An efficient method is given to reconstruct the current profile parameters, the plasma shape, and a current profile consistent with the magnetohydrodynamic equilibrium constraint from external magnetic measurements, based on a Picard iteration approach which approximately conserves the measurements. Computational efforts are reduced by parametrizing the current profile linearly in terms of a number of physical parameters. Results of detailed comparative calculations and a sensitivity study are described. Illustrative calculations to reconstruct the current profiles and plasma shapes in ohmically and auxiliarily heated Doublet III plasmas are given which show many interesting features of the current profiles.

Integral relations for the average poloidal beta J3 p and the plasma internal inductance 8j are derived from the magnetohydrodynamic (MHD) equilibrium equation for an axisymmetric torus. The volumedependent parameters that appear depend only weakly on the actual current density distribution inside the plasma and can be evaluated approximately, given the plasma shape and boundary poloidal magnetic field. In practice, these can be accurately and efficiently obtained for both diverted and limited plasmas from measured external poloidal magnetic field and flux values by approximating the plasma current distribution using a few filaments or distributed sources. For a tokamak plasma with a non-circular cross-section of sufficient elongation, J3 p and 8j can then be approximately determined separately. This is demonstrated for analytic equilibria of known shape as well as for actual Doublet III (D-III) plasmas for which /3 p and Z{ have been determined by using other methods. Results of a sensitivity study are described.

The occurrence of giant edge localized modes (ELMs) in DIII-D has previously been correlated with the violation of the ballooning stability criterion at the plasma edge. These results are extended in the paper. It is demonstrated theoretically that flux surfaces near the separatrix of properly elongated and triangulated plasmas may be moved into the connection region between the first and second stability regions for ideal MHD ballooning modes, when q is high and the shear is low near the plasma surface. The edge flux surfaces are then predicted to have no limit to the sustainable pressure gradient. Experimentally, giant ELMs disappear in these highly shaped plasmas. However, the edge pressure gradient does not increase and ‘grassy’ ELM behaviour appears instead. These results lend further support to the hypothesis that giant ELMs in DIII-D are triggered by ideal ballooning mode instabilities, but they indicate that giant ELM and grassy ELM behaviour may arise from somewhat different mechanisms.

A Poynting's Theorem method is used for evaluating the volt-second consumption in a tokamak discharge. The method accurately identifies the inductive and resistive components of the volt-second consumption, and allows both quantities to be determined from magnetic measurements made outside the plasma. Only simple computational techniques are required. Application of the method to typical Doublet III nearcircular plasmas (R = 1.43 m, a = 0.44 m, b/a = 1.2) indicates that the flux at the plasma surface required to establish the current flat-top is 2.0 ± 0.2 V-s/MA. Approximately 40% of this flux is consumed in resistive dissipation. This division between resistive and inductive flux differs significantly from that obtained using an alternative data analysis method in which the resistive loss is evaluated at the plasma axis. The reasons for the difference are discussed.

The dependence of plasma energy confinement on minor radius, density and plasma current is described for Ohmically heated near-circular plasmas in Doublet III. A wide range of parameters is used for the study of scaling laws; the plasma minor radius defined by the flux surface in contact with limiter is varied by a factor of 2 (a = 44, 32 and 23 cm) , the line average plasma density, n̄e, is varied by a factor of 20 from 0.5 to 10 × 1013 cm−3 (n̄e R0/BT = 0.3 to 6 × 1014 cm−2·kG−1) and the plasma current, I, is varied by a factor of 6 from 120 to 718 kA. The range of the limiter safety factor, qL, is from 2 to 12. – For plasmas with a = 23 and 32 cm, the scaling law at low n̄e for the gross electron energy confinement time can be written as (s, cm) where qc = 2πa2BT/μ0IR0. For the 44-cm plasmas, is about 1.8 times less than predicted by this scaling, possibly owing to the change in limiter configuration and small plasma-wall separation and/or the aspect ratio change. At high n̄e, saturates and in many cases decreases with n̄e but increases with I in a classical-like manner. The dependence of on a is considerably weakened. The confinement behaviour can be explained by taking an ion thermal conductivity 2 to 7 times that given by Hinton-Hazeltine's neoclassical theory with a lumped-Zeff impurity model. Within this range the enhancement factor increases with a or a/R0. The electron thermal conductivity evaluated at half-temperature radius where most of the thermal insulation occurs sharply increases with average current density within that radius, but does not depend on a within the uncertainties of the measurements.

