Table of contents

The physics of divertors in tokamaks is reviewed, primarily from an experimental point of view, although where possible simple analytic modelling is included. The paper covers the four main subject areas at issue in divertor research: (1) the wide dispersal of plasma power exhausted from the main plasma, (2) the production of sufficiently high gas pressures in the vicinity of pump ducts to enable the removal of fuel and helium (`ash') gas from the system, (3) the elimination or reduction of impurity production and (4) the screening of impurities produced, or intentionally added, at the plasma boundary from the plasma core. A simple analytic model, the `two-point' model, is introduced early in the paper and provides a framework for comparison of the experimental results, drawn from many machines, with simply derived expectations. Conclusions regarding the direction of future research priorities are made.

The Hamiltonian formulation of the guiding centre drift orbits for three-dimensional (3D) toroidal configurations with general time-dependent electric and magnetic field structures has been extended to cover relativistic particles. For static 3D magnetic fields with nested magnetic surfaces, a mapping procedure from the equilibrium to the canonical coordinates is outlined. This transformation is shown to be so complicated that it renders impractical most applications in canonical coordinates. For magnetic coordinates, the transformation is straightforward. The relativistic guiding centre drift equations are explicitly derived with a constrained perturbed magnetic field that allows these coordinates to adopt a canonical structure.

This paper deals with the nonlinear stability properties of external, ideal magnetohydrodynamic (MHD) modes with helical symmetry in a tokamak. Based on an analysis of bifurcated equilibria in cylindrical geometry, the investigation is concerned with non-resonant, nearly marginal modes with poloidal mode numbers . The analysis is to a large extent analytical and based on an expansion in the helical mode amplitude. The final results, however, are obtained numerically.

A systematic investigation of the dependence of the nonlinear effect on poloidal mode number, current profile and wall distance is performed, including current profiles which are peaked off-axis. The results show that helical modes with with realistic wall distances are, in principle, nonlinearly stable, i.e. the bifurcation is supercritical, for all studied current profiles. The stabilizing effect increases with m and depends strongly on the mode number. For high m, the nonlinear effect is significant even at very small mode amplitude and, consequently, the amplitudes of helical states with high m are very small. Also, the stabilizing effect depends strongly on the current profile and increases when the profile is peaked. However, if too much current is flowing in a region near the plasma edge, the bifurcation is still supercritical but the amplitudes of the bifurcated equilibria are very large, thus indicating a situation where nonlinear stability would not be obtained in practice. This finding may be of interest in connection with high-performance tokamaks operating with a large fraction of bootstrap current. The requirement of reduced current density near the plasma edge is most stringent for the m = 2 mode.

Neutral density profiles have been derived along the outboard divertor target of Alcator C-Mod and inside the last closed flux surface (LCFS). Local emission rates are obtained by a tomographic inversion of measured brightness profiles. Electron temperatures and densities provided by a divertor Langmuir probe array are then used to calculate the local neutral density, , from the emissivity profile. For points inside the LCFS, electron cyclotron emission (ECE) and interferometry data were used for electron density and temperature, respectively. Along the divertor target, steep gradients in neutral density persist during regular ohmic attached discharges, with . Plasma detachment leads to values of that can reach up to several times in the bottom of the divertor with much shallower pressure gradients to the midplane. Modelling of the parallel plasma momentum decrease due to charge exchange (CX) and elastic ion - neutral collisions indicates that neutral densities well below those observed are sufficient to explain the measured drop in parallel plasma pressure. This suggests that significant momentum is carried by the neutrals in the divertor resulting in decreased efficiency of momentum transfer between ions and neutrals.

An extensive series of experiments in the Extrap mode has been carried out on Extrap T1-U in an attempt to obtain hot, collisionless discharges. Using no external axial magnetic field, performance has been limited to low temperatures and low currents at high loop voltages kV, leading to energy confinement times of only a few s or Alfvén times. The discharge length is typically of the order of greater than 100 Alfvén times.

Imposing a weak axial field at peak current) the temperature could be increased to at toroidal currents . Energy confinement times up to 15 Alfvén times were then obtained.

