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.

Recent experiments in the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] show that the resistive wall mode (RWM) can be stabilized by smaller values of plasma rotation than previously reported. Stable discharges have been observed with beta up to 1.4 times the no-wall kink stability limit and ion rotation velocity (measured from CVI emission) less than 0.3% of the Alfvén speed at all integer rational surfaces, in contrast with previous DIII-D experiments that indicated critical values of 0.7%–2.5% of the local Alfvén speed. Preliminary stability calculations for these discharges, using ideal magnetohydrodynamics with a drift-kinetic dissipation model, are consistent with the new experimental results. A key feature of these experiments is that slow plasma rotation was achieved by reducing the neutral beam torque. Earlier experiments with strong neutral beam torque used “magnetic braking” by applied magnetic perturbations to slow the rotation, and resonant effects of these perturbations may have led to a larger effective rotation threshold. In addition, the edge rotation profile may have a critical role in determining the RWM stability of these low-torque plasmas.

Seed magnetic island formation due to a dynamically growing external source in toroidal confinement devices is modeled as an initial value, forced reconnection problem. For an external source whose amplitude grows on a time scale quickly compared to the Sweet-Parker time of resistive magnetohydrodynamics, the induced reconnection is characterized by a current sheet and a reconnected flux amplitude that lags in time the source amplitude. This suggests that neoclassical tearing modes, whose excitation requires a seed magnetic island, are more difficult to cause in high Lundquist number plasmas.

The requirements of the DIII-D physics program have led to the development of many operational control results with direct relevance to ITER. These include new algorithms for robust and sustained stabilization of neoclassical tearing modes (NTM) with electron cyclotron current drive (ECCD), model-based controllers for stabilization of the resistive wall mode (RWM) in the presence of ELMs, coupled linear-nonlinear algorithms to provide good dynamic axisymmetric control while avoiding coil current limits, and adaptation of the DIII-D Plasma Control System (PCS) to operate next-generation superconducting tokamaks. Development of integrated plasma control, a systematic approach to model-based design and controller verification, has enabled successful experimental application of high reliability control algorithms requiring a minimum of machine operations time for testing and tuning. The DIII-D PCS hardware and software and its versions adapted for other devices can be connected to integrated plasma control simulations to confirm control function prior to experimental use. This capability has been important in control system implementation for tokamaks under construction and is expected to be critical for ITER.