A clear correlation between incoherent magnetic fluctuations and transport in the outer region of the plasma was observed in a set of Doublet III beam-heated discharges which experienced repetitive transitions between a poor-confinement phase and an improved-confinement phase. The fluctuations and associated transport are consistent with a model based on an assembly of saturated microtearing modes.PACS numbers: 52.55. Fa, 52.25.Fi, Observations of improved energy confinement ("//mode" discharges) in tokamaks 1 " 3 suggest that edge confinement plays a critical role in the determination of global energy confinement, i.e., longer edge confinement leads to longer core confinement. Plausible theoretical models have been advanced to explain this relationship, 4 ' 5 and acceptance of this viewpoint shifts the problem of confining a fusion plasma to one of understanding and improving the confinement at the plasma edge.To this end, this Letter reports observations from the Doublet III tokamak wherein the level of magnetic turbulence is directly correlated with (and thus may be responsible for) edge transport. The turbulence is low frequency (5-50 kHz) and broadband, 6 and increases with P p , as previously observed on the ISX-B tokamak. 7 The correlation here is established more directly than in previous experiments 6 " 10 because the observed incoherent magnetic-fluctuation amplitude abruptly changes simultaneously with transitions into and out of the H mode. A model based on microtearing modes will be shown to be consistent with the observed turbulence with regard to the spatial amplitude dependence, frequencies, magnitude of heat transport, and the existence of a temperature threshold to the H mode as observed on the ASDEX tokamak. * Magnetic fluctuations are detected by two arrays (poloidal and toroidal) of Mirnov coils that sense the poloidal magnetic field. They are located just inside the Doublet III vacuum vessel [see Fig. 1(a)] which acts as a perfectly conducting shell in the frequency range of interest (f>2 kHz). Each coil is inside a stainless-steel shield that excludes electrostatic pickup while reducing electromagnetic signals by only 10% at 25 kHz. The highest measurable frequency, 50 kHz, is determined by the maximum data-acquisition rate.In Doublet III (B T <2A T, I p < 1 MA, R = 1A4 m, a =0.4 m), as with other tokamaks, it is found that as neutral-beam heating power is increased in discharges defined by a material limiter, the global energyconfinement time ?E decreases (L mode). 1 ' 11 If, however, the plasma is well diverted, the confinement deterioration is more modest, and XE is typically a factor of 2 higher than limiter discharges at high beam-heating levels. In the Doublet III poloidal divertor configuration, neutral-particle sources are localized in the divertor region, whereas a limited discharge exhibits larger sources, mainly near the limiter. Marginally diverted discharges are intermediate, with recycling at both limiter and divertor regions, and are observed to undergo repetitive transitions...

The dependence of the ideal ballooning β limit on aspect ratio, A, and elongation κ is systematically explored for nearly 100% bootstrap current driven tokamak equilibria in a wide range of the shape parameters (A = 1.2–7.0, κ = 1.5–6.0 with triangularity δ = 0.5). The critical βN is shown to be optimal at κ = 3.0–4.0 for all A studied and increases as A decreases with a dependence close to A−0.5. The results obtained can be used as a theoretical basis for the choice of optimum aspect ratio and elongation equilibria for future high performance steady-state tokamaks.

The physics of enhanced confinement regimes in tokamaks is reviewed and some directions for further enhancements are assessed. The H-mode confinement regime is examined. A number of other observations of enhanced confinement, having in common peaked density profiles, are compared to the theory of ion temperature gradient modes. Two schemes of promise in enhancing confinement, second stability and control of electric fields, are discussed. The contributions of alternate concepts to understanding tokamak transport are described.