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.

Highly peaked density and pressure profiles in a new operating regime have been observed on the Tokamak Fusion Test Reactor (TFTR). The qprofile has a region of reversed magnetic shear extending from the magnetic axis to r / u-0.3-0.4. The central electron density rises from 0.45 x lo2' m-3 to nearly 1.2 x lo2' m-' during neutral beam injection. The electron particle diffusivity drops precipitously in the plasma core with the onset of the improved confinement mode and can be reduced by a factor of N 50 to near the neoclassical particle diffusivity level.

A detailed comparison is made between the tearing-type modes observed in TFTR supershot plasmas and the nonlinear, neoclassical pressure-gradient -driven tearing mode theory. Good agreement is found on the nonlinear evolution of single helicity magnetic islands (m/n = 3/2, 4/3, or 5/4, where m and n are the poloidal and toroidal mode numbers, respectively). The saturation of these neoclassical tearingtype modes requires 6' ( 0 (where 5' is the well-known parameter for classical current-driven tearing instability), which is also consistent with the numerical calculation using the experimental data.PACS numbers: 52.55. Fa, 52.30.Jb, 52.35.Py, Understanding the tearing-type MHD (magnetohydrodynamic) instabilities observed in TFTR neutral-beam (NB) heated supershot [1] plasmas has long been a challenge for plasma theory. These modes typically have low frequency ( f (50kHz) and low mode numbers (m/n = 3/2, 4/3, and 5/4). The m/n = 2/1 modes are not usually seen in the high-performance supershot plasmas. The important effects of these MHD modes on plasma performance have been discussed in Ref. [2]. It is found that when these modes are large they can cause a strong deterioration in plasma performance [2] as measured by the DD or DT neutron rate, plasma-stored energy, energy confinement time, etc. Considerable effort has been expended on the theoretical interpretation and numerical simulation of these modes. These works have been mostly based upon the classical current-driven tearing mode theory [3,4]. However, the results have been unsatisfactory [5,6]. In this Letter, we compare the experimental results with a relatively new theory, the neoclassical pressure-gradient-(7'p) driven tearing mode theory [7,8]. The results are found to be very encouraging.The evolution of two typical tearing-type modes in the high power NB heated, high P (plasma pressure/magnetic field pressure) supershot plasmas is shown in Fig. 1.Discharge A developed an m/n = 3/2 mode. Discharge B developed an m/n = 4/3 mode. Detailed analyses of the MHD modes and their deterioration effect on plasma transport [see Fig.

Models are developed for estimating the effects of macroscopic phenomena in tokamaks (sawteeth, Mirnov oscillations, edge localized modes (ELMs), etc.) on plasma global energy confinement. The analysis is based on a recently developed formalism for determining the incremental energy confinement time τinc from a local transport model. The macroscopic phenomena are assumed to influence the plasma only in the regions where they occur, without changing the heat diffusivity elsewhere in the plasma. General expressions are presented in terms of a magnetic flux surface label (ρ). Simplified formulas for the effects are also given for a cylindrical geometry. For the Mirnov oscillation case (m/n = 2/1 or 3/1 tearing modes), two models (for ‘belt’ and island influenced regions) are investigated and compared. When a number of macroscopic phenomena are present simultaneously (but not overlapping) their net effect is shown to be a sum of the individual effects. Finally, for time dependent phenomena such as sawteeth and ELMs, appropriate time averages of their net effects are developed.

After many years of fusion research, the conditions needed for a D–T fusion reactor have been approached on the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. For the first time the unique phenomena present in a D–T plasma are now being studied in a laboratory plasma. The first magnetic fusion experiments to study plasmas using nearly equal concentrations of deuterium and tritium have been carried out on TFTR. At present the maximum fusion power of 10.7 MW, using 39.5 MW of neutral-beam heating, in a supershot discharge and 6.7 MW in a high-βp discharge following a current rampdown. The fusion power density in a core of the plasma is ≊2.8 MW m−3, exceeding that expected in the International Thermonuclear Experimental Reactor (ITER) [Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239] at 1500 MW total fusion power. The energy confinement time, τE, is observed to increase in D–T, relative to D plasmas, by 20% and the ni(0) Ti(0) τE product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter-H-mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high-βp discharges. Ion cyclotron range of frequencies (ICRF) heating of a D–T plasma, using the second harmonic of tritium, has been demonstrated. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP [Nucl. Fusion 34, 1247 (1994)] simulations. Initial measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from He gas puffing experiments. The loss of alpha particles to a detector at the bottom of the vessel is well described by the first-orbit loss mechanism. No loss due to alpha-particle-driven instabilities has yet been observed. D–T experiments on TFTR will continue to explore the assumptions of the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor.

Off-axis sawteeth are often observed in reversed magnetic shear plasmas when the minimum safety factor q is near or below 2. Fluctuations with m/n = 2/1 (m and n are the poloidal and toroidal mode numbers) appear before and after the crashes. Detailed comparison has been made between the measured Te profile evolution during the crash and a nonlinear numerical magnetohydrodynamics (MHD) simulation. The good agreement between the observation and simulation indicates that the off-axis sawteeth are due to a dou ble-tearing magnetic reconnection process.

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The toroidal Alfvén eigenmodes (TAE) are calculated to be stable in the presently obtained deuterium–tritium plasmas in the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Res. 26, 11 (1984)]. However, the core localized TAE mode can exist and is less stable than the global TAE modes. The beam ion Landau damping and the radiative damping are the two main stabilizing mechanisms in the present calculation. In future deuterium–tritium experiments, the alpha-driven TAE modes are predicted to occur with a weakly reversed shear profile.