric (QAS) and quasi-helically symmetric (QHS) configurations is explained by considering the variation of the areas of the magnetic surface cross-sections. A triangular modulation is utilized effectively to form a magnetic well by shifting the magnetic axis outward compared with the centre of mass of the magnetic surface cross-section. The spatialization of the magnetic axis or the bumpy modulations of the plasma boundary are rather important for reducing the toroidicity in the magnetic field, which can lead to QHS configurations. Some stellarator magnetic configurations at present in the design stage or in existing experimental devices are discussed from the point of view of plasma boundary modulations. On the basis of these main findings about plasma boundary modulations, examples of the essential approach to QAS and QHS configurations are demonstrated step by step. The possibility of a quasi-bumpy (or poloidally) symmetric (QBS) configuration is also mentioned.

The conventional configuration of a radiation driven target for heavy ion fusion is a quasi-cylindrical hohlraum containing a fusion capsule with radiation converters placed at opposite ends of the hohlraum. Ion beams enter each converter from opposite directions and are stopped by the material inside the converters. The first comprehensive two dimensional (2-D) simulations are presented for this configuration using the radiation hydrodynamics code LASNEX. The fusion capsule inside the hohlraum absorbs 1 MJ of radiation energy and can give a yield of 430 MJ if the illumination symmetry condition and the pulse shape requirements are satisfied. To drive this capsule, the total ion beam energy input into the hohlraum is about 22 MJ, which results in a target gain of only about 20. This yield is substantially lower than the previous estimate of greater than 80. The reason is that the initial length of the converters has to be reasonably long to prevent the hot beam stopping material from leaking into the hohlraum and causing unacceptable implosion asymmetry, without other target modifications. Furthermore, as the beam stopping material inside the converters is being heated, it expands substantially in the axial direction. This stretches the length of the converters, and, consequently, the ratio of opening area to volume of the converters decreases. These factors make it difficult for the radiation to escape from the converters and substantially reduce the efficiency of converting ion beam energy into radiation. It is concluded that the gain of this type of target is too low for commercial fusion and an alternative hohlraum configuration that can provide higher gain should therefore be sought.

Through compact toroid (CT) injection experiments on the TEXT-U tokamak (with B_T ≃ 10 kG and I_P ≃ 100 kA), it has been shown that the acceleration electrode configuration, particularly in the vicinity of the toroidal field (TF) coils of the tokamak, has a strong effect on penetration performance. In initial experiments, premature stopping of CTs within the injector was seen at anomalously low TF strengths. Two modifications were found to greatly improve performance: (a) removal of a section of the inner electrode and (b) increased diameter of the `drift tube' (which guides the CT into the tokamak after acceleration). It is proposed that the primary drag mechanism slowing CTs is toroidal flux trapping, which occurs when a CT displaces transverse TF trapped within the flux conserving walls of the acceleration electrodes (or drift tube). For a simple two dimensional (2-D) geometry, a magnetostatic analysis produces a CT kinetic energy requirement of ¹/₂ρv² ⩾ α(B₀²/2μ₀), with α = 2/(1-a²/R²) a dimensionless number that is dependent on the CT radius a normalized by the drift tube radius R. For a typical CT, this can greatly increase the required energies. A numerical analysis in 3-D confirms the analytical result for long CTs (with length L such that L/a ≳ 10). In addition to flux trapping, the CT shape is also shown to affect the energy criterion. These findings indicate that a realistic assessment of the kinetic energy required for a CT to penetrate a particular tokamak TF must take into account the interaction of the magnetic field with the electrode walls of the injector.

CREATE-L, a simple and reliable linearized plasma response model for the control of the plasma current, position and shape in tokamaks, is presented. The basic assumption made is that the plasma behaviour is described using three degrees of freedom, related to the total plasma current, internal inductance and poloidal beta. The state variables are the coil and plasma currents; the inputs are the applied voltages, whereas poloidal beta and internal inductance play the role of disturbances. The outputs are field and flux values and some basic plasma parameters. The model is tested against non-linear codes and validated via comparison with experimental results.

An experiment was done with TFTR DT plasmas to measure the effect of the q(r) profile on the alpha particle ripple loss using a radially movable scintillator detector 20° below the outer midplane. The experimental results were compared with toroidal field (TF) ripple loss calculations done using a Monte Carlo guiding centre orbit following code (ORBIT). Although some of the experimental results are consistent with the ORBIT code modelling, the measured variation of the alpha particle loss with q(r) could not be explained by this code. This inconsistency is most likely due to the effect of limiter shadowing on alpha particle diffusion into this detector, which cannot be modelled with ORBIT.

