Breakthroughs in Understanding Tokamak Plasma Turbulence

W. Dorland , M. Kotschenreuther (U. Texas), M. A. Beer, G.W. Hammett, S.A.Smith (Princeton), R. Waltz (General Atomics) , G. Kerbel (NERSC)

In the quest to develop fusion as a practical energy source, one of the biggest challenges has been to understand and control plasma turbulence. This turbulence causes hot particles to leak out of the magnetic bottle, reducing the efficiency of the fusion power plant. Ways to reduce this turbulence have recently been found, which could lead to a more cost-effective fusion reactor design.

Plasma Turbulence Plasma turbulence is a very complicated problem, and previous theories had great difficulty in matching actual experiments. The situation was so confusing that, as recently as a year ago, a report by the National Research Council ("Plasma Science", 1995, p. 145) stated:
However, we believe that this statement is now out of date, that because of recent breakthroughs we are now able to predict the turbulence levels in at least the main core region of many tokamak plasmas. Much more work is needed to develop a complete turbulent transport model (which includes the edge region as well, and a broader range of plasma conditions including sheared flows and particle transport), but the present level of agreement, as illustrated below, is quite encouraging.

Comparison of the IFS-PPPL Transport Model With TFTR Experiments

IFS-PPPL transport model compared with an L-mode and a Supershot in TFTR. The simulations (solid lines) capture much of the enormous variation in the ion temperature between Supershots and L-modes. [From Dorland and Kotschenreuther]

Caveats: The red and green curves are for different impurity profile assumptions. The measured temperature at r/a=~0.8 (about R_maj = 3.15 m) is used as a boundary condition to predict the interior temperature profile. The colder edge region is not yet fully understood. Also, the measured convective component of the heat flow is used, which is actually dominant in the core of the supershot. Nevertheless, the fact that this model reproduces the dramatic change in the conduction component of the heat flow is a major step forward, particularly since this model contains no adjustable parameters to fit to experiments.

Breakthrough in Turbulence Simulations:
IFS-PPPL theory agrees with TFTR better than empirical fit

The IFS-PPPL transport model predicts the global confinement time for a wide range of L-mode better than a widely used empirical scaling (ITER-89P).

This is made possible by recent breakthrough in our theoretical understanding of this plasma turbulence and our ability to simulate it with advanced supercomputers. We have developed a transport theory based on nonlinear, 3-D gyrofluid simulations of tokamak turbulence and on comprehensive linear gyrokinetic stability calculations. This is a "first-principles" theory in which there are no adjustable parameters which are fit to experiments.

A complete description of this work, and its caveats, can be found in:

Background: Fusion Energy and Turbulence

Fusion energy research has made significant scientific progress over the years, as demonstrated by the recent (1994) production of 10 Megawatts of fusion power in the Tokamak Fusion Test Reactor (TFTR) at Princeton. One of the main scientific challenges of fusion research is the problem of small-scale plasma turbulence, which appears to control the quality of the thermal insulation provided by the confining magnetic field. Understanding and controlling this turbulence would help improve the economic attractiveness of future fusion power plants. Plasma turbulence has been a very challenging scientific problem, as it involves the complex, nonlinear, 3-dimensional, and chaotic physics of interactions between particles and electromagnetic waves. To date, few quantitative features of plasma turbulence have been elucidated analytically; certainly, despite considerable scientific effort, a fundamental theory of turbulence does not yet exist.

More background info at the Fusion Energy Educational Web Site

Recent Progress in Gyrofluid Turbulence Simulations

In our work, we have combined innovative physical models and supercomputer simulations to tackle this problem. We have developed "gyro-Landau fluid" equations to model kinetic effects (such as parallel and toroidal drift resonances and associated Landau damping) (cite Beer's thesis, and papers by Hammett, Waltz, Dorland, Smith, which play important roles in plasma turbulence. We solve these equations using a 3-D pseudo-spectral code in an efficient flux-tube coordinate system (cite Beer and Cowley paper), primarily using the Cray C-90 at NERSC. Comparisons of the predicted thermal confinement have been carried out with over 50 experiments in the Tokamak Fusion Test Reactor, finding excellent agreement in the core (r/a < 0.8) region of plasmas in the L-mode operating regime (cite Dorland's IAEA paper) . The edge turbulence has been more of a puzzle, but we are investigating possible explanations of that as well. A number of important issues remain to be worked out (such as extensions to trapped electron modes, simulating particle transport as well as heat transport, and confinement in other operating regimes), but this work demonstrates that major progress has been made in developing realistic simulations of tokamak turbulence. Such a predictive capability can be an important tool in optimizing the performance of future fusion power plants.

For more information:

Last Revised 3-July-96 by Greg Hammett