TTF Portland, April 28 – May 1, 1999
Ed Synakowski, Core Working Group Head
David Newman, Deputy Working Group Head

This year, a few significant themes emerged during the core transport working group sessions. This report is organized along those themes. In addition, a description and comments regarding a discussion session on ExB flow shear effects on turbulence is included.

The topics discussed are as follows:

I. Zonal flows:  Much work from theory; so far, little for experiment to say

II. Electron thermal transport: Continued characterization from experiment; still theory mysteries

III. Turbulence measurements: From characterization to efforts to quantitatively close the loop with theory. Imaging?

IV. Simple ideas revisited:  Poloidal rotation, anomalous toroidal flows, confinement scalings and ST’s, diffusion and SOC behavior

V. ExB flow shear discussion:
 

A general theme in the summary is to ask about theory and experiment comparisons: where is it balanced, and where is it skewed? The first two items above were identified as topics where the dialogue is not balanced, and progress is limited by a lack of input from one or the other side.

There was one area that was conspicuous by its absence, namely, local transport control through modification of turbulence with externally generated flow shear. It is generally agreed that such a tool would be of tremendous impact in enabling progress in the optimization of most confinement concepts, the advanced tokamak, for example. Yet this difficult union of RF physics, local turbulence and transport modification, and subsequent pressure profile manipulation remains elusive, and any advances in the foundations for the theory of such flow shear generation were not described at this meeting.

I. Zonal flows

A great deal of progress regarding zonal flow generation was reported from the theory side. However, experimentally there is little new to offer, precisely because theoretical indications are that while zonal flows are a fundamentally important player in governing turbulence dynamics, they possess attributes that are particularly difficult to detect. Some of the discussion regarding zonal flows pertains to how in fact we might detect signatures of them with existing diagnostics, and what sorts of advances are required to investigate them further, as is discussed below.

Presentations regarding zonal flow theory came from Beer, Diamond, Hahm, and Malkov. Much of the work centered about zonal flow damping, and the effects of collisions. In general, zonal flows are expected to govern the saturation amplitude of the turbulence. The zonal flows themselves are expected to be damped by collisions, as suggested by earlier work by Diamond (IAEA ’98) in the weak turbulence regime. As such, it is qualitatively expected that a collisionality dependence should be found in local transport. This is now seen explicitly in gyrokinetic code results for plasmas with temperature profile gradients slightly above the critical gradient, as described by Hahm in an invited presentation. These results emerged this year alongside a paper from the DIII-D group by Petty indicating that, for plasmas with H-mode like profiles, non-dimensional scaling studies reveal a collisionality dependence. Hahm also gave a description of expected experimental signatures of zonal flows. Some of the signatures pointed to the need for measurements of the plasmas fluctuating potential. Spectroscopic determination of the fluctuating poloidal flows requires time resolution that can separate this from the macroscopic mean Er. This represents a significant diagnostic challenge. There is some suggestion by Nazikian that a statistical signature of zonal flow activity might be found in the modulation of the turbulence frequency spectrum measured by reflectometry.

Mike Beer made a presentation on recent gyrofluid theory developments. His gyrofluid calculations now include the undamped component of zonal flows. Inclusion of this physics yields a 40% reduction in calculated thermal conductivities.

Pat Diamond asked the group to consider the influence/importance of a fluttering magnetic field. He used a drift-Alfven model to look at the interaction between magnetic Reynolds stress involving fluctuations in the poloidal and radial magnetic field and the more familiar electrostatic case. The significant point is that flows generated by such flutter tend to counteract the electrostatic zonal flows. This leads to speculation that it may yield a critical beta where zonal flows are quenched, and large increases in fluctuation amplitudes might result. Related to this, Diamond described the notion that strong magnetic fluctuations might yield a "current sheet mode." This magnetic analog to a zonal flow might be important in devices such as RFP’s. Speculation was offered that these might themselves be the source of small dynamos in a RFP plasma, and therefore play a fundamental role in the magnetic turbulence dynamics.

As suggested above, a fundamental issue for the community is that experiment still has quite little to add to the discussion about zonal flows, primarily because direct evidence for them is difficult to come by. In discussions, it was suggested that perhaps the place to look for them is in the plasma and turbulence dynamics implied by the presence of zonal flow activity. One specific suggestion is centered about the issue bursty turbulence activity. Bursting is seen to be a consequence of zonal flow activity in gyrofluid and gyrokinetic simulations under some circumstances. However, it is also a consequence of the interplay between instability drive and ExB flow shear suppression in some circumstances in dynamical modelling. It is possible, though, that the detailed shape of fluctuation bursts as a function of time may be different for the two processes. A more detailed examination of the shapes of density amplitude bursts, for example, might then provide clues as to which, if either, process is responsible for the bursting activity observed in some devices.

