Transient Transport

Summary of Working Group Presentations

Burlington, Vermont 26-29 April 2000

Ken Gentle

The study of transients was introduced as a tool for improving the accuracy and removing ambiguities in transport measurements. It continues to demonstrate its value for this purpose. The results presented can be summarized under two headings.

I. Continuing Electron Saga. Transient experiments have shown peculiarities in the electron heat conduction channel for several years now. At this meeting, the importance and challenge of the electron channel was broadly accepted. Many of the earlier transient experiments have been extended with new results and analysis presented at this meeting.

Super cold pulse. P. Mantica showed the result from the RTP tokamak in which a pellet-driven cold pulse caused a doubling (1.5 to 3 keV) of the central temperature in a discharge heated by strong, slightly off-axis ECH. The magnitude of the effect strains our understanding. A peculiar aspect is that the maximum temperature rise occurs when the ECH deposition is off axis but just inside the q=1 surface.

TEXT current ramp. Following the calculations of Kinsey et al., Gentle showed a critical gradient model with coupled electron and ion channels that reproduced the TEXT cold pulse semi-quantitatively. However, when the model was applied to the inverse experiment, edge heating with a current ramp, the model failed to reproduce the transient decrease in central electron temperature. The model also failed to fit the TEXT experiment in which the initial state was heated with ECH and then subjected to a cold pulse.

ASDEX lacks Ti increase in cold pulse experiments. A consistent feature of the critical gradient coupled electron-ion models applied to cold pulses is a strong increase in ion temperatures. Although there is an indication of this in cold pulses on C-Mod, S. Jacchia reported that no increase in ion temperature accompanied the core electron temperature increase in cold pulses on ASDEX. As an additional puzzle, the core heating was also produced by a deuterium pellet at the edge, which cools both electrons and ions, leaving Ti/Te generally unchanged.

ASDEX matched edge drop/rise. ASDEX has developed a unique experimental capability of producing repetitive edge (rho = 0..8) temperature perturbations of either sign but similar shapes. Impurity injection cools, and edge ECH heats. S. Jacchia showed data of high quality for these perturbations. Models like the IFS-PPPL one can fit the cold pulses, but work remains for the hot ones. The ASDEX capability will be a unique resource for careful experiment-model-theory comparisons.

FTU fast switch. FTU has high power ECH, which has permitted them to repeat experiments reported by Stroth in Wendelstein in a tokamak. S. Jacchia showed that the same prompt switching of thermal diffusivity with applied power occurs in FTU. With central heating power, the heat flux is linearly proportional to electron temperature gradient across the plasma. However, when the heating power was reduced from 800 kW to 400 kW, the constant of proportionality -- the thermal diffusivity -- immediately dropped almost 50%, although the linear relation remained. Beyond the striking speed of the switch (~3 ms) is that the values persist without change during the relaxation to the new equilibria, which includes large changes in temperature, etc.

As S. Jacchia emphasized, it is important to move beyond phenomenological descriptions and compare experiment with theory and models. We are making considerable progress and testing a range of hypothesis. However, as we broaden the range of experiments and require that a proper understanding must encompass the full scope of transport experiments, we realize that we are nowhere near the end of the path.

II. Are rational q special for transport? The hypothesis that q and the q profile might effect transport arose early in the history of tokamaks, and with the development of current profile diagnostics and improved radial resolution in temperature measurements, one can now separate regions near (low-order) rational q from other regions and ask whether they differ. The evidence, as illustrated at this meeting, is accumulating that there may be some such effects.

RTP Steps. The step-wise reduction in central electron temperature as the ECH deposition radius was moved outward on RTP was reiterated by P. Mantica. The steps coincide with the radii of the low-order rational q surfaces.

Modulation implies convection. Mantica then applied modulated ECH at the critical deposition radii to measure the transport coefficients. The striking qualitative observation was that the maximum amplitude of the modulation occurred inside the deposition radius for ECH-heated discharges. For ohmic discharges, the amplitude decayed with distance from the deposition radius, the usual diffusive result. The implication is that there is a strong inward convection -- a heat pinch. The result is familiar from density perturbation experiments, where pinches are common, and the shift disappears at higher frequencies (the harmonics) as expected for convection. Additional evidence for a heat pinch is the observation that the maximum value of electron temperature occurs at a minor radius slightly less than the radius of deposition. A model consistent with the various RTP observations is a conventional thermal diffusivity and narrow bands of inward convection at rational q; the cold pulse decreases the diffusivity over a broad range of radii.

DIII-D jumps at rational qmin. M. Austin showed preliminary results from a recent DIII-D experiment to elucidate the jumps in electron and ion temperature that occur during the temperature rises of negative central shear discharges. As the current rises and the minimum value of q falls, the temperatures rise. However the rise is not uniform, sometimes not even monotonic. There are brief episodes of rapid increase. The electrons and ions rise simultaneously, and the jumps seem to coincide with rational values of minimum q: 2, 2.5, 3, 4,... In discharges with different values of density, temperature, current, etc., the timing of the jumps is locked to the timing of q, not other parameters. The effect is strongest at low density and high heating power; it disappears at high density.

Tantalizing as these effects are, one must also recall that careful scans on TFTR for a range of conditions and on TEXT for ohmic and moderate ECH heating failed to find any discontinuities or anomalies in the gradient of electron temperature with radius. The picture will be complex.

Future Work: Predictions/suggestions for transient experiments in the near future.

1. Extension of Ti(r,t) experiments. The spatial and most especially the temporal resolution of ion temperature measurements has been improving rapidly. This should be exploited both with electron transients (modulated ECH and cold pulses) to elucidate the coupling between ion and electron channels and directly to refine the ion channel inferences. It was good ion temperature profile measurements that proved that ion transport was not neoclassical ("times two"). Considering the number of puzzles that remain, we might uncover yet more surprises.

2. Modulated localized power deposition: ECH, etc. P. Mantica's results from RTP serve as a reminder of the power of modulated power deposition experiments. We have opportunities on several machines, using both ECH and other forms of localized rf heating, that should not be lost.

3. Density modulation experiments. Particle transport has been even more neglected than electron thermal transport, and experimentally it is much less tractable. However, diagnostic improvements may permit useful experiments with modest spatial resolution both for total density and for impurities. Establishing the relation of these channels to other transport channels is especially important.