This figure shows the radial heat flux from the pg3eq 3D PIC code as a function of the radial coordinate, x (in units of the ion gyroradius) and time, t (in units of the thermal transit time). There is a transition at about t = 4100 from low-confinement regime to a high-confinement regime. The low confinement regime (t < 4000) is characterized by large heat pulses excited by plasma microturbulence which propagate both up (toward smaller values of x) and down (toward larger values of x) the ambient temperature gradient. These large heat pulses are absent in the high confinement regime (t > 4200)

B. Cohen, A. Dimits, G. Kerbel, D. Shumaker, and W. Nevins, Lawrence Livermore National Laboratory
W. Lee, M. Beer, G. Hammett, and Z. Lin, Princeton Plasma Physics Laboratory
J.-N. Leboeuf and R. Sydora, University of California, Los Angeles
V. Lynch, Oak Ridge National Laboratory
Y. Chen, S. Parker, and C. Kim, University of Colorado
P. Snyder, R. Waltz, Y. Omelchenko, and J. Candy, General Atomics
J. Cummings, Los Alamos National Laboratory
W. Dorland and S. Novakovski, University of Maryland
D. Ross, University of Texas

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
We are utilizing three main classes of simulation algorithms to study core tokamak microturbulence: gyrokinetic particle-in-cell (GK PIC), 5D Eulerian gyrokinetic (EGK), and gyro-Landau-fluid (GLF). In each case, the simulation domain can be either global or annular (flux tube). (1) The GK PIC simulations are based on PIC methods for the self-consistent solution of Poisson's equation (or Maxwell + Poisson in electromagnetic extensions) and plasma equations of motion, and domain decomposition methods to run efficiently in parallel. (2) The EGK algorithm solves for the 5D distribution function and Maxwell's equations on a mesh that includes two velocity space coordinates (energy and magnetic moment). Four of five dimensions are distributed among PEs for efficient parallel operation. The linear terms are treated implicitly. (3) The GLF algorithm is most similar to conventional fluid dynamics approaches, since a set of fluid moments of the gyrokinetic equation are solved together with Maxwell's equations. Typically, four to six velocity space moments per plasma species are evolved explicitly.

Accomplishments
In the last year, we have reached several important milestones:

We completed a lengthy exercise benchmarking turbulence simulations from several different codes.

We completed: (1) A much more extensive systematic set of nonlinear gyrokinetic simulation parameter scans of ITG-driven transport than before, exploring parts of the physical parameter space new for such nonlinear studies as well as revealing new dependences in regions that had been explored before but not as systematically. (2) Nonlinear investigations of the effect of radial velocity shear on ITG-driven transport, leading to the discovery of significant new parameter dependences that were hidden in previous nonlinear studies and in widely used transport models. (3) A study in which the transport reduction by radial profile gradient variation was discovered to be highly sensitive to the various terms in the equilibrium radial force balance. (4) A characterization of the event-size dependence of the thermal flux carried by transport events of a given size in ITG-driven turbulence. This provides a key qualitative constraint on any theory that claims to describe ITG-driven turbulence.

We elucidated the importance of zonal flows in ITG-driven turbulence, particularly near marginal stability, and particularly in the weakly collisional limit that is appropriate for the fusion program.

We presented the first toroidal electromagnetic simulations of tokamak microturbulence at invited talks at three major scientific meetings, and in the literature. We also discovered that electron scale turbulence (ETG modes) can, under some conditions, cause transport comparable to that resulting from ITG modes.

We discovered a collisionless instability which regulates zonal flows in ITG turbulence.

We presented detailed simulations of plasmas in experimental devices including UCLA's Electric Tokamak, TEXTOR-94, DIII-D, and Alcator C-Mod.

	3D rendering of potential fluctuations from global gyrokinetic particle calculations of ITG-driven turbulence in a large aspect ratio tokamak plasma without and with externally imposed localized sheared toroidal flow.

We have begun to exercise our 3D toroidal hybrid model having gyrokinetic ions and drift fluid electrons. We have been exploring Alfvénic ITG-driven turbulence at moderate plasma with this code. In addition, we have recently developed a drift-kinetic electron model using the canonical parallel momentum formulation and the split-weight scheme. We have been using this code to study kinetic electron effects and electron transport at low plasma . Finally, we have been actively developing a PIC method compatible with finite elements and unstructured grids that can be used for adding a kinetic pressure term to the nonlinear MHD code NIMROD. We have developed a new parallel algorithm for PIC which we call "domain cloning," which augments a 1D domain decomposition without the complications of a second dimension. Multiple copies of the sub-domains are spread across processors, allowing for a much larger number of particles and many more processors than grid cells in the domain-decomposed direction.

Significance
Experiments have shown that control of drift-type modes in tokamak fusion experiments leads to major improvements in plasma energy confinement and, hence, fusion conditions. NTTP simulations are leading to a deeper understanding of anomalous transport in current experiments. Since controlling the energy transport has significant leverage on the performance, size, and cost of fusion experiments, reliable simulations can lead to significant cost savings and improved performance in future experiments.

F. Jenko, W. Dorland, M. Kotschenreuther, and B. N. Rogers, "Electron temperature gradient driven turbulence," Phys. Plasmas 7, 1904 (2000).

Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. B. White, "Gyrokinetic simulations in general geometry and applications to collisional damping of zonal flows," Phys. Plasmas 7, 1857 (2000).