SUMMARY OF THE CORE FLUCTUATIONS AND TRANSPORT
March, 18-21 1998 TTF Meeting
Ed Synakowski


In Atlanta this year, the Transport Task Force met for the eleventh time. The core transport physics discussions were quite active. This summary emphasizes the core transport sessions, and I distilled it in the hopes that it might be useful and of interest to those who could not attend the meeting, or to those who could not attend Saturdays summary. I also include some accounts of core-transport-related work that occurred in other sessions that was described to me, but which I did not see. I don’t pretend to cover all topics (I could not see all of the talks), but I have tried to identify themes that represented where much of the energy of the meeting was focused.

In addition to the physics issues, we also had a good discussion pertaining to needs and directions. Here, I give a few words from that discussion regarding diagnostic needs. We also talked about the transport community’s sense of what would make a viable, worthwhile, and stimulating fusion research program in this new era of rethinking our directions and priorities. That will be described in another message from Martin that outlines the meeting as a whole.

Overarching themes

It is impossible (indeed undesirable) to cleanly separate much of the theory work from the experimental, as many of the experimental talks made laudably explicit theoretical comparisons. A few dominant ex perimental/theoretical themes did emerge:

1. Transport barriers and dynamics

2. Electron thermal transport results from various machines differed, as did the theoretical approaches for addressing them:

3. Extending the picture of ExB shear

In addition, there were cautionary tales. For example, newly developed computational tools are yielding insight into the limits of commonly made assumptions in instability theory.

Transport barriers and dynamics

In the invited session, David Newman presented an overview of a dynamical model that self-consistently evolves the plasma profiles, transport, and ExB shear stabilization effects. This model reproduces many observed experimental trends. With externally supplied information regarding pa rticle and heat sources and radial profiles of the form of microinstability drives, a wide array of observed barrier dynamics are found in the modeling, include bifurcations, barrier propagation, hysteresis, bursting core fluctuations, and differences in forward and backward transition time scales. Future work includes expanding the model to self-consistently include momentum transport and rotation, and to investigate the possibility that Reynolds stress-induced flows might be responsible for the core transport bifurcations observed in some TFTR ERS plasmas.

Many of the experimental discussions were centered around barrier dynamics and characterization. Max Austin presented data indicating that core barrier formation in some low current DIII-D reverse shear plasmas that were intended for ECH studies show a correlation between barrier formation times and low-order rational q values of qmin. Similarities in this behavior and phenomena observed on the RTP tokamak with ECH heating were obse rved. Max's talk touched on issues that were also discussed by Ed Synakowski and Keith Burrell. Synakowski presented an overview of an experiment performed in a collaboration between PPPL and DIII-D that aimed at obtaining steady-state plasmas with core barriers. The route to steady- state used plasmas with low current and low density. Step-wise barrier formation was found, like in Austin’s experiment, except that here the q profile was monotonic. Nevertheless, the dynamics of these plasmas was r eminiscent of a class of low power TFTR plasmas with reverse shear: barrier formation that is seen most clearly in the ion temperature (unlike the strong density rise found in high power TFTR ERS plasmas); reproducibility in timing of the barrier formation from shot to shot. The monotonic q profiles in the DIII-D plasmas indicates that, while shear reversal may facilitate core barrier formation, it is not a necessary component of the picture. Ultimately, these plasmas did achieve steady-state in a ll measured profiles, including the q profile.

Keith Burrell's data indicated that, while the reproducibility of the step-wise barrier formation suggests that the current evolution may play an important role in barrier formation, identifying all of the barrier steps with a picture as simple as a low order rational q crossing is not adequate. Nevertheless, in the plasmas with monotonic q profiles and core barriers discussed above, Burrell identified a fascinating correlation between the emergence o f q(0) = 2 in the plasma and a step-wise steepening of the ion temperature profile (note that on TFTR, the barrier formation in low power reverse shear plasmas takes place when qmin, which is off-axis, = 2). The top of the ion temperature profile, and not the footpoint, was correlated with the subsequent location of the q=2 surface.

