Design of Optimized Three-Dimensional Magnetic Fusion Confinement Geometries
D. A. Spong, S. P. Hirshman, and J. C. Whitson, Oak Ridge National Laboratory
P. M. Valanju and B. Miner, University of Texas
Research Objectives
Stellarators rely on three-dimensional shaping of the outer magnetic surface to provide good plasma confinement and stability without the need for the externally driven currents that are necessary in tokamaks. The flexibility offered by three-dimensional shaping opens up a vast design space of possible configurations. The design of stellarator devices with desirable properties relies strongly on high-performance computing, both with respect to the nonlinear, multiparameter space optimizations and in the evaluation of the transport and stability properties of the resulting configurations.
Computational Approach
Our stellarator optimization is built around the three-dimensional plasma equilibrium code VMEC. VMEC calculates the magnetic structure within the plasma volume based on a specification of the outer magnetic surface shape. From this magnetic field structure, a variety of optimization targets are evaluated, such as the longitudinal adiabatic invariant (determines plasma confinement), the Mercier criterion (determines plasma stability), the aspect ratio (determines compactness of the device), the rotational transform, etc. The outer plasma surface shape (which is characterized by 20-30 Fourier amplitudes) is then varied, using a Levenberg-Marquardt optimization loop to achieve overall minimization of the target functions in a root mean squared sense. As a second step, modular magnetic field coil geometries that will produce the required outer magnetic surface shape are determined. Following the optimization, the confinement of the configuration is evaluated in more depth, using particle simulation techniques. The optimizer is written in Fortran-90, extensively uses dynamic memory allocation techniques, and runs on the Cray C90 and J90 computers. The Monte Carlo particle simulation currently runs on the J90, but is being adapted to run in parallel on the T3E using MPI (Message Passing Interface).
Accomplishments
This project has led to compact magnetic configurations that provide improved plasma confinement and stability over previous approaches. These efforts are part of the National Compact Stellarator Experiment (NCSX) project and are expected to lead to the construction of proof-of-principle (POP) and concept exploration (CE) devices within the next few years. The POP device will be based on the quasi-axisymmetric optimization technique, while the CE device will be based on the quasi-omnigenous (QO) approach (see figure).
Top and side views of 3- and 4-field-period optimized low-aspect-ratio stellarators based on the quasi-omnigenous approach. Filamentary magnetic field coils are shown in light blue. The coloration of the magnetic surface is proportional to the local magnetic field strength.
Significance
This work contributes to the development of innovative new magnetic fusion concepts that will avoid the disruptive current-driven instabilities of the tokamak and thus lead to improved, more reliable reactors. These configurations should also offer improved confinement, heating efficiency, and a more compact design than more conventional stellarator designs.
Publications
S. P. Hirshman, D. A. Spong, J. C. Whitson, D. B. Batchelor, B. A. Carreras, V. E. Lynch, and J. A. Rome, "Transport optimization and MHD stability of a small-aspect-ratio toroidal-hybrid stellarator," Phys. Rev. Lett. 80, 528 (1998).
D. A. Spong, S. P. Hirshman, J. C. Whitson, D. B. Batchelor, B. A. Carreras, V. E. Lynch, and J. A. Rome, "J* optimization of small-aspect-ratio stellarator/tokamak hybrid devices," Phys. Plasmas 5, 1752 (1998).
D. A. Spong, "Scientific visualization of 3-dimensional optimized stellarator configurations," in Proc. of the 16th International Conf. on the Numerical Simulation of Plasmas, Santa Barbara, California (1998).