Numerical Tokamak Turbulence Project

B. I. Cohen, Lawrence Livermore National Laboratory
J. M. Dawson, University of California, Los Angeles
J. V. W. Reynders, Los Alamos National Laboratory
V. K. Decyk, University of California, Los Angeles
W. D. Dorland, University of Maryland
G. W. Hammett, Princeton Plasma Physics Laboratory
G. D. Kerbel, Lawrence Livermore National Laboratory
J.-N. Leboeuf, Oak Ridge National Laboratory
W. W. Lee, Princeton Plasma Physics Laboratory
S. E. Parker, University of Colorado, Boulder
R. E. Waltz, General Atomics
A. M. Dimits, D. E. Shumaker, and W. M. Nevins, Lawrence Livermore National Laboratory
M. Beer and Z. Lin, Princeton Plasma Physics Laboratory
R. Sydora, University of California, Los Angeles, and University of Alberta
V. Lynch, Oak Ridge National Laboratory
S. Smith and T. Williams, Los Alamos National Laboratory

Research Objectives

The primary research objective of the Numerical Tokamak Turbulence Project (NTTP) is to develop a predictive ability in modeling turbulent transport due to drift-type instabilities in the core of tokamak fusion experiments, through the use of three-dimensional kinetic and fluid simulations and the derivation of reduced models.

Computational Approach

Two classes of three-dimensional initial-value simulation algorithms, gyrokinetic (GK) and gyro-Landau-fluid (GLF), are being applied to the simulation of tokamak turbulent core transport. The GK simulations are based on particle-in-cell (PIC) methods for the self-consistent solution of Poisson's equation (reduced to a quasi-neutrality relation) and plasma equations of motion, and domain decomposition methods to run efficiently in parallel on the T3E and other parallel computers. The GLF algorithm is based on an alternative solution of the fundamental GK and quasi-neutrality equations, in which fluid moment equations are solved instead of particle equations. The GLF simulations have been performed on both massively parallel and parallel vector computers, particularly the T3E and C90 at NERSC. Both flux-tube, i.e., toroidal annulus, and global toroidal GK and GLF simulations are being performed to study tokamak turbulence.

Accomplishments

We continue to conduct detailed parameter studies with our GK and GLF simulations, addressing discharge #81499 in the General Atomics DIII-D tokamak as a base case because of its relevance to the International Thermonuclear Experimental Reactor (ITER). Careful comparisons have been made between the results of the GLF and GK simulations of shot 81499 and variants to determine parametric dependences and points of agreement between the simulation algorithms (as part of the Cyclone Project, the purpose of which was to study the physics basis and reliability of the various transport models used for ITER projections).

We have compared flux-tube and global gyrokinetic code results. Previous simulations have shown that global codes have significantly lower flux (as much as 20 times lower). In addition, global codes show a global structure to the radial E x B shear flow mode, whereas the flux-tube simulations show a shorter scale radial mode structure. We have implemented profile variation and bounded radial boundary conditions in a flux-tube code. This allows more direct comparisons of the two types of domain representations. We have found that flux-tube simulations including profile variation now agree well with small global simulations, both in terms of heat flux and radial mode structure. We have also found that large global simulations with weak profile variation have a heat flux only 30% lower than similar flux-tube simulations. In addition, these simulations show a broken-up radial mode structure with wavelengths on the order of 20 ion Larmor radii, qualitatively similar to flux-tube simulations.

Much of our effort during this past year has been in comparing the gyrokinetic, gyrofluid, IFS-PPPL and multi-mode models for core transport in tokamaks (e.g., the Cyclone Project). Cyclone Project results indicate that the IFS-PPPL and gyrofluid models predict heat diffusivities that are high compared to gyrokinetic simulations. These differences are significant enough to impact previous ITER projections made by the IFS-PPPL model. Discussion of the Cyclone Project work has recently appeared in Science and Nature.

The NTTP simulations have demonstrated the importance of flow shear and negative central magnetic shear in reducing drift-wave turbulence in tokamaks as observed in experiments. In particular, the simulations demonstrated that equilibrium scale E x B shear flows are important when the linear-mode growth rates are comparable to the E x B shear rates. This criterion has become a standard part of routine experimental transport analysis and incorporated in reduced models. The dynamics of turbulence-driven E x B zonal flows have been systematically studied in fully three-dimensional gyrofluid flux-tube codes and gyrokinetic simulations of microturbulence in magnetically confined toroidal plasmas using massively parallel computers, including the NERSC T3E.

A new electromagnetic fluid model has been developed and has been incorporated into a toroidal gyrofluid code. These fully nonlinear electromagnetic simulations are computationally more demanding (typically by 5x) than previous electrostatic simulations, since they resolve the faster shear-Alfven time scale, and will be able to make great use of NERSC resources.

New schemes for treating nonadiabatic and adiabatic responses for the passing and trapped electrons in tokamaks have been developed. One is based on a careful treatment of the electron weights in different parts of phase space, and another is a new bounce-averaged delta-f scheme. These new schemes will enable us to remove the parallel CFL restriction while retaining the correct linear and nonlinear wave-particle interactions for the electrons, and will also have significant statistical advantages relative to previous particle-based drift-kinetic electron algorithms.

Nonlinear gyrokinetic particle simulations, including electromagnetic effects, are being used to investigate anomalous electron thermal transport from small-scale drift magnetic islands. The regimes where the islands interact radially or remain isolated from each other are considered. The growth and nonlinear formation of gyroradius scale islands with real frequency above the electron diamagnetic drift frequency are observed. The growth and saturation dynamics are sensitive to the electron temperature gradient relative to the density gradient. Work is in progress to evaluate the anomalous radial heat flux and its scaling with plasma parameters.

Significance

The NTTP simulations are being used to produce linear and nonlinear calculations of drift-type instabilities in realistic tokamak equlibria, which are leading to a deeper understanding of anomalous transport in current experiments and to improving their performance. This simulation work is providing a basis for reduced transport models that fit current experimental databases and from which it is hoped that performance in future experiments can be reliably predicted and optimized. As controlling the energy transport has significant leverage on the performance, size, and cost of fusion experiments, reliable NTTP simulations can lead to significant cost savings and improved performance in future experiments.

Publications

L. Garcia, B. A. Carreras, V. E. Lynch, J.-N. Leboeuf, and D. E. Newman, "Resistive pressure gradient driven turbulence at stellarator plasma edge," Phys. Plasmas 4, 3282-3292 (1997).

Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. B. White, "Turbulent transport reduction by zonal flows: Massively parallel simulations," Science 281, 1835 (1998).

R. E. Waltz, R. L. Dewar, and X. Garbet, "Theory and simulation of rotational shear stabilization of turbulence," Phys. Plasmas 5, 1784 (1998).