Dalton Schnack and Scott Kruger,
Science Applications International Corp.

Numerical simulation of the nonlinear MHD evolution of shot 86144 in the DIII-D Tokamak at General Atomics, San Diego. Deformed pressure surfaces and magnetic field line trajectories are shown. The simulation used a realistic value of the plasma resistivity and was performed with the NIMROD code on the NERSC T3E.

Research Objectives
Our research objective is to provide computational tools and support for the study of macroscopic instabilities in the magnetic confinement fusion community, especially the DIII-D Tokamak. All of our codes use the (extended) magnetohydrodynamic (MHD) equations, and are nonlinear, initial-value codes.

Computational Approach
We use NERSC resources for several of our MHD codes, but the primary one is NIMROD, a relatively new code developed by a multi-institutional team to take advantage of new computer architectures. It uses a combined finite element/Fourier series spatial representation with a time-split, semi-implicit advance. The semi-implicit time advance requires the inversion of matrices which are extremely ill-conditioned due to the anisotropy caused by the magnetic field and the disparate time scales of the instabilities we wish to study (Alfvén wave time scale much shorter than instability growth time). The matrices are inverted using either a NIMROD-developed conjugate gradient solver or the AZTEC software package. NIMROD is an extremely sophisticated code that works in axisymmetric geometries and for problems requiring the extended MHD equations (MHD + 2-fluid + advanced closures).

Accomplishments
Many numerical problems were discovered in trying to simulate a high- disruption of the DIII-D tokamak. Most of the problems were found to be due to the preprocessing of the DIII-D data. Now that the problems are solved, work is under way to compare theory to experiment.

A tearing mode unstable case was identified in a simple (cylindrical) geometry, and efforts were made to run this case as high in magnetic Lundquist number as possible. Linearly, NIMROD was able to achieve converged solutions at a Lundquist number of 10⁹ due to grid packing. Nonlinearly, converged solutions were achieved at 10⁷. Efforts are now under way to extend this type of parameter pushing to realistic DIII-D equilibria.

Significance
The codes described here are designed to do nonlinear, initial-value simulations of long-wavelength phenomena in fusion-relevant plasmas. These types of motions severely constrain the operating regime of fusion experiments. By developing and applying powerful computational tools to the study of these problems, our understanding of these operational limits will increase, leading to better design and operation of fusion experiments. Our primary focus is support of the DIII-D Tokamak, the largest fusion experiment in the U.S. program.

Publications

A. H. Glasser, C. R. Sovinec, R. A. Nebel, T. A. Gianakon, S. J. Plimpton, M. S. Chu, D. D. Schnack, and the NIMROD Team, "The NIMROD code: A new approach to numerical plasma physics," Plasma Phys. and Control. Fus. 41, A747 (1999).

http://nimrodteam.org/