A model for sawtooth oscillations in tokamak experiments is outlined. A threshold criterion for the onset of internal kink modes and a prescription for the relaxed profiles immediately after the sawtooth crash have been implemented in a transport code that evolves the relevant plasma parameters. In this paper, applications of this model to the prediction of the sawtooth period and amplitude in projected ITER discharges are discussed. It is found that sawteeth can be stabilized transiently by the fusion alpha particles in ITER for periods that are long on the energy confinement timescale (τ E ≈ 5 s). The sawtooth period depends on the amount of reconnected flux at the preceding sawtooth crash. When Kadomtsev's full reconnection model is used, the period can exceed 100 s. The sawtooth mixing radius following long duration sawtooth ramps can easily exceed half the plasma minor radius, raising questions about the desirability of transient sawtooth suppression.

The maximum normalized beta achieved in long-pulse tokamak discharges at low collisionality falls significantly below both that observed in short pulse discharges and that predicted by the ideal MHD theory. Recent long-pulse experiments, in particular those simulating the International Thermonuclear Experimental Reactor ͑ITER͒ ͓M. Rosenbluth et al., Plasma Physics and Controlled Nuclear Fusion ͑International Atomic Energy Agency, Vienna, 1995͒, Vol. 2, p. 517͔ scenarios with low collisionality e * , are often limited by low-m/n nonideal magnetohydrodynamic ͑MHD͒ modes. The effect of saturated MHD modes is a reduction of the confinement time by 10%-20%, depending on the island size and location, and can lead to a disruption. Recent theories on neoclassical destabilization of tearing modes, including the effects of a perturbed helical bootstrap current, are successful in explaining the qualitative behavior of the resistive modes and recent results are consistent with the size of the saturated islands. Also, a strong correlation is observed between the onset of these low-m/n modes with sawteeth, edge localized modes ͑ELM͒, or fishbone events, consistent with the seed island required by the theory. We will focus on a quantitative comparison between both the conventional resistive and neoclassical theories, and the experimental results of several machines, which have all observed these low-m/n nonideal modes. This enables us to single out the key issues in projecting the long-pulse beta limits of ITER-size tokamaks and also to discuss possible plasma control methods that can increase the soft ␤ limit, decrease the seed perturbations, and/or diminish the effects on confinement.

Analysis of MHD activity in pellet enhanced performance (PEP) pulses is used to determine the position of rational surfaces associated with the safety factor q. This gives evidence for negative shear in the central region of the plasma. The plasma equilibrium calculated from the measured q values yields a Shafranov shift in reasonable agreement with the experimental value of about 0.2 m. The corresponding current profile has two large off-axis maxima in agreement with the bootstrap current calculated from the electron temperature and density measurements. A transport simulation shows that the bootstrap current is driven by the steep density gradient, which results from improved confinement in the plasma core where the shear is negative. During the PEP phase (m,n)=(1,1) fast MHD events are correlated with collapses in the neutron rate. The dominant mode preceding these events usually is n=3, whereas the mode following them is dominantly n=2. Toroidal linear MHD stability calculations assuming a non-monotonic q-profile with an off-axis minimum decreasing from above 1 to below 1 describe this sequence of modes (n=3,1,2), but always give a larger growth rate for the n=1 mode than for the n=2 mode. This large growth rate is due to the high central poloidal beta of 1.5 observed in the PEP pulses. Finally, a rotating (m,n)=(1,1) mode is observed as a hot spot with a ballooning character on the low field side. The hot spot has some of the properties of a 'hot' island consistent with the presence of a region of negative shear

On the basis of several confinement scaling relations, the prediction has been made that tokamak performance, expressed as the volume averaged fusion triple product (nT) tau , should increase as the plasma is elongated by reducing the horizontal minor radius from the outer (low field) boundary with fixed heating power, safety factor and electron density. Experiments in DIII-D confirm this prediction, with performance enhancements of up to 40% observed as elongation is increased by 15%. It is recognized, of course, that such experiments do not constitute a simple test of elongation scaling, since the change to elongation was rather small, and other parameters, such as toroidal field, are allowed to change. Nevertheless, this `engineering test' of the effects of such small changes indicates possible advantages to the slightly modified shape. This enhancement appears most visibly as increased ion and electron temperatures. A surprising feature of the high elongation plasmas is the existence of a VH-mode-like `spin-up', where the high elongation plasmas tend to rotate with velocities as high as twice those in the low elongation plasmas. The resulting region of enhanced toroidal rotation gradient is associated with significant reductions in transport

Near breakeven conditions have been attained in the JET tokamak [Fusion Technol. 11, 13 ( 1987) 1, with beryllium as the first-wall material. A fusion triple product (n,r, Ti ) of 8-9 x 10" m -3 set keV has been reached (within a factor of 8 of that required in a fusion reactor). However, this has only been achieved transiently. At high heating powers, an influx of impurities still limits the achievement of better performance and steady-state operation. In parallel, an improved quantitative understanding of fusion plasmas has emerged from the development of a particular plasma model. Good quantitative agreement is obtained between the model and JET data. The main predictions are also consistent with statistical scaling laws. With such a model, a predictive capability begins to emerge to define the parameters and operating conditions of a DEMO, including impurity levels. Present experimental results and model predictions suggest that impurity dilution is a major threat to a reactor. A divertor concept must be developed further to ensure impurity control before a DEMO can be constructed. A New Phase for JET is planned in which an axisymmetric pumped divertor configuration will be used to address the problems of impurity control, plasma fueling, and helium ash exhaust. It should demonstrate a concept of impurity control and the operational domain for such a device. A single Next Step facility (ITER) is a high risk strategy in terms of physics, technology, and management, since it does not provide a sufficiently sound foundation for a DEMO. A Next Step program is proposed, which could comprise several complementary facilities, each optimized with respect to specific clear objectives. In a minimum program, there could be two Next Step tokamaks, and a Materials Test Facility. Such a program would allow division of effort and sharing of risk across the various scientific and technical problems, permit cross comparison, and ensure continuity of results. rt could even be accomplished without a significant increase in world funding.