The poor confinement is attributed to the weak axial magnetic field, generating strong instability-induced fluctuations and related radial transport in the core plasma. A turbulence core plasma transport model is suggested, based on theoretical evidence of linear instability in the kinetic regime.

Self-generation of axial magnetic field is observed when the magnetic X-points, generated by the plasma current and an external octupole field, approach or pass beyond the wall.

Edge transport appears to be dominated by line radiation and heat conduction to the wall along open field lines.

An analysis of the local ion energy transport is performed for more than one hundred well documented ohmic ASDEX discharges. These are characterized by three different confinement regimes: the linear ohmic confinement (LOC), the saturated ohmic confinement (SOC) and the improved ohmic confinement (IOC). All three are covered by this study.

To identify the most important local transport mechanism of the ion heat, the ion power balance equation is analysed. Two methods are used: straightforward calculations with experimental data only, and a comparison of measured and calculated profiles of the ion temperature and the ion heat conductivity, respectively. A discussion of the power balance shows that conductive losses dominate the ion energy transport in all ohmic discharges of ASDEX. Losses due to sawtooth activity play a role only inside the q = 1 surface, while at the edge convective fluxes and CX losses influence the ion energy transport. Both methods lead to the result that both the ion temperature and the ion heat conductivity are consistent with predictions of neoclassical theory. Enhanced heat losses as suggested by theories, e.g. on the basis of modes, can be excluded.

The propagation of a wave beam through an electron cyclotron resonance layer is analysed in two-dimensional slab geometry in order to assess the deviation from cold plasma propagation due to resonant, warm plasma changes in wave dispersion. For quasi-perpendicular propagation, , an O-mode beam is shown to exhibit a strong wiggle in the trajectory of the centre of the beam when passing through the fundamental electron cyclotron resonance. The effects are largest for low temperatures and close to perpendicular propagation. Predictions from standard dielectric wave energy fluxes are inconsistent with the trajectory of the beam. Qualitatively identical results are obtained for the X-mode second harmonic. In contrast, the X-mode at the fundamental resonance shows significant deviations from cold plasma propagation only for strongly oblique propagation and/or high temperatures. On the basis of the obtained results a practical suggestion is made for ray tracing near electron cyclotron resonance.

Let me say from the start that opening this book on electron cyclotron resonance ion sources (ECRIS) and ECR plasmas is a real pleasure. The book is written by a well known recognized expert in the field, an inquisitive experimentalist with a solid theoretical background. During the many years that Geller has worked in the field, he has clearly accumulated a lot of experience, so that his expert eye allows him to give us a superb overall survey.

The book always gives an attractive historical perspective, which shows how the subject developed and gives the opportunity for novices to profit from former trials and errors, the `things' that take time in a growing field. The book aways gives the final word to experiment.

The content of the first half of this book covers several aspects of fundamental basic plasma physics, such as wave - plasma interaction (particularly in the EC range), ionization phenomena, confinement of plasma and diffusion in a magnetic field, wave launchers and coupling structures. It is a clever and knowledgeable introduction to the aim of the book, namely the second part, which describes the different ECRIS sources and sheds light on their historical development and on the plasma characteristics of such sources.

Thinking about the multidisciplinary interest this book should raise, let us take overdense discharges as an example. The production of discharges at densities above the O-mode cut-off of electron cyclotron waves is an important practical result of ECRIS research, although our understanding of the mechanisms at work has not been fully clear for a long time. Detailed hints are given in this book, suggesting the successive conversion of O- to X- and then to electron Bernstein waves, citing overdense heating ray-tracing calculations of a toroidal magnetic fusion plasma, proposed more than two decades ago. But clear experimental proof of the existence of overdense heating in a toroidal plasma following the above-predicted wave conversion mechanism appeared only last year. This example of cross-disciplinary fertilization indicates the strong interest this book should raise among the different research fields sharing the use of EC waves.

This book is up-to-date, the author is well aware of the field and the presentation is clear and attractive. The numerous figures illustrating the text are well designed and meet the high level of pedagogical and communication aims of the book.

