Although the simple scaling that the power threshold P_th is proportional to nBS may capture some important trends in P_th, it does not fully or adequately describe the P_th scaling. The experiments suggest that "hidden" variables are also at work since it is easy to vary P_th by factors of 2 or more for a given nBS. Present thinking is that neutrals, grad B drifts, sawteeth and perhaps MARFEs can have a significant effect on the threshold.

Neutral effects are being examined in C-Mod by Boivin who is attempting to measure the CX power leaving the plasma and in DIII-D by Carreras and Owen who are using DEGAS modelling to estimate neutral density distributions. The latter work finds a correlation between P_th and the neutral penetration length in the plasma edge. A crucial issue is that we start getting some real measurements of neutral densities at the plasma edge. Boivin hopes to go that direction with his work and an attempt will be made in DIII-D to calibrate a tangential D-alpha TV for this purpose.

Carlstrom's work has suggested that grad B drifts can carry significant amounts of power across the separatrix (both in and out of the core) and thus may have a significant effect on the amount of heating power required to get the transition. Simple modelling suggests that these effects could explain several trends observed in P_th in the experiments. Some quantification of this effect is required and will be attempted. An experiment in DIII-D will be run to measure the SOL temperature gradients, which are the drivers for the effect. In addition, Rognlien is developing UEDGE in such a direction that it can also evaluate the cross-field fluxes.

There is good evidence that sawteeth can have a large effect on the power threshold in some regimes. In addition, there is some suspicion that MARFEs in the L-mode may affect the H-mode transition and perhaps P_th. However, I know of no planned work to examine these phenomena.

Finally, Petty and Luce have obtained data to compare the power thresholds in DIII-D and JET in a dimensionless way. They do not have a result which they want to quote, but this work may ultimately provide some information on the size scaling of the H-mode power threshold and also answer the question as to whether the H-mode transition is controlled by plasma physics variables only or whether atomic physics must be included.

EDGE PARAMETER STUDIES AND PHYSICS MODELS

The long term goal of the L-H group in the TTF is to obtain a quantitative model of the H-mode transition. In support of this goal, a major focus of the group for the last 2-3 years has been to experimentally characterize the temperatures, densities and gradients at the plasma edge which are required to produce H-mode. Simultaneously, there has been on-going theoretical work to develop 3D non-linear simulations to model edge turbulence. These efforts show evidence of converging - that is, we have at least one model (and perhaps two) which predict enough of the features seen in the experiments that we are quite hopeful that much of the essential physics has been captured. This development is a very exciting one and I want you to be aware of it.

One model is that of Drake and colleagues at UMd and is a 3-D simulation in shifted-circle geometry. The other model is that of Xu and colleagues at LLNL and is a 3-D simulation in realistic geometry of turbulence in the SOL and the region just inside the separatrix. Both models contain many sources of turbulence and handle both the electrostatic and electromagnetic limits of edge turbulence.

The UMd model captures many of the qualitative experimental features seen in the H-mode and makes quantitative predictions which are in rough agreement with experiment, at least in a preliminary sense. This model predicts that two non-dimensional parameters, the standard ballooning alpha and a diamagnetic alpha, strongly control what happens at the edge. The simulations show a dramatic reduction in turbulence along a trajectory in this two-dimensional space and this reduction is linked by the UMd group to the H-mode transition. When experimental data from both C-Mod and DIII-D are plotted in terms of these dimensionless parameters, it is found that this parameterization provides a generally reasonable division between L-mode and H-mode points and that the division occurs within a factor of roughly 1-3 of that predicted by the model. I believe that there has been a similar comparison with ASDEX data but I am not really familiar with that. The model also predicts a regime of very high turbulence and Drake suspects that this may correspond to the L-mode density limit. Suttrop at ASDEX has examined this from the experimental side. One requirement for the model to be valid is that the electron collisionality be high. Indeed, checks of the databases for ASDEX-U, C-Mod and DIII-D indicate that the average collisionality at the very edge just before the transition is in the range of 20-35. Of course, there is a fairly substantial range in collisionality and it can be close to unity at low density. Whether those data are a problem for the model has not been addressed.

The qualitative trends of the UMd model are that when the edge beta of the plasma is increased enough, a regime of reduced turbulence, which is being called H-mode, is observed. Very recent results, reported at the TTF meeting, show that as time progresses in the simulations, a steep gradient in pressure develops and reaches a limiting value due to the development of some turbulence. Once this limiting value has been achieved, the width of the steep gradient region increases until an "ELM-like" event is observed which destroys the edge confinement. This event occurs with the pressure gradient at about twice the ideal ballooning limit. It is my understanding that these results have been very recently obtained and so there is not much characterization of what variability might occur as the model parameters are changed. I think it is clear that the model reproduces much of the essential phenomenology seen in the experiments. For example, ExB flow is crucial for the turbulence reduction seen in the model. The "transition" is accompanied by a transient increase in the poloidal rotation which is rapidly damped away. This transient lasts of order 100 microseconds and the plasma's pressure gradient starts to balance the radial electric field. This behavior appears to be consistent with preliminary experimental results on the main ion force balance which were presented at the meeting. In addition, this behavior appears to be similar to or identical to the "phase transition" model of Diamond, Carreras and coworkers.

