Global simulation of ion-temperature-gradient turbulence in a tokamak showing the influence of sheared flow on moderating the turbulence. Contours of density fluctuations. (Figure by Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. B. White, Princeton Plasma Physics Laboratory)

B. Cohen, A. Dimits, G. Kerbel, D. Shumaker, and W. Nevins, Lawrence Livermore National Laboratory
W. Lee, 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
W. Dorland and S. Novakovski, University of Maryland
D. Ross, University of Texas

Research Objectives
The primary research objective of the Plasma Microturbulence Project (PMP, a follow-on to 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 utilize three main classes of simulation algorithms to study core tokamak microturbulence: gyrokinetic particle-in-cell (GK PIC), 5D Eulerian gyrokinetic (EGK), and to a lesser extent 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). (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.

Accomplishments
There has been significant progress in two areas of code development: developing efficient simulation algorithms for electromagnetic simulations with kinetic electrons, and developing a global continuum Vlasov model. Our flux-tube continuum Vlasov code has undertaken simulations of both electron and ion temperature gradient instability with electromagnetic effects, and this code has a growing user community. We have developed a toroidal electromagnetic code with kinetic electrons that works well at low plasma b, and a hybrid fluid electron/gyrokinetic ion code that works well at finite b. We have continued global gyrokinetic simulations of DIII-D plasma discharges that emulate the correlation reflectometry diagnostic in the experiment with good success. We have extended our database of flux-tube gyrokinetic simulations quantifying the dependence of the transport of ion thermal flux on magnetic shear, safety factor, E x B velocity shear, and toroidal velocity shear. Flux-tube gyrokinetic simulations and a continuum Vlasov simulation have revealed the inadequacy of the approximate rule that shear in the E x B flow equal to the typical linear growth rate is needed to stabilize drift-type instabilities.

Significance
NTTP/PMP simulations are having increasing success in agreeing with experiments and 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.

Z. Lin and L. Chen, "A fluid-kinetic hybrid electron model for electromagnetic simulations," Phys. Plasmas 8, 1447 (2001).

Y. Chen and S. Parker, "A gyrokinetic ion zero electron inertia fluid electron model for turbulence simulations," Phys. Plasmas 8, 441 (2001).

http://fusion.gat.com/theory/pmp/