Fusion Energy Sciences

NERSC has historically been the leading computer center for fusion energy research. Insights resulting from computational studies at NERSC have contributed to the progress of both the magnetic confinement (tokamak and stellarator) and the inertial confinement (heavy ion) fusion programs.

A major contribution to magnetic confinement research this year was a numerical study of tokamak plasmas that cleared up a discrepancy between theory and experimental results by showing that toroidal flows have a stabilizing effect on sawtooth instability. Another study comparing magnetohydrodynamics (MHD) stability code calculations with high-resolution diagnostic measurements from the DIII-D tokamak experiment showed close quantitative agreement in many cases, demonstrating the maturity of the codes. And the NIMROD code was used for detailed exploration of the onset mechanisms of instabilities in the DIII-D on multiple time scales.

In heavy ion fusion research, simulations of alternative beam transport schemes revealed the strengths and weaknesses of each approach, contributing valuable information to assist in the design of both the accelerator and the fusion target. And to improve the accuracy of heavy ion fusion simulations, researchers are developing algorithms to synthesize the 4D phase space distribution of ion beams from the reduced 2D experimental data.

Stabilization of Sawteeth in Tokamaks with Toroidal Flows

The maximum temperature in tokamak experiments is often limited by the occurrence of sawteeth. During a discharge with sawteeth, there is a rapid, fractional drop in the central temperature, followed by a slower increase as the temperature recovers. This process then repeats periodically. The resulting time trace of the central temperature resembles sawteeth.

MHD theory predicts that tokamak plasmas are unstable to sawteeth when the safety factor q is less than unity. But experiments on tokamaks have demonstrated that tokamaks can be free of sawteeth even when q < 1. Kleva and Guzdar have used NERSC computers to numerically study the stability of tokamak plasmas with q < 1, including the effect of a sheared toroidal flow in the plasma.

	Figure 1   Mode structure with increasing flow speed. The real part of the pressure perturbation of the n = 1 mode is plotted in the poloidal plane (R, z) for Mach number M = (a) 0.2, (b) 0.4, and (c) 0.5. The light area is the region where the pressure perturbation is positive, while the region of negative perturbed pressure is dark.

Their numerical results demonstrate that when the magnitude of a sheared toroidal flow approaches the speed of sound, the resulting centrifugal force becomes large enough to impact the toroidal equilibrium (Figure 1); a toroidal flow can completely stabilize the n = 1 mode in tokamaks with q₀ < 1. In the absence of flows, the growth rate of the n = 1 mode rises as increases because of the increasing pressure gradient. However, the addition of a toroidal flow to the equilibrium has a stabilizing effect. As the magnitude of the flow approaches the speed of sound, the n = 1 mode can be completely stabilized, eliminating sawteeth. The simulations demonstrate that, in addition to the current and pressure profiles, the toroidal velocity profile must be included in sawtooth stability analyses of tokamaks.

INVESTIGATORS
P. N. Guzdar, W. Dorland, J. Drake, A. Hassam, and R. G. Kleva, University of Maryland.

PUBLICATION
R. G. Kleva and P. N. Guzdar, “Stabilization of sawteeth in tokamaks with toroidal flows,” Phys. Plasmas 9, 3013 (2002).

URL
http://www.ireap.umd.edu/Theory/research.htm