The model of Xu is quite complementary to the UMd model. It appears to me that these two models are attempting to capture much of the same physics. Strengths of Xu's code are that he uses realistic geometry and that he models both turbulence in the SOL and in the region just inside the separatrix. This model is being used to predict features of the turbulence at the edge, such as fluctuation levels and turbulence frequency spectra. Initial comparisons of code results with experimental turbulence spectra, as measured by Rick Moyer, have been initiated. A clear prediction of this code is that there should be ideal MHD modes in the transport barrier and this prediction may be a point of contact with the "quasi-coherent" mode which has been observed in the transport barrier in many machines.

I am quite enthusiastic by what has transpired. Certainly, though, there is a long road ahead to determine how good these models really are and to address a variety of issues which have been raised. Some developments of the models are quite desirable - the UMd model will be extended to realistic geometry and Xu's model should have ExB flows added to the region inside the separatrix. The experimental data must be refined and extended. More parameters - Zeff is a major one - must be examined. The people doing the experimental and theoretical work are willing and eager to push hard for further development and check-out of the models. In my TTF capacity, I intend to encourage and support such work as much as possible. We had some discussions at the TTF meeting about what we could do and we produced some homework assignments.

PEDESTAL

There is a fair amount of pedestal work being done outside the TTF. The picture I offer here is based somewhat on my DIII-D experience and somewhat on my TTF experience. The general picture which I have is that ideal ballooning modes, either infinite-n or perhaps finite-n, are the most likely culprits which limit the pressure gradient. This hypothesis will be fleshed out more by planned experiments and I hope by more theoretical work. In the last year, it has become clear that the edge current density, which is expected to be large from the bootstrap effect, can have a profound effect on edge stability and may act to improve edge stability in some regimes. A planned experiment in DIII-D will attempt to measure this current. Another experiment is planned to make the ASDEX-U shape in DIII-D and to see if similar pressure gradients and widths are obtained in DIII-D as in ASDEX-U under those conditions.

The world community is still in a process of characterizing the pedestal width and of searching for the controlling mechanism. From the experimental point of view, the poloidal gyroradius does not appear to be the answer. On the other hand, there is compelling evidence that the width has at least some dependence on machine size. For instance, at the TTF meeting, Granetz presented results from an edge X-ray diode array which show that the width of the pedestal is roughly in the range of 2-9 mm in C-Mod. Widths of 1-2 cm are reported from DIII-D and ASDEX-U and widths of up to several cm have been reported from JET and JT-60. The JT-60 data are obtained with high spatial resolution edge diagnostics. The evidence for the width increasing with machine size is persuasive although we don't know how strong the scaling is.

There are some intriguing experimental results emerging regarding transport in the transport barrier. Data from Rhodes and Moyer indicate that the density fluctuations peak markedly in the transport barrier. I presume that the fluctuations are from the "quasi-coherent" mode although I am not 100% sure if that is correct. Probe data from TEXTOR (Boedo) and DIII-D (Moyer) show that turbulence accounts for a significant fraction of the particle transport in the transport barrier. In addition, the models discussed previously make predictions that turbulence drives transport in the transport barrier. These experimental and theoretical results suggest that we may be starting to get a handle on the transport mechanisms in the transport barrier. I know of no planned experiments to go after more of this data although I hope that we get some in piggyback mode in DIII-D. Data-code comparisons of the quasi-coherent mode will continue.

CORE-SOL COUPLING

There is a growing sense in the L-H community, as in the larger fusion community, that SOL/divertor physics affects the L-H transition and thus studies of SOL-core coupling are of great interest. At the TTF meeting, there were some discussion of SOL-core coupling by Krasheninnikov, Porter and Rognlien. The main results presented at the meeting were for UEDGE which spans into the core plasma, albeit with a simple core transport model. Porter presented interesting analysis with UEDGE which suggested that the recycling particle flux across the plasma edge accounts for the "wall effect" in confinement. Rognlien has put a model for the electrostatic potential spanning the separatrix into UEDGE and he showed initial data. To my knowledge, the main thrust of SOL-core coupling in the US is from the LLNL group who have nearly completed the coupling of CORSICA to UEDGE. In addition, note that the turbulence model of Xu spans the separatrix and uses a UEDGE plasma solution as input. The UMd turbulence model also contains a simple SOL model. So, there has been quite a bit happening in this area.

In summary, there have been many interesting and encouraging developments in the H-mode area which suggest that we are making progress towards understanding the transition. Perhaps I am being overly-optimistic. However, even in my optimism I realize that there is a lot of work ahead to prove out or disprove the existing models. But the fact that we now have a couple of sophisticated models which are worth looking at from the point of view of the experiments is a very significant development.