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.

An efficient method is given for self-consistent reconstruction of the tokamak current profiles and their associated magnetic topology using the magnetohydrodynamic (MHD) equilibrium constraint from external magnetic measurements, kinetic profile measurements, internal poloidal magnetic field measurements, and topological information from soft X-ray (SXR) measurements. Illustrative examples for beam heated H-mode divertor discharges in the DIII-D tokamak are presented, using the experimentally measured kinetic profile information and external magnetic data from the existing diagnostics. Comparative reconstructions of the current profile using various combinations of diagnostics are given. Also presented is an alternative magnetic analysis method in which the MHD equilibrium is reconstructed using external magnetic data and a constraint on the edge pressure gradient. The results of a sensitivity study are given which show that the axial safety factor q(0) can be more accurately determined when additional information from internal poloidal magnetic measurements is used in conjunction with the external magnetic, kinetic and SXR topological data.

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There is considerable interest in the development of low voltage startup scenarios for large tokamaks since it is proposed that in ITER the electric field which will be applied for ionization and plasma current ramp-up will be limited to values of E ≤ 0.3 V/m. Studies of low voltage startup have been carried out in DIII-D with and without electron cyclotron preionization and preheating. Successful Ohmic startup has been achieved with E ∼ 0.25 V/m by paying careful attention to error fields and prefill pressure, while electron cyclotron heating (ECH) assisted startup with E ∼ 0.15 V/m has been demonstrated. ECH assisted startup gives improved reliability at such low electric fields and permits operation over an extended range of prefill pressures and error magnetic fields. Using ECH, startup at E = 0.3 V/m with |B⊥| > 50 G over most of the vessel cross-section has been demonstrated. Such an error field represents an increase by more than a factor of two over the highest value for which Ohmic startup was achieved at the same electric field. During low voltage Ohmic startup with extreme values of prefill pressure and/or error magnetic fields, excessive breakdown delays are observed. The experimental data agree well with theoretical predictions based on the Townsend avalanche theory. ECH assisted startup is always prompt. The primary effect of ECH during the plasma current ramp-up is a decrease of the resistive component of the loop voltage Vrcs. A significant reduction (∼30%) in Vres is achieved for low ECH powers (PRF ∼ 300-400 kW), but a further large increase in PRF results in only a modest additional decrease in Vres. ECH was not applied over the whole ramp-up phase in these experiments and produced a reduction in volt-second consumption up to the current flat-top (Ip ∼ 1 MA) of ⪅ 10%. These experiments confirm that the low electric fields specified in the ITER design are acceptable and demonstrate the substantial benefits which accrue from the use of ECH assisted startup.

It is shown that the theoretical predictions and experimental observations of toroidicity-induced AlfvCn eigenmodes (TAE's) are now in good agreement, with particularly detailed agreement in the mode frequencies. Calculations of the driving and damping rates predict the importance of continuum damping for low toroidal mode numbers and this is confirmed experimentally. However, theoretical calculations in finite+?, shaped discharges predict the existence of other global AlfvCn modes, in particular the ellipticity-induced AlfvCn eigenmode (EAE) and a new mode, the beta-induced Alfvtn eigenmode (BAE). The BAE mode is calculated to be in or below the same frequency range as the TAE mode and may contribute to the experimental observations at high fl. Experimental evidence and complementary analyses are presented confirming the presence of the EAE mode at higher frequencies.