The time scales for sawtooth repetition and heat pulse propagation are much longer (10's of msec) in the large tokamak TFTR than in previous, smaller tokamaks. This extended time scale coupled with more detailed diagnostics has led us to revisit the analysis of the heat pulse propagation as a method to determine the electron heat diffusivity, x e) in the plasma. A combination of analytic and computer solutions of the electron heat diffusion equation are used to clarify previous work and develop new methods for determining x e-Direct comparison of the predicted heat pulses with soft X-ray and ECE data indicates that the space-time evolution is diffusive. However, the x e determined from heat pulse propagation usually exceeds that determined from background plasma power balance considerations by a factor ranging from 2 to 10, Some hypotheses for resolving this discrepancy are discussed.

Recent calculations have shown that when external momentum sources and plasma rotation are included in the neoclassical theory, the standard results for impurity transport can be strongly altered. Under appropriate conditions, inward convection is reduced by co-injection and enhanced by counter-injection. In order to examine the theoretical predictions, several observations of impurity transport have been made in the ISX-B tokamak during neutral-beam injection for comparison with the transport seen with Ohmic heating alone. Both intrinsic contaminants and deliberately introduced test impurities display a behaviour that is in qualitative agreement with the predicted beam-driven effects. These correlations are particularly noticeable when the comparisons are made for deuterium where the impurity transport in the Ohmically heated discharges exhibits neoclassical-like characteristics, i.e. accumulation and long confinement times. Similar but smaller effects are observed in beam-heated hydrogen discharges; neoclassical-like behaviour is not seen in Ohmically heated hydrogen sequences. Emphasis has been placed on measuring toroidal plasma rotation, and semiquantitative comparisons with the theories of beam-induced impurity transport have been made. It is possible that radial electric fields other than those associated with momentum transfer and increased anomalous processes during injection could also play a role.

Neutral-beam injection of up to 2.5 MW into plasmas in the ISX-B tokamak (R0 = 0.93 m, a = 0.27 m, BT = 0.9–1.5 T, Ip = 70–210 kA, n̄e = 2.5–10×1013 cm−3) has created plasmas with volume-averaged beta of up to ∼ 2.5%, peak beta values of up to ∼ 9%, and root-mean-square beta values of up to ∼ 3.5%. Energy confinement time is observed to decrease by about a factor of two as beam power goes from 0 to 2.5 MW; the decrease is caused predominantly by the electron confinement time falling below the predictions of ‘Alcator scaling’ by a factor of 3–4 at high beam power. An empirical relationship of the form fits our measurements over a wide range of plasma parameters. The function f(Pb), where Pb is the beam power, is linear for Pb ≤ 1.2 MW but tends to saturate for 1.2 MW ≤ Pb ≤ 2.5 MW. Although the equilibria attained in ISX-B are predicted to be above the threshold for the ideal magnetohydrodynamic (MHD) ballooning instability, no evidence of these modes is observed.

The transport effects induced by resistive ballooning modes are estimated from a theory, and are found to be mainly thermal electron conduction losses. An expression for electron thermal diffusivity x e is derived. The theoretical predictions agree well with experimental values of x e obtained from power balance for the ISX-J3 plasmas at high poloidal beta.PACS numbers: 52.25.Fi, 52.30. + r, 52.55.Gb A deterioration in confinement is observed in ISX-B tokamak experiments 1 ' 2 with high neutral injection power at high poloidal plasma beta (p p ). From a theoretical point of view, resistive pressure-driven ballooning modes are a possible cause of this deterioration, linked to high-^ plasmas. There have been several linear studies 3 "" 5 of these instabilities in the past. Recently, numerical and analytical work has been done 6 to understand the linear and nonlinear properties of resistive ballooning modes in the framework of the incompressible resistive magnetohydrodynamic (MHD) equations. Below and near the critical j3 for ideal instabilities (j3^1), the fastest growing mode, with a given torodial mode number n, has a growth ratewhere S is the ratio of resistive time r R to poloidal AlfvSn time r hp , (3 0 = 2p{0) \±JB T 2 , p is the pressure, q is the safety factor, B T is the toroidal magnetic field, e is the inverse aspect ratio, L p =[(-dp/dp)/p{0)]-\ and p (with 0 ^p ^1) is a flux surface label. These modes are extended greatly along magnetic field lines, with a characteristic width given by -7(P 8 S)]-I/4 , w. ••WS*n*y n T hpwhere S=[p(dq/dp)/q] and a is the minor radius. Their linear properties are similar to resistive interchanges. 7 With use of the nonlinear resistive MHD equation in the ballooning representation, a calculation of the renormalized response has been performed. 6 This calculation shows that the dominant nonlinear effect is due to the pressure-convective nonlinearity, which reduces the turbulent pressure response p to <£, the electrostatic perturbation. This causes a reduction of the interchange destabilizing term, without changing the basic structure of the eigenfunction. A physical interpretation is that the resistive ballooning modes saturate when the pressure fluctuation mixes dp/dp over the radial extent A of each poloidal subharmonic; thus, p-Adp/dp. Since the pressure is mainly convected, p ~inq" 1 ) 2 ' Details on the stability theory of these modes will be given elsewhere. In this Letter we limit ourselves to the consideration of the induced transport effects and consequences for confinement in ISX--B. We consider two main effects of the saturated modes, the diffusion induced by the convective nonlinearity and the anomalous electron conduction induced by the magnetic field-line stochastization.The radial diffusion induced by the convective term is given by D*(\(n'q/p)y nf \ 2 /y n _ n ,) = y n A 2 .Using the reciprocity of 3; (ballooning) space and position s...

The ISX-A (Impurity Study Experiment) tokamak operated with major radius R =92 cm, minor radius a =26 cm, and relatively low toroidal magnetic field B T < 15 kG. 1 * 2 Only Ohmic heating was appliedo Studies of plasma confinement in this device yielded unusually favorable results in comparison with empirical scaling formulas., For example, the gross-energy-confinement times, r E = !&[/(n e T e +W|Ti)dv]/Po m E. 9 exceeded the values expected from the scaling of Jassby et at? by factors of 1-3 (lo6 average) and were larger than the values predicted by the Hugill-Sheffield formula 4 [with scaling l-l] by factors of 1.5-4.5 (3.1 average). At line-average densities (n e ) above 10 13 cm" 3 , the ISX-.A data are closest to the scaling proposed by Mirnov, 5 r E = (3 x 1(T 9 )a(cm) x/(A)« e l72 sec (n e is given in units of 10 13 cm" 3 ), although they still exceed the expectations by an average value of 1.2. Also, the maximum value of n e achieved before a major disruption occurred was 7xl0 13 cm" 3 , a factor almost 4.5 times larger than that anticipated by B T /R 0 scaling. 6 The largest values of toroidal beta, P T (0) equal to No. GA-A14133, 1976 (to be published); see also Ref" 5, above. 7 G. R. Hopkins and John M. Rawls, Nucl. Technol. 36, 171 (1977), and references contained therein. 8 P