Perhaps related to the experiments discussed above, Guiding Wang discussed results from a from probe measurements on a small tokamak in China that indicate that fluctuation-driven fluxes can have spatial structures that are qualitatively consistent with a theoretical picture put forward by Carreras. In this picture, low order rational q surfaces are expected to have a more vigorous microinstability activity. Speculation can be made about the role of such surfaces in interrupting barrier expansion until the local shear builds up to the point that the local instability drive can be overcome. In this sense, perhaps these measurements of Wang’s are related to the stepwise barrier evolution observed on DIII-D. George McKee used the low density plasmas with barrier formation on DIII-D to make measurements of fluctuations deeper on the plasma core than had been possible previously. The BES system measurements indicate that fluctuation amplitudes were greatly reduced across the step-wise barrier formation. In addition, the poloidal array measurements indicate that the group velocity of the fluctuations develops a shear layer upon barrier formation: a direct correlation was found between reduced turbulence, increased poloidal velocity shear, and increased Ti. Preliminary work has begun in assessing the viability of separating the measured group velocity from the ExB flow velocity in an effort to identify the direction of propagation in the plasma frame of the fluctuations.

Wayne Houlberg presented results from particle transport experiments on DIII-D performed by Mickey Wade. The essential point of the discussion was that in enhanced core confine ment regimes on DIII-D (VH-mode and NCS), many aspects of observed impurity behavior is consistent with expectations from neoclassical theory. These include Z-dependent impurity peaking in NCS plasmas, and temperature-dependent “screening” effects in VH-Modes. Remarkable impurity behavior includes the observation of radially hollow impurity profiles in some circumstances; the location of the off-axis maximum in the impurity profiles is predicted by the NCLASS code. Future work includes a compariso n of the dynamics of the impurity profiles with those expected from neoclassical theory.

The electron thermal channel

Electron thermal transport represented another major theme in the meeting. Two invited talks focused on it. Barry Stollard presented results from DIII-D. The general observation is that electron thermal transport is found to be fairly stubborn in the presence of ion thermal transport barriers. Here, the case was made that ETG modes could account for the electron thermal transpo rt observed in NCS plasmas. The growth rates for these modes is generally much larger than E?B shearing rates encountered, and despite their large k_theta values, yield values of chi-e that are consistent with experiment. However, the shearing rates are calculated to be large enough to stabilize ITG modes. King-Lap Wong’s invited talk focused on the observation of a short wavelength feature in the electron thermal channel in TFTR ERS plasmas. The amplitude of this feature was correlated with gradients in the electron temperature profile in the low power (7 MW) phase of these plasmas. He argued that it was the absence of other modes in this reverse shear regime that might have made these short wavelength modes visible in these experiments.

Mike Zarnstorff presented data from other ERS plasmas. During a 14 MW steady-state period, the plasma was “jogged” several centimeters, sweeping it past an array of fixed detectors on the electron temperature diagnostic. This provided for a spatial calibration of the diagnostic, and Te measurements with spatial resolution that rivaled the detector spot size in the plasma. The resultant Te profile was found to be remarkably flat (gradients ~ 10 eV/cm), implying a lower bound for chi-e in the flat region of ~ 25 m^2/s. In the steep gradient region, chi-e was indeed reduced. The profile shape and transport coefficients suggested transport barrier “layers,” rather than “regions,” similar to those seen on JT-60U. The challenge is: what is the mode responsible for the rapid electron thermal transport? Magnetically stochastic processes are certainly suggested.

Extensions of ExB shear

The familiar picture of ExB shear stabilization was discussed in two different contexts. First, two talks discussed how this picture might account for the generation of core enhanced confinement regimes. Darin Ernst discussed the role of the electric field shear in TFTR confinement. The assumption that the local instability growth rates are balanced by the local ExB shearing rate in the plasma core reproduces many confinement trends observed in the continuum between L mode and supershot. In particular, the dependence of confinement on edge particle fueling, the energy confinement dependence on isotope observed in DT, and the local scaling of thermal ion transport with ion temperature are all predicted by this model.

Uli Stroth made a presentation of two distinct confinement regimes on W7-AS. With neutral beam heating, a “slow” bifurcation to an enhanced con finement regime has been observed. It was suggested that the bifurcation is determined by a feedback loop between the instability drive and ExB shear which is dominated by the plasma pressure. As a result of the pressure drive, the time scale for the bifurcation is a transport time scale.

