Table of contents

An expression for the average energy loss rate of beam ions due to nuclear elastic scattering (NES) in Maxwellian plasmas is derived, by taking into consideration the thermal motion of the background ions. The NES effect on deuterium beam injection plasma heating is examined using the expression derived. As a result of the scattering due to NES of the slowing down deuterons up to the higher energy range, the average energy loss rate due to NES of 1 MeV deuterons in 20 keV deuterium plasmas decreases by about 60% compared with the case of cold background plasmas. An examination is also made of the fraction of the beam energy deposited to ions. It is shown that when the beam energy is higher than 1 MeV, the increase in the fraction due to NES becomes appreciable.

The operation conditions to avoid runaway electron generation at the major disruption have been investigated in JT-60U tokamak plasmas. It has been found that runaway electrons are not observed for low B_t of ⩽ 2.2 T or low plasma current quench rates (I_γ ≡ -(dI_p/dt)/I_p) of <50 s^-1. Furthermore, they are not observed for low effective safety factors defined at the plasma edge (q_eff) of ⩽ 2.5 even for high I_γ of 300-400 s^-1, which is the case for uncontrolled disruptions accompanied by large plasma displacements (e.g., vertical displacement events (VDEs)). On the other hand, in controlled disruptions with small plasma shifts, q_eff easily increases above 8, and runaway electrons are observed even for low current quench rates of 50-100 s^-1. Furthermore, it has been found that in these position controlled disruptions the runaway current tail can rapidly decay even for zero or weakly positive plasma surface voltages. These observations of the avoidance and termination of runaway electrons suggest an anomalous loss mechanism for runaway electrons.

Magnetic fluctuations, observed in the Alcator C-Mod experiment, are modelled via the instability of microtearing modes with ratio of poloidal to toroidal mode number m/n = 4. These modes are predominantly electromagnetic in nature, although the electrostatic component is non-vanishing, are driven by the steep temperature gradient at the plasma edge and are shown to have a relatively broad spectrum for typical experimental parameters.

The features of a number of theoretical models proposed to explain the cross-field transport in the SOL are summarized. Simple balances of transport parallel and perpendicular to the magnetic field in the SOL allow the derivation of predictions from these models for the power law scalings of the SOL width Δ with the plasma parameters in the two cases of a collisionless and a collisional SOL. Data on the SOL widths for a collisionless SOL from COMPASS-D and for a collisional SOL from JET and Alcator C-Mod are then used to test these models. Remarkably, the data from COMPASS-D, JET and Alcator C-Mod all favour the same small subset of these models. Furthermore, direct comparisons of the theoretical models for the cross-field thermal diffusivities with SOL data from JET and Alcator C-Mod provide some support for this finding. These `best models' can be used to make predictions for MAST, the spherical tokamak at Culham Science Centre, and for ITER.

Tritium has been injected into TFTR supershots using a gas feed containing 2% tritium and 98% deuterium in one or more neutral beam sources. A total of 38 beam-injected tritium shots required about 400 Ci of tritium, of which less than 5% actually entered the plasma. The ratio of D-T to D-D neutron rates varied from about 0.5 to 4.5. A peak neutron rate of 7.7 × 10¹⁶ D-T n/s together with 1.7 × 10¹⁶ D-D n/s was attained with eight 2% tritium beams delivering 18.7 MW. The measured D-T neutron rates are extrapolated to fusion powers in 50:50 D-T operation with similar plasma parameters. The experiments have also provided data for the D-T calibration of neutron and lost alpha particle detectors and for optimizing tritium beam injection. With the aid of a multichannel neutron collimator, these experiments have enabled the comparison of radial profiles of D-T neutron production and global neutron output with the predictions of simulation codes.