II. Electron thermal transport

A general comment about electron thermal transport physics is that there continues to be much characterization of the process. While there has been some progress in this field, a robust theory of electron thermal transport and its reduction is lacking. Chuck Greenfield’s presentation of results from DIII-D indicate that even when the electron thermal conductivity is reduced, it still remains well above neoclassical values. Still, suppression of ETG modes was predicted in many circumstances were the transport is indeed reduced below the usual levels.

If strong magnetic shear is a requirement for reduction of electron thermal transport in the electron channel, as is seen on DIII-D, then the Tore Supra results have to be confronted as well. On Tore Supra, electron thermal barriers are routinely generated with weak magnetic shear, as reported by Hoang. Other interesting dynamics in the electron thermal channel reported from this device include the observations of slow transitions. These provide a challenge for any dynamical model that purports to explain the dynamics of bifurcations of electron pressure-driven systems.

The lack of a robust theory of electron thermal transport suggests that the answer may not lie in the detailed analysis of the tools we have at our disposal, but rather we might have look in unexpected areas. A suggestion that this is the case comes from measurements of high k fluctuations on DIII-D. Gyrokinetic simulations predict no unstable ballooning modes at these k values, yet they are present and may be associated with the observed electron thermal transport.

Another body of work suggests a different approach. In an invited presentation, Satish Puri (IPP-Garching) argued that the usual electron-electron collisionality calculations are missing fundamental physics associated with Kirchoff radiation, or the emission and reabsorption of electron Bernstein radiation. According to Puri, this process yields significant enhancements over the usual calcualtions of electron-electron collisionality, and suggests that in some cases the high rates of electron thermal conduction may be due to this enhancement. It was suggested that the work might be brought to bear on existing datasets where fluctuation amplitudes are measured to be greatly reduced from the more typical cases. In these circumstances, thermal transport could be calculated in the context of Puri’s model and compared to fluxes inferred from power balance analysis.

III. Turbulence measurements

It is appropriate to begin this discussion by acknowledging the contribution to the meeting from Maarten Rutgers (U. Pittsburgh). He presented results from an elegant series of experiments pertaining to soap film turbulence that demonstrated the power of imaging of turbulent systems. In so far as these films represent 2-D systems, some analogies can be made with turbulence dynamics in magnetized plasmas. The discussions that resulted from Rutgers’ presentation and participation in the meeting include the possibility of designing a soap film experiment that may be relevant to examining the physics of shear flow stabilization effects in magnetic confinement devices. This work from outside of the plasma physics community represented an important contribution to the meeting overall, and the TTF plans to continue to develop such dialogues. Also at the meeting were presentations of initial measurements of low temperature plasma turbulence in the PISCES device (Luckhardt), and a proposal for performing such measurements with a reflectometry-based system by Park. Also described by Zweben was a proposal for an imaging system using emission from puffed impurities.

There is increasing interest in the physics of enhanced confinement regimes such as the RI mode where the presence of added impurities play an important role. However, the physics of these modes is not well understood. An important step in understanding the physics of such modes was described in an invited talk by George McKee. In that talk, fluctuation measurements made during impurity puffing were described. With the puffing of neon, local impurity amplitudes dropped dramatically as confinement improved and transport rates dropped. Also reported was a surprising flow reversal upon the introduction of neon, as measured with beam emission spectroscopy.

Hamada reported HIBP measurements from the core of JIPP-T-IIU. There, both density and potential fluctuation measurements allowed the determination of core particle fluxes and allowed some characterization of the transport dynamics. Chapman reported on significant turbulence stabilization on the MST RFP at Wisconsin which occurred upon modification of the plasma’s parallel electric field as well as plans to further improve the confinement. Turbulence characterization was also reported from the RFX RFP by Martines.

On Tore Supra, the up-down asymmetry of measured fluctuations was explored both from the point of view of theory (Garbet) and experiment (Fenzi). It was argued that the up-down asymmetry in core fluctuations can ultimately be attributed to asymmetries in the edge plasma facing components. In fact, when a movable limiter is inserted and approaches the last closed flux surfaces, fluctuation amplitudes increased first in the edge and subsequently in the core as the gap between the limiter and the LCFS was reduced. The spatial localization of the fluctuations was estimated from the doppler shift of the observed modes by assuming that the ExB flow velocity dominated the mode propagation. In the theory work, the asymmetry is attributed to an asymmetry of edge parallel flows.

Reduced correlation lengths in internal transport barriers on JT-60U were reported by Nazikian. The measurements were made with core reflectometry. This reduction is expected to occur if ExB flow shear effects are dominant in the ITB formation. Before and after the formation of the ITB, fluctuation amplitudes do not change. This may be an indication of changes in the instability drive that occur in the absence of shear flow effects and with changing background gradients. However, this conclusion has not been assessed quantitatively.

Universality of turbulence dynamics was discussed by Carlos Hidalgo. In his presentation, he described similarities of frequency spectra of turbulence over a wide range of devices.

