The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient(ITG)instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transportmodels, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the models show good agreements in their predictions and assumptions for the linear growth rates and frequencies. There are some differences associated with different equilibria. However, there are significant differences in the transport levels between the models. The causes of some of the differences are examined in some detail, with particular attention to numerical convergence in the turbulence simulations (with respect to simulation mesh size, system size and, for particle-based simulations, the particle number). The implications for predictions of fusion plasma performance are also discussed.

Comparisons and physics basis of tokamak transport models and turbulence simulations

Transport Processes in the Plasma

This paper describes capabilities, evolution, performance, and applications of the Global Arrays (GA) toolkit. GA was created to provide application programmers with an inteface that allows them to distribute data while maintaining the type of global index space and programming syntax similar to that available when programming on a single processor. The goal of GA is to free the programmer from the low level management of communication and allow them to deal with their problems at the level at which they were originally formulated. At the same time, compatibility of GA with MPI enables the programmer to take advatage of the existing MPI software/libraries when available and appropriate. The variety of applications that have been implemented using Global Arrays attests to the attractiveness of using higher level abstractions to write parallel code.

/pdf/advances-applications-and-performance-of-the-global-arrays-6j5g16c9x3.pdf

Advances, Applications and Performance of the Global Arrays Shared Memory Programming Toolkit

Flow over periodic hills – Numerical and experimental study in a wide range of Reynolds numbers

Fundamental Statistical Descriptions of Plasma Turbulence in Magnetic Fields

In 1992, our group began exploring the requirements for a comprehensive simulation code for toroidal magnetic fusion experiments. There were several motivations for taking this step. First, the new machines being designed were much larger and more expensive than current experiments. Second, these new designs called for much more sophisticated control of the plasma shape and position, as well as the distributions of energy, mass, and current within the plasma. These factors alone made it clear that a comprehensive simulation capability would be an extremely valuable tool for machine design. The final motivating factor was that the national Numerical Tokamak Project (NTP) had recently received High Performance Computing and Communications (HPCC) Grand Challenge funding to model turbulent transport in tokamaks, raising the possibility that first-principles simulations of this process might be practical in the near future. We felt that the best way to capitalize on this development was to integrate the resulting turbulence simulation codes into a comprehensive simulation. Such simulations must include the effects of many microscopic length- and time-scales. In order to do a comprehensive simulation efficiently, the length- and time- scale disparities must be exploited. We proposed to do this by coupling the average or quasistatic effects from the fast time-scales to a slow-time-scale transport code for the macroscopic plasma evolution. In FY93-FY96 we received funding to investigate algorithms for computationally coupling such disparate-scale simulations and to implement these algorithms in a prototype simulation code, dubbed CORSICA. Work on algorithms and test cases proceeded in parallel, with the algorithms being incorporated into CORSICA as they became mature. In this report we discuss the methods and algorithms, the CORSICA code, its applications, and our plans for the future.

/pdf/corsica-a-comprehensive-simulation-of-toroidal-magnetic-2pwd1237ku.pdf

CORSICA: A comprehensive simulation of toroidal magnetic-fusion devices. Final report to the LDRD Program

POOMA is a templated C++ class library for use in the development of large-scale scientific simulations on serial and parallel computers. POOMA II is a new design and implementation of POOMA intended to add richer capabilities and greater flexibility to the framework. The new design employs a generic Array class that acts as an interface to, or view on, a wide variety of data representation objects referred to as engines. This design separates the interface and the representation of multidimensional arrays. The separation is achieved using compile-time techniques rather than virtual functions, and thus code efficiency is maintained. POOMA II uses PETE, the Portable Expression Template Engine, to efficiently represent complex mathematical expressions involving arrays and other objects. The representation of expressions is kept separate from expression evaluation, allowing the use of multiple evaluator mechanisms that can support nested where-block constructs, hardware-specific optimizations and different run-time environments.

/pdf/array-design-and-expression-evaluation-in-pooma-ii-4iip9mf73p.pdf

Array Design and Expression Evaluation in POOMA II

Numerical flow simulations are used to study the effect of coherent structures on transport in the context of a two‐field, two‐dimensional model of dissipative drift‐wave turbulence. The presence and nature of structures are found to depend on the adiabaticity parameter α=k∥2 VT2/2νeiωs which controls the degree to which the electrons respond to parallel electric fields. Transport estimates based on quasilinear and mixing‐length models are compared with the simulations. In the regime with long‐lived coherent structures, the turbulent particle transport predicted by a standard quasilinear or mean‐field estimate is found to exceed that actually observed in the presence of coherent structures.

Structure formation and transport in dissipative drift‐wave turbulence

The statistical dynamics of a two‐field model of dissipative drift wave turbulence is investigated using the EDQNM (eddy damped quasinormal Markovian) closure method [J. Fluid Mech. 41, 363 (1970)]. The analyses include studies of statistical closure equations, derivation of an H theorem, and its application to formulation of selective decay hypotheses for turbulent relaxation process. The results show that the dynamics of the two‐field model is fundamentally different from that of the familiar, one‐field Hasegawa–Mima model [Phys. Fluids 21, 87 (1978)]. In particular, density fluctuations nonlinearly couple to small scales, as does enstrophy. This transfer process is nonlinearly regulated by the dynamics of the density–vorticity cross correlation. Since density perturbations are not simply related to potential perturbations, as is vorticity, their transfer rate is greater. As a result, turbulent relaxation processes exhibit both dynamic alignment of density and vorticity and coherent vortex formation.

Statistical dynamics of dissipative drift wave turbulence

A new code, named SUPERCODE, has been developed to fill the gap between currently available zero dimensional systems codes and highly sophisticated, multidimensional plasma performance codes. The former are comprehensive in content, fast to execute, but rather simple in terms of the accuracy of their physics and engineering models. The latter contain state-of-the-art plasma physics modeling but are limited in engineering content and are time consuming to run. The SUPERCODE upgrades the reliability and accuracy of systems codes by calculating the self consistent 1 1/2-D plasma evolution in a realistic engineering environment. By a combination of variational techniques and careful formulation there is only a modest increase in CPU time over 0-D runs, thereby making the SUPERCODE suitable for use as a systems studies tool. In addition, we have expended considerable effort to make the code user- and programmer friendly, as well as operationally flexible, with the hope of encouraging wide usage throughout the fusion community.

J. A. Crotinger

Papers

CORSICA: A comprehensive simulation of toroidal magnetic-fusion devices. Final report to the LDRD Program

Array Design and Expression Evaluation in POOMA II

Structure formation and transport in dissipative drift‐wave turbulence

Statistical dynamics of dissipative drift wave turbulence

A “SuperCode” for Systems Analysis of Tokamak Experiments and Reactors