# Gyrofluid Contributions to the 1994 PPPL Annual Report:

Comparison of Gyrofluid Turbulence Simulations with Experiments

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Significant advances have recently been made in comprehensive gyrofluid simulations of tokamak turbulence, leading to encouraging comparisons with experimental measurements. These simulations now include a number of effects important for realistic comparisons with experiments, including toroidal geometry and the associated toroidal curvature destabilization mechanisms\cite(Beer94, Waltz92), turbulence-generated fine-scale poloidal flows\cite{Dorland93,Beer94}, kinetic effects such as Landau-damping and gyro-averaging\cite{Dorland93}, impurities and beams\cite{Dorland93}, all in a high-resolution field-line coordinate system\cite{Beer94b}.

Researchers at the Institute for Fusion Studies at the University of Texas,\cite{Dorland94, Kotschenreuther94} in collaboration with PPPL, have developed a model for the thermal conductivity $chi$ based on these nonlinear gyrofluid simulations\cite{Beer94}, aided by a linear gyrokinetic code for more accurate determination of critical temperature gradients and quasilinear estimates of $\chi_e/\chi_i$. Careful comparisons have been carred out with a wide range of TFTR experiments. This IFS-PPPL transport model contains several scaling trends that might be expected from various previous theories, but it is unique in being directly based on first-principles, detailed, toroidal simulations. The simulations indicate that a particular instability (the Ion Temperature Gradient instability, or ITG mode) is the dominant instability for most TFTR L-mode plasmas. However, even the ITG mode is found to be only marginally unstable in the inner half of many plasmas, leading naturally to a chi(r) that increases with minor radius over most of the plasma. The predicted chi(r) eventually gets too small very near the plasma edge, where some other transport mechanism presumably dominates, so our comparisons with experiments have focussed on the core region (r/a < 0.85) using the temperature at r/a=0.85 as a boundary condition. The present IFS-PPPL transport model focuses on regimes where the ITG instability is dominant, and uses a quasilinear estimate of $chi_e$. The nonlinear gyrofluid simulations have recently been extended to include a sophisticated model of trapped electrons\cite{Beer94,Hammett94}, so we can now begin to study regimes dominated by the trapped electron mode, and can study particle transport in addition to heat transport.

This first-principles transport model (with no experimentally adjustable parameters) has been compared with the core region (r/a < 0.85) of more than 50 TFTR L-mode discharges, typically predicting the ion and electron temperature profiles T_i(r) and T_e(r) within the experimental error bars throughout the confinement zone. An example of this is found in the power scan in (Fig. 1). The dramatic increase of the central ion temperature observed in supershots (from 5 keV to 30 keV) is also reproduced (Fig. 2), though in order to get the detailed temperature profile shapes correct it appears necessary to upgrade the transport model to include the collisionless trapped electron mode. A number of effects are responsible for the improved supershot performance but the key mechanism appears to be via high Ti/Te (the ratio of ion to electron temperature), which raises the threshold for the ITG instability and lowers the conductive part of the ion heat flux so that the (experimentally measured) convection part dominates near the core. The low edge recycling of a supershot gives a high edge ion temperature, which eventually leads to enhanced confinement all the way in to the core.

This level of quantitative agreement with experiments is very encouraging, but there are a number of transport issues which remain under study, such as the edge region, favorable isotope scaling in supershots, Bohm scaling in L-mode, density transport, various perturbative and time-dependent phenomena, effects of elongation and triangularity, high beta, etc. Possible explanations for some of these effects are being pursued, one of them being the issue of Bohm vs. gyro-Bohm scaling. The marginal stability effects in the IFS-PPPL transport model (and using the measurements at $r/a=0.85$ as a boundary condition) can partially mask the raw gyro-Bohm scaling of the model so it is closer to the Bohm scaling results on TFTR than a purely gyro-Bohm scaling. Results from flux-tube vs. full-torus simulations suggest the existence of a transition from Bohm to gyro-Bohm scaling\cite{Hammett94}, but a detailed theory of this transition has not yet been worked out. D-IIID has recently found experimental evidence of such transitions in various regimes\cite{Luce94}.

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Fig. 1 IFS-PPPL transport model compared with a TFTR power scan. The predicted T_i(r) profiles agree reasonably well with the measured profiles as the power is varied a factor of 4. [From Ref. Dorland94.] Here and in Fig. 2, the model is used to predict the temperature in the main plasma region (r/a < 0.85) using r/a=0.85 as a boundary condition.

Fig. 2 IFS-PPPL transport model compared with a TFTR L-mode/Supershot pair. The simulations capture much of the enormous variation in the ion temperature between Supershots and L-modes. Nonlinear simulations that include trapped electron dynamics will probably fit the data better. [From Ref. Dorland94.]

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Citations:

Beer94: Michael Alan Beer, "Gyrofluid Models of Turbulent Transport in Tokamaks", Ph.D. Dissertation, Princeton University (1994).

Waltz92: R.E. Waltz, R.R. Dominguez, G.W. Hammett, "Gyro-Landau fluid models for toroidal geometry", Phys. Fluids B 4, 3138 (1992).

Beer94b: M.A. Beer, S.C. Cowley, G.W. Hammett, "Field-aligned coordinates for Nonlinear Simulations of Tokamak Turbulence", PPPL-3040 (1994), submitted for publication.

Dorland93: W. Dorland, "Gyrofluid Models of Plasma Turbulence", Ph.D. Dissertation, Princeton University (1993).

Dorland94: W. Dorland, M. Kotschenreuther, M.A. Beer, G.W. Hammett, R.E. Waltz, R.R. Dominguez, P.M. Valanju, W.H. Miner, Jr., J.Q. Dong, W. Horton, F.L. Waelbroeck, T.Tajima, M.J. LeBrun. "Comparisons of Nonlinear Toroidal Turbulence Simulations with Experiment". 15th IAEA Conference, (Seville, Spain, September 1994). (IEAE-CN-60/D-P-I-6).

Kotschenreuther94: M.~Kotschenreuther, W.~Dorland, M.~A.~Beer and G.~W.~Hammett, "Quantitative Predictions of Tokamak Energy Confinement from First Principles Kinetic Simulations", Invited Talk, APS-DPP meeting (Nov. 1994), submitted to Physics of Plasmas (1995).

Hammett94: G.W. Hammett, M.A. Beer, J.C. Cummings, W. Dorland, W.W. Lee, H.E. Mynick, S.E. Parker, R.A. Santoro, M. Artun, H.P. Furth, T.S. Hahm, G. Rewoldt, W.M. Tang, "Advances in Simulating Tokamak Turbulent Transport", 15th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, Seville, Spain, 1994 (IAEA-CN-60/D-2-II-1).

Luce94: T. Luce, Petty, et.al., ??, 15th IAEA (1994).