Theory presentations included one by Paul Terry. He presented a cautionary tale regarding familiar "rules of thumb," i.e. mixing length arguments, comparisons of linear growth rates to shearing rates, etc.. With a simple nonlinear model of the collisionless trapped electron mode, he argued that these simple rules can be inadequate or even misleading. Wendal Horton discussed the possible role of the magnetic shear profile in governing bifurcations to states of enhanced confinement. His work indicates that difference in radial coupling of modes near qmin may play a role in bifurcation dynamics..

Finally, Ron Bravenec and Dave Ross described their work in which experimentally determined turbulent transport characteristics, including fluctuation amplitudes, fluxes, and ultimately measured frequency spectra, are compared to theoretical predictions. Sensitivity studies have begun in which background plasma profiles are varied within their uncertainties, and transport and turbulence characteristics are compared to predicted values with these variations in mind. A central tenet of their work is that, in transport theory work, getting the predicted transport to agree with measured rates is much weaker evidence for a successful theory than is getting the characteristics of the turbulence correct.

IV. Seemingly simple ideas revisited

A. Toroidal rotation and its origins – Ian Hutchinson gave an update on the interpretation of C-Mod rotation data. Examination of ohmic H modes indicates that anomalous toroidal rotation exists not only when RF heating is present in the plasma. Ohmic H mode plasmas also possess some degree of toroidal rotation. In fact, the data are consistent with the toroidal rotation in the core varying with the plasma stored energy, regardless of the origin of a given increment in plasma pressure. While the role of RF effects, such as those suggested by Chang, may be present in the RF-heated plasmas, the physics underlying the rotation seen in ohmic plasmas is not understood.

B. Poloidal rotation measurements: reinterpretation of an old technique - Ron Bell gave an invited talk on new interpretations of core poloidal rotation measurements made in TFTR. The work is based on analysis of a recently discovered and important atomic physics effect that in principle can influence poloidal rotation measurements made in plasmas of typical tokamak fields temperatures in the keV range and above. Importantly, results identified as not being qualitatively altered by this effect include the poloidal rotation and electric field precursor seen prior to transitions to the ERS regime on TFTR, as well as the IBW flow shear generation results published by LeBlanc in a Physical Review Letter earlier this year. However, the Ti scaling of the local carbon poloidal rotation is likely an artifact of this effect.

C. Revisiting scaling laws – Energy confinement from the START devices was discussed in a presentation by Alan Sykes. Scaling laws of the ITER-89P form are found not to capture the results from START. However, it was found that if simple modifications to this scaling law are added, namely including the plasma elongation and the value of q at the 95% flux surface, then the START results do line up with the results from the moderate aspect ratio tokamak.

D. Revisiting diffusive transport – Ben Carreras presented a provocative idea regarding non-local diffusion. He argued that SOC behavior yields flows of widely different time scales. When an SOC system’s dynamics are cast in the form of a simple diffusion law, behavior that is loosely termed "non-local" results. This behavior is the consequence of different classes of transport events, including those that are resemble diffusive transport with small spatial step sizes, and those that are characterized by large steps and rapid spatial excursions.

V. The ExB Discussion Session – This discuss session emphasized the issue of how we as a community can do better in assessing the successes and limits of the ExB flow shear paradigm. Presentations were made from many within the TTF (P. Terry, U. Wisconsin, R. Moyer, UCSD, S. Zweben, PPPL, G. Tynan, UCSD, K. Burrell, GA, C. Hidalgo, Spain). Terry provided a thoughtful tutorial on flow shear and why its stabilizing effects are difficult to see in neutral fluids. Rick Moyer emphasized issues where more detailed measurements are needed to examine predictions of turbulence characteristics in the presence of flow shear. Stewart Zweben pointed out what he felt are unresolved issues in the community, and highlighted the many different definitions of flow shear effects that are used in the literature. To him, understanding of the effects of flow shear cannot be considered demonstrated until a more quantitative understanding of the turbulence itself and the effects on it from flow shear are in hand. George Tynan presented his plans for a linear device that could be used to measure turbulent characteristics in detail in low temperature plasmas with and without a sheared ExB flow applied.

Keith Burrell argued that the effects of flow shear can be inferred from at least four tests of causality that have been performed in tokamaks. Here the emphasis is on the dynamics of the plasma and turbulence response expected in the face of temporally and spatially varying radial electric fields. He also argued that the framework is compelling in part because of the universality the framework provides in capturing plasma dynamics in a wide range of device types. Finally, Carlos Hidalgo presented results pertaining to Reynolds stress. This represented what many felt to be an important step in characterizing a quantity central to the physics of turbulence-generated flows. Such flows have been the object of theoretical speculations for some time, but measurements of the quantities central to Reynolds stress-induced flow generation have generally been scarce. Throughout the discussion, all involved agreed that the community must strive for a more complete understanding of turbulence dynamics, despite the successes of the framework of ExB flow shear stabilization and decorrelation. This is true not only from the point of view of fundamental understanding, but from the practical point of view of developing plasma pressure profile control tools that might have as their basis local turbulence modification.