High fusion power experiments using DT mixtures in ELM-free H mode and optimized shear regimes in JET are reported. A fusion power of 16.1 MW has been produced in an ELM-free H mode at 4.2 MA/3.6 T. The transient value of the fusion amplification factor was 0.95±0.17, consistent with the high value of n_DT(0)τ_E^diaT_i(0) = 8.7 × 10²⁰±20% m^-3 s keV, and was maintained for about half an energy confinement time until excessive edge pressure gradients resulted in discharge termination by MHD instabilities. The ratio of DD to DT fusion powers (from separate but otherwise similar discharges) showed the expected factor of 210, validating DD projections of DT performance for similar pressure profiles and good plasma mixture control, which was achieved by loading the vessel walls with the appropriate DT mix. Magnetic fluctuation spectra showed no evidence of Alfvénic instabilities driven by alpha particles, in agreement with theoretical model calculations. Alpha particle heating has been unambiguously observed, its effect being separated successfully from possible isotope effects on energy confinement by varying the tritium concentration in otherwise similar discharges. The scan showed that there was no, or at most a very weak, isotope effect on the energy confinement time. The highest electron temperature was clearly correlated with the maximum alpha particle heating power and the optimum DT mixture; the maximum increase was 1.3±0.23 keV with 1.3 MW of alpha particle heating power, consistent with classical expectations for alpha particle confinement and heating. In the optimized shear regime, clear internal transport barriers were established for the first time in DT, with a power similar to that required in DD. The ion thermal conductivity in the plasma core approached neoclassical levels. Real time power control maintained the plasma core close to limits set by pressure gradient driven MHD instabilities, allowing 8.2 MW of DT fusion power with n_DT(0)τ_E^diaT_i(0) ≈ 10²¹ m^-3 s keV, even though full optimization was not possible within the imposed neutron budget. In addition, quasi-steady-state discharges with simultaneous internal and edge transport barriers have been produced with high confinement and a fusion power of up to 7 MW; these double barrier discharges show a great potential for steady state operation. © 1999, Euratom

An overview of JET experimental results in DT plasmas directly relevant to ITER modes of operation is presented. Experiments in D:T mixtures varying from 100:0 to 10:90 and those carried out in hydrogen plasmas show that the H mode threshold power has an approximately inverse isotope mass dependence. Matching some of the key dimensionless parameters to the ITER values, the ITER similarity experiments with ITER shape and safety factor q show that the global energy confinement time is practically independent of isotopic mass (∼A^0.03±0.08), where A is the atomic mass of the hydrogenic species. Subtracting the edge pedestal energy (which scales as ∼A^0.57±0.2) from the total stored energy leads to a ∼A^-0.17±0.1 dependence of confinement in the plasma core, very similar to that expected from the gyro-Bohm transport (∼ A^-0.2) model. The observed scaling of the edge pedestal energy is consistent with a model in which the edge pressure gradient saturates at the ballooning limit over a region of width that scales as the ion poloidal Larmor radius governed by the average energy of the fast ions in the edge. The steady state total stored energy for a given input power in both ICRH and NBI discharges is the same despite the lower edge pedestal in the ICRH case, which is compensated for by more peaked power deposition profiles in ICRH. The ELM frequency is smaller with NBI; it decreases with isotopic mass in both NBI and ICRH discharges. A steady state, type I ELMy H mode discharge with ITER shape and q at 3.8 T/3.8 MA with an input power of 22 MW produced a Q ≈ 0.18 for 3.5 s and extrapolates well to ignition with ITER parameters. Here, Q is the ratio of fusion output power to input power. The thermal ELMy H mode confinement in both deuterium and tritium gas fuelled plasmas decreases significantly when the plasma density exceeds 0.75 of the Greenwald (n_GW) limit, and the maximum density achieved is 0.85n_GW. In L mode, the density limit decreases with increasing isotope mass roughly in accordance with code predictions. ITER reference ICRH scenarios have been evaluated. Second harmonic heating of tritium at the densities available in JET produces strong tails and heats electrons predominantly as expected. The ³He minority in 50:50 D:T and tritium dominated plasmas showed strong bulk ion heating leading to ion temperatures up to 13 keV with ICRH alone. Deuterium minority ion cyclotron heating in tritium plasmas at a power level of 6 MW produced steady state record values of Q ≈ 0.22 for more than 2.5 s.

