Outer magnetic flux isosurface (color contours show magnetic field strength) and magnet coils (light blue) for a three-field-period, high (23%), quasi-poloidal stellarator. This configuration has been numerically designed using physics-based stability and confinement optimization targets.

Don Spong, Vickie Lynch, Steven Hirshman, Ben Carreras, and Donald B. Batchelor, Oak Ridge National Laboratory

Research Objectives
The ORNL Fusion Theory Group is pursuing computational research in four areas: stellarator optimization and physics, stellarator transport and heating, plasma turbulence and its effects on transport, and radio frequency (rf) heating of plasmas.

Computational Approach
Stellarator optimizations are carried out using a steepest-descent method to minimize a variational form for the 3D plasma equilibrium. The plasma optimization is then carried out with a Levenberg-Marquardt algorithm. We are using a 3D model of turbulence- induced transport to evaluate the role of avalanches. We have also used particle tracers to estimate the anomalous diffusion exponent associated with this model. Coupled partial differential equations for the ion density, parallel velocity, and temperature are evolved in time in the presence of a noise source in the temperature equation (to simulate heating). Finite differences in radius and Fourier expansions in the toroidal and poloidal angles are used. The time stepping scheme is time-implicit for the linear terms and time-explicit for the nonlinear terms. Rf heating uses combinations of Fourier and finite difference representations for the time-varying electric and magnetic fields used in plasma heating and current drive. Maxwell's equations coupled with various forms of the plasma dielectric tensor are then solved over the plasma volume.

Accomplishments
New stellarator physics optimization targets added during the past year include the self-consistent bootstrap current, ballooning stability, direct targeting of transport coefficients using the DKES code, and confinement improvement using the longitudinal adiabatic invariant. These targets have allowed us to design compact stellarators with higher ballooning stability limits (up to 23% stable ) and improved neoclassical confinement properties. The stellarator Monte Carlo code has been extensively used to analyze the transport physics of existing stellarator configurations and new designs generated by the stellarator optimization code. This code identified the greatly improved transport that can be achieved for the recently developed high (23%) configurations.

Using a 3D model of turbulence-induced transport, we are evaluating the role of avalanches. We have also used particle tracers to estimate the anomalous diffusion exponent associated with this model. Preliminary results indicate that the tracer particle transport is closer to ballistic than diffusive.

The 2D spectral code for rf heating can now solve up to 120,000 dense equations with direct (noniterative) ScaLAPACK solutions and achieves up to 0.6 teraflop/sec performance. This code is being used to analyze high harmonic fast-wave propagation in the National Spherical Torus Experiment at Princeton Plasma Physics Laboratory.

Significance
The development of new compact stellarators allows larger-volume plasmas to be designed at a fixed cost. Larger-volume plasmas are less edge-dominated, lose less energy from charge exchange, and as a result allow better science to be carried out. Compact plasmas could also lower development costs and allow smaller, more modular devices to be built. If successful, this could significantly improve the economics of fusion power. Improved understanding of transport and rf heating could lead to smaller, more reliable, and less costly fusion reactors.

Publications
B. A. Carreras, V. E. Lynch, and D. E. Newman, "Self-organized criticality and plasma fluctuation dynamics," J. Plasma Fus. Res. 2, 8 (1999).

S. P. Hirshman, D. A. Spong, et al., "Physics of compact stellarators," Phys. Plasmas 6, 1858 (1999).

E. F. Jaeger, L. A. Berry, and D. B. Batchelor, "Full-wave calculation of sheared poloidal flow driven by high-harmonic ion Bernstein waves in tokamak plasmas," Phys. Plasmas 7, 3319 (2000).