Quasi-Poloidal Stellarator (QPS) optimized stellarator plasma surface with magnetic field line (white) superimposed.

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

Research Objectives
The ORNL Fusion Theory Group is addressing the major scientific issues relating to the magnetic confinement of hot plasmas in both axisymmetric (tokamak) and non-axisymmetric (stellarator) devices. Specific areas of research include stellarator optimization and physics, toroidal plasma turbulence, anomalous transport, rf antenna design, and physics databases for future burning plasma experiments.

Computational Approach
(1) Stellarator optimization: The plasma optimization uses a Levenberg-Marquardt algorithm. The control variables are the coefficients of a Fourier expansion for the shape of the outermost closed magnetic flux surface. The coil optimization uses the minimization of the normal magnetic field component on the outer magnetic plasma surface as a target. We are currently merging the plasma and coil optimizations into a single code. (2) Stellarator transport and heating: Collections of particles are followed by solving coupled ordinary differential equations in time on parallel processors. The time integration is periodically stopped and random changes made in the particles' velocities to simulate inter-particle collisions. (3) Stellarator drift kinetic solver: This model uses a variational procedure to obtain upper and lower bounds on the entropy production rates for plasmas confined in 3D configurations. This project is developing new representations for the pitch angle dependence of the distribution function (B-splines instead of Legendre polynomials) and also converting over to band and iterative matrix solvers in place of the currently used Thomas algorithm. (4) Plasma turbulence models: We follow the motion of tracer particles and use several of the diagnostics that we have used in the case of sandpile models. We calculate the different moments of particle positions and consider their time evolution. The use of the nonlinear Lyapunov number approach has been very useful for such determination. We have successfully tested this method in sandpiles and simple turbulence systems and we are planning to make a more extensive application of this method to 3D plasma turbulence models.

Accomplishments
An optimized compact stellarator QPS (quasi-poloidal stellarator) has been developed and passed through a successful physics validation review, and will be proposed as a future experiment at Oak Ridge National Laboratory. Some specific accomplishments in stellarator were neoclassical transport studies of the QPS device, Monte Carlo studies of neutral beam heating and alpha particle confinement in the National Compact Stellarator Experiment (NCSX) and QPS concepts, development of scenarios for access to second ballooning stability in both the QPS device and its reactor embodiment, and synthesis of coilsets for the QPS and NCSX devices that accurately preserve flux surface integrity.

We have investigated the transport properties of a 3D pressure-gradient-driven turbulence. This system was characterized by subcritical transport by avalanches when a noise source was introduced in the equations. Similar properties of avalanche transport are found in the supercritical regime. The use of particle tracers in this system has allowed us to characterize through different diagnostics the transport properties of the tracers in such systems. The main result is that the transport is superdiffusive with a transport exponent of 0.88. There is no change of the exponent, within the error bars, in going from subcritical to supercritical transport. Several of the methods used in calculating this exponent lead to the same result.

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 the development costs and allow smaller, more modular devices to be built. If successful, this could significantly improve the economics of fusion power.

Publications
J. N. Leboeuf, V. E. Lynch, and B. A. Carreras, "Linear and nonlinear resistive magnetohydrodynamic stability of tokamak discharges with negative central shear," Phys. Plasmas 8, 3358 (2001).

H. R. Hicks and B. A. Carreras, "Quasicoherent fluctuations associated with a transport barrier in the sandpile model," Phys. Plasmas 8, 3277 (2001).

D. A. Spong, S. P. Hirshman, et al., "Physics issues of compact drift optimized stellarators," Nuclear Fusion 41, 711 (2001).

http://www.ornl.gov/fed/Theory/theory.htm