A feedforward neural network with two hidden layers is used to forecast major and minor disruptive instabilities in TEXT tokamak discharges. Using the experimental data of soft X ray signals as input data, the neural network is trained with one disruptive plasma discharge, and a different disruptive discharge is used for validation. After being properly trained, the networks, with the same set of weights, are used to forecast disruptions in two other plasma discharges. It is observed that the neural network is able to predict the occurrence of a disruption more than 3 ms in advance. This time interval is almost 3 times longer than the one already obtained previously when a magnetic signal from a Mirnov coil was used to feed the neural networks. Visually no indication of an upcoming disruption is seen from the experimental data this far back from the time of disruption. Finally, by observing the predictive behaviour of the network for the disruptive discharges analysed and comparing the soft X ray data with the corresponding magnetic experimental signal, it is conjectured about where inside the plasma column the disruption first started.

Langmuir probes and a Mach probe were used for measuring edge fluctuations and parallel plasma flow, respectively, on the CT-6B tokamak. A maximum radial gradient in parallel flow was observed to be located roughly at the maximum E_r shear layer (or, namely, the poloidal velocity shear layer). E_r shear is found to be very possibly consistent with a regulating effect on edge turbulence features. Non-linear analysis indicates that non-linear phase coupling in turbulence may be influenced by E_r shear, or that there exist coherent structures induced by strong E_r shear, and the phase coupling processes show an intermittent character. The results provide some new observations for a better understanding of the basic mechanisms of edge turbulence.

Report on the IEA Workshop held at Princeton, New Jersey, United States of America, 16-18 March 1998.

Recent experience with the use of tritium fuel in the TFTR and JET, together with progress in developing the technical design of ITER, has expanded the technical knowledge base for tritium issues in fusion. This paper reports on an IEA workshop that brought together scientists and engineers to share experience and expertise on all fusion related tritium issues. Extensive discussion periods were devoted to exploring outstanding issues and identifying potential R&D avenues to address them. The presentations, discussions and recommendations are summarized.

Stellarators and tokamaks are the most advanced devices that have been developed for magnetic fusion applications. The two approaches have much in common; tokamaks have received the most attention because their axisymmetry justifies the use of simpler models and provides a more forgiving geometry. However, recent advances in treating more complicated three dimensional systems have made it possible to design stellarators that are not susceptible to disruptions and do not need plasma current control. This has excited interest recently. The two largest new magnetic experiments in the world are the LHD device, which commenced operation in Toki, Japan, in 1998 and W7-X, which should become operational in Greifswald, Germany, in 2004. Other recently commissioned stellarators, including H-1 in Canberra, Australia, TJ-II in Madrid, Spain, and IMS in Madison, Wisconsin, have joined these in rejuvenating the stellarator programme. Thus, it is most appropriate that the author has made the lecture material that he presents to his students in the Graduate School of Energy Science at Kyoto University available to everyone.

Stellarator and Heliotron Devices provides an excellent treatment of stellarator theory. It is aimed at graduate students who have a good understanding of classical mechanics and mathematical techniques. It contains good descriptions and derivations of essentially every aspect of fusion theory. The author provides an excellent qualitative introduction to each subject, pointing out the strengths and weaknesses of the models that are being used and describing our present understanding. He judiciously uses simple models which illustrate the similarities and differences between stellarators and tokamaks. To some extent the treatment is uneven, rigorous derivations starting with basic principles being given in some cases and relations and equations taken from the original papers being used as a starting point in others. This technique provides an excellent training ground for students without detracting from the usefulness of the book for knowledgeable fusion physicists.