The obvious purpose of reading this book is to learn about ECRIS and it will be highly appreciated by specialists and newcomers alike, but the book will also be of interest in other fields of plasma physics, for example in magnetic fusion. Overdense heating, which may be on the verge of becoming an experimental tool in toroidal magnetic confinement and which has been the basis of the functioning of ECRIS for many years, stands as a good example.

This stimulating book can also be taken as a source of imagination for new experiments and in related fields. Due to its width and breadth, it should interest people in plasma physics, plasma - wave interactions, industrial and applied plasma physics, as well as electron cyclotron resonance heating in nuclear magnetic confinement machines, etc ...

7 - 18 July 1997 34th Culham Plasma Physics Summer School (UKAEA/Euratom) Oxford, UK Contact: Mrs J Bright, UKAEA Fusion, Culham, Abingdon, Oxfordshire, OX14 3DB, UK. Tel +44-1235-463773, Fax +44-1235-463474, E-mail julie.bright@ukaea.org.uk. Application deadline: 9 May 1997 (later applications may be accepted depending on accommodation constraints).

27 August - 2 September 1997 International Conference on Superstrong Fields in Plasmas Villa Monastero, Varenna (Lc), Italy Contact: Mrs D Pifferetti, Secretariat Villa Monastero, 1 Piazza Venini, 22050 Varenna, Italy. Tel +39-341-831261, Fax +39-341-831281, E-mail ccvm@ccvm.cil.lc.it (abstracts should be sent to Dr M Lontano, Istituto di Fisica del Plasma, Consiglio Nazionale delle Ricerche, Via Cozzi 53, 20125 Milano, Italy. Tel +39-2-66173260, Fax +39-2-66173239, E-mail lontano@ifp.mi.cnr.it). Application and abstract deadline: 13 June 1997

4 - 12 September 1997 International Workshop on Diagnostics for Experimental Fusion Reactors Villa Monastero, Varenna, Italy Contact: D Pifferetti, Centro di Cultura `Villa Monastero', 1 Piazza Venini, 22050 Varenna (Lc) Italy. Tel +39-341-831261, Fax +39-341-831281, E-mail ccvm@ccvm.cil.lc.it. Application and abstract deadline: 13 June 1997.

8 - 12 September 1997 12th International Conference on Gas Discharges and their Applications Greifswald, Germany Contact: Dr G Babucke, Inst. f. Niedertemperatur-Plasmaphysik, Robert-Blum-Str. 8 - 10, 17489 Greifswald, Germany. Tel +49-3834-554411, Fax +49-3834-554301, E-mail gd97@public.inp.uni-greifswald.de.

8 - 19 September 1997 3rd Carolus Magnus Summer School on Plasma Physics Spa, Belgium Contact: Dr G van Oost, c/o Institut für Plasmaphysik, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany. Tel +49-2461-61-5626, Fax +49-2461-61-3331, E-mail vanoost@fusion.rma.ac.be. Application deadline: 15 May 1997, abstract deadline: 15 July 1997.

8 - 10 October 1997 7th European Fusion Theory Conference Jülich, Germany Contact: A L Rogister, Institut für Plasmaphysik, Forschungszentrum Jülich GmbH, EURATOM-FZJ Association, D-52425 Jülich, Germany. Tel +49-2461-61-5440, Fax +49-2461-61-2970, E-mail d.petschner@kfa-juelich.de.

13 October - 7 November 1997 Autumn College on Plasma Physics Miramare-Trieste, Italy Contact: S M Mahajan, International Centre for Theoretical Physics, Autumn College on Plasma Physics, PO Box 586, I-34100 Trieste, Italy. Tel +39-40-2240357, Fax +39-40-224163, E-mail smr1012@ictp.trieste.it. Application deadline: 30 April 1997.

10 - 14 November 1997 Topical Workshop on Plasma Physics: New Perspectives of Collective Effects Miramare-Trieste, Italy Contact: P K Shukla, International Centre for Theoretical Physics, PO Box 586, I-34100 Trieste, Italy. Tel +39-40-2240357, Fax +39-40-224163, E-mail smr1014@ictp.trieste.it. Application deadline: 31 March 1997.