The final way in which ExB shear’s landscape was expanded is in the issue of zonal flows. On this topic of short wavelength, radial m,n = 0,0 modes, no experimental data can be brought to bear on the problem as of yet. However, a large number of theorists are concentrating on the problem. It served as one of the starting points of the recent gyrofluid/gyrokinetic code calculation comparisons. The issue as I understand it is: does the plasma turbulence itself generate short radial wavelength poloidal flows that can modify expected transport rates?

The discussion took two forms, a. attempts to develop an analytic understanding of these flows and b. tests done in codes to see if the effect is important. Pat Diamond and Jason Fleischer presented analytic work aimed at understanding the origin of the flows and their impact on transport. Pat suggested that the zonal flow is analogous to a Reynolds stress-induced mean flow. With Reynolds stress, anisotropy in real space of turbulence is required to generate the mean flow. For zonal flows, anisotropy in k space is required, and the resultant flows result in a sort of diffusion in k space. Tests were performed by Mike Beer for strongly turbulent plasma s. It was argued that the tests show that turbulent damping keeps zonal flows from growing, and that the influence on transport is therefore minimal in the gyrofluid treatments. Finally, work by TS Hahm was presented that parameterized extension of his shearing rate expressions that includes the effects of these flows.

Other theory work

Finally on the theory front, Paul Terry performed tests with a nonlinear model and examined the limits of assumptions that are frequently made. The issues addressed include the validity of mixing length arguments, quasilinear flux calculations, and the assumption of the near-equality of linear growth rates and shearing rates when flow shear effects become important. Significant differences between his nonlinear calculations and what was found under the usual assumptions in all three categories was found. At the root of the problem is the fact that instability properties in the linear phase of instability growth are radically different from the non-linea r (saturated) phase.

Aaron Redd has begun a series of tests with the FULL code of Greg Rewoldt. Aaron is investigating the influence of geometry on finite ? kinetic ballooning mode transport and ITG transport. For the KBM, it was found that growth rates drop dramatically in going from circular to elongated plasmas, and the peak in the k spectrum shifts to larger k. The two combine to make for precipitous drops in gamma/k^2 for this mode in the hot plasma core. The effect of ITG modes was found to be weaker. Future work will expand the range of variation in elongation.

Wendall Horton reported results from work with with Erba and Ottaviani for testing the ITG-trapped electron mode transport formulas on 20 discharges in the ITER profile data base using the ASTRA transport code. He argued that there was no clear support for the complex parameterizations of the IFS/PPPL model over simpler formulas containing only the essentail dependences on q and R/Lt (the temperature gradient). Modeling theory was invoked to show that it is much more difficult to validate a theoretical model containing a large number of parameters than a model with a few parameters.

Finally, Bill Nevins performed a sandpile experiment by going to a fairly sophisticated sandbox, i.e. Dimits’ gyrokinetic code. By looking at the heat fluxes calculated by the code, Bill found evidence for behavior suggested by SOC (self-organized criticality) models, including flux “events” of various scales, inward and outward pr opagation of these events, and a 1/f scaling of the size of the event. This work has just started; questions pertaining to the distance of his test system from criticality, and the possible mitigating role of flow shear effects, were discussed.

Discussion

The core transport group held a discussion session on the last afternoon of the workshop. Two main issues were addressed. Keith Burrell highlighted the continuing necessity to measure fluctuating quantities in greater detail. The gap between th eoretical predictions and experimental capabilities continues to grow (in both directions). For example, there is still a scarcity of experimental results that point to “smoking gun” signatures of drift wave turbulence. No capability exists on any machine to measure Ti and V? fluctuations that might provide a signature for ITG modes. Detecting ETG modes, which might be responsible for electron transport in some regimes, presents an enormous challenge even to existing FIR systems that can in princi ple look in the appropriate range of k values. Wong made a poignant argument for the development of multifrequency scattering systems early in the meeting: the cost and complexity of the system might be outweighed by the savings in run time to achieve spatial and spectral resolution, not to mention the value of making a clean and compelling measurement unhindered by issues like shot-to-shot variability. The heightened theoretical interest in zonal flows should be mirrored in the experimental com munity by an attempt to measure some aspect of them; how to do this is just starting to be discussed. Ultimately, tremendously powerful comparisons with theory would be made if we could measure fluctuations in Er and particle and heat fluxes, but there are few clues as to how to go about this, especially in a time of limited resources.


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