After a short, somewhat historical, introduction, Chapter 2 contains a good treatment of the basic properties of a toroidal magnetic configuration (the concepts of magnetic surfaces, rotational transform, shear and magnetic wells), averaging techniques which can often be used to simplify the calculations, helically invariant configurations, magnetic islands and line tracing techniques. Derivations and discussions of the basic tools of plasma theory, including the Vlasov equation, magnetohydrodynamic equations and their reduced form for low-β, large aspect ratio systems, properties of MHD waves, the drift kinetic equation and transport equations, are given in Chapter 3. Chapter 4 contains a good treatment of MHD equilibria, including a derivation of the three dimensional Grad-Shafranov equation, a discussion of the calculation of equilibria with a planar magnetic axis with both averaged equations and a variational approach, a comparison of the results of the two techniques, a formulation for stellarators with a helical magnetic axis and a good discussion of the Pfirsch-Schlüter current. The treatment of MHD instabilities in Chapter 5 is also excellent. It starts with a good derivation and discussion of the energy principle, gives a detailed treatment of ballooning modes where the wavelengths of the perturbation perpendicular to the field are short while those along B are long and derives the Mercier criterion from the ballooning mode equation. I personally prefer to obtain this criterion by making the low mode number assumption that dξ/dΨ>>dξ/dθ ≈ dξ/dζ, since non-ideal effects such as finite gyration radius corrections may provide less stabilization to these modes. A careful treatment of the resistive interchange mode is followed by a discussion of the role of localized stability criteria in the analysis of experiment and design studies, a study of Pfirsch-Schlüter current driven magnetic islands and the interpretation of sawtooth instabilities in Heliotron E. The treatment of particle orbits in Chapter 6 includes a derivation of drift equations, a discussion of the characteristics of trapped particle confinement in a heliotron and one of the Monte Carlo method for studying transport phenomena. A good treatment of neoclassical transport in a stellarator, with emphasis on the relation between parallel viscosity driven fluxes and bootstrap current, is given in Chapter 7. This is the best treatment I have found, outside of the original references, but it is still demanding. In addition, a radial electric field is introduced into the energy transport equations. The treatment of heating and confinement of heliotron plasmas in Chapter 8 is a good combination of providing results from experiments on the Heliotron E and DR heliotrons and the ATF and CHS stellarators and showing how theoretical interpretation is formulated. The discussions of ray tracing and energy absorption for both ECRH and ICRF heating techniques, as well as a treatment of neutral beam injection, are very clear. Measurements of bootstrap current and plasma rotation, as well as the density limits associated with pellet injection, are discussed. The chapter ends with a discussion of what may be the author's favourite topic, pressure gradient driven turbulence, in which he describes mixing length and scale invariance techniques. Finally, a discussion of the characteristics of a steady state fusion reactor, including a treatment of the containment, slowing down and energy transfer of the alpha particles, one of the toroidal Alfvén modes driven by these particles and some physics of divertors are given in Chapter 9.

A reviewer is usually expected to find some faults. I had no problem in finding one as soon as I received the book: indeed, I did not like its title. I have always maintained that Lyman Spitzer defined a stellarator as any toroidal device in which the rotational transform is generated by coils outside the plasma, either through imposition of a helical magnetic axis as in a figure-8 stellarator or a heliac, or through the generation of helical magnetic fields, as in a classical stellarator, a torsatron or a quasi-helical stellarator such as W7-X. The author notes that the heliotron (as it was invented by Uo in Japan) is the same as the torsatron (first proposed by Gourdon and his colleagues in Europe) in his introduction, but cannot bring himself to ignore Uo's desire to maintain a distinction between stellarators and heliotrons. Enough typographical errors are present to make one have to be careful before relying on the book for specific formulas. Nevertheless, it will prove to be a useful reference.

I have always respected the author for the quality of students he produces. He provides a list of some of them in the preface, which justifies this opinion. These students are a good demonstration of the usefulness of this book.