Ion cyclotron emission (ICE) observed during deuterium and deuterium-tritium experiments in TFTR can be driven by both fusion products and injected beam ions. The emission driven by fusion products is a result of the excitation of the fast magnetoacoustic wave through toroidicity affected cyclotron resonance, the magnetoacoustic cyclotron instability. For beam driven ICE, the excitation mechanism, outlined by R.O. Dendy et al. (Phys. Plasmas 1 (1994) 3407) for the cylindrical case, is generalized by including the curvature and ∇B drift in the local resonance condition. The phase velocity of the destabilized, predominantly electrostatic, wave is typically an order of magnitude smaller than the Alfvén velocity. For both fusion and beam driven ICE, it is found that the instability growth rate is greatly increased as compared with the cylindrical case and reaches its maximum for nearly perpendicular propagation. The results of the numerical and analytical stability analysis are consistent with the experimental observations and provide an explanation for the simultaneous excitation of sequential multiple cyclotron harmonics of the fast ions, the sublinear correlation of the growth rate with the fast ion density and the stabilizing effect of the increasing fast ion velocity spread.

This book provides the basic concepts necessary for an introduction to the classical theory of radiation. The reader is first introduced to Maxwell's equations and then led through their basic properties (Chapters 1 and 2). Non-uniform plane waves are treated in Chapter 3 with a discussion of the two and three dimensional cases. Many examples of two and three dimensional electromagnetic fields are given, and the physics of practical devices is also analysed. Geometrical rays, as well as the notion of a Gaussian beam, are introduced at this stage, and the link between electromagnetism and optical principles is amplified in Chapter 4 (the Huyghens principle, transmission through an aperture, scattering cross-section). The electromagnetic radiation from charge and current distributions is obtained in a general form from potential theory (Chapter 5), followed quite naturally by the classic illustration of the fields produced by a moving charge in the classical (v/c <<1) and relativistic (v/c∼1) cases. Important physical examples (synchrotron radiation, Cherenkov radiation) are also considered in detail. The last two chapters treat the various problems associated with dipole radiation, from scattering by small objects (with, as an example, the colour and polarization of sky light) to the determination of the fields from various shapes and configurations of antenna.

The reader is provided throughout all the chapters with abundant problems and examples. A much appreciated feature is the inclusion in the text, whenever necessary, of the required mathematical bases: numerical solutions of Maxwell's equation, Fourier transforms (Chapter 1), the stationary phase method (Chapter 3), the Dirac function (Chapter 5) and a review of vector analysis (Annex B). These mathematical sections will be specially useful for advanced undergraduates who may need some mathematical tools and, thus, will not need to search for these in more specialized books.

The main focus of the book is to provide the reader with the fundamentals of the classical theory of radiation. This aim is well complemented by examples from a variety of fields. Since the purpose of the book is not to provide a general treatment of electromagnetism or electrodynamics, the reader cannot expect to find some of the topics usual in other electrodynamics texts, such as relativistic transforms of electromagnetic fields (although the Lorentz condition is mentioned) or a discussion of the causality principle in the derivation of the Green function. However, within the scope of the book, these topics are not essential for an understanding of electromagnetic radiation and can therefore be omitted.

I feel that the author has covered the essentials of the subject of electromagnetic radiation. The reader, even the advanced undergraduate, will be able to follow the mathematical steps, as well as the physical insights. A historical introduction (paragraphs 1.1 and 2.7) also broadens the reader's knowledge of the field, a feature rarely found in other texts. The large number of figures and the numerous examples also facilitate the reading of the book.

This book appears to me to be a very useful textbook that is accessible to a very broad category of readers, from advanced undergraduates to researchers, since it starts with the basic physics and covers quite extensively the field of electromagnetic radiation. For a reader who is interested in electromagnetism and electrodynamics, it is an excellent companion to the classical and more fundamental text books, such as Jackson's Classical Electrodynamics, Landau and Lifshitz's The Classical Theory of Fields or Stratton's Electromagnetics Theory.

In summary, I heartily recommend this book, An Introduction of Classical Electromagnetic Radiation, to all my colleagues who teach the subject of electromagnetic radiation, to students who follow such courses and to researchers active in this field.

Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field.

Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered.

This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy-Green tensors, the Eulerian or Almansi strain tensor, distortional components, strain rate tensors, rate of deformation tensors, spin tensors and objectivity. The standard Cauchy stress tensor is mentioned in passing, and then virtual work and work conjugacy lead to alternative stress representations such as the Piola-Kirchoff representation. Chapter 5 concentrates on hyperelasticity (where stresses are derived from a stored energy function) and its subvarieties. Chapter 6 proceeds by linearizing the virtual work statement prior to discretization and Chapter 7 deals with approaches to solving the formulation. In Chapter 8 the FORTRAN finite element code written by Bonet (available via the world wide web) is described.

In summary this book is written by experts, for future experts, and provides a very fast review of the field for people who already know the topic. The authors assume the reader is familiar with `elementary stress analysis' and has had some exposure to `the principle of the finite element method'. Their goals are summarized by the statement, `If the reader is prepared not to get too hung up on details, it is possible to use the book to obtain a reasonable overview of the subject'. This is a very nice summary of what is going on in the field but as a stand-alone text it is much too terse. The total bibliography is a page and a half. It would be an improvement if there were that much reference material for each chapter.