Computer modeling aids understanding of plasma physics

All-orders spectral calculation in three dimensions of minority ion cyclotron heating for a 10-field period stellarator. Individual cross sections show the intensity of ion heating at various toroidal angles. Click here for more photos.

Fusion energy research has a long history of employing supercomputers to solve highly complex mathematical equations. Fusion researchers have long used the National Energy Research Scientific Computing Center (NERSC) at the Department of Energy’s Lawrence Berkeley National Laboratory in California, which started life in the late 1970s as the Magnetic Fusion Energy Computer Center at DOE’s Lawrence Livermore National Laboratory. “The ORNL Fusion Theory program uses the large computers at both NERSC and ORNL,” says Don Batchelor, head of the Plasma Theory Group in ORNL’s Fusion Energy Division (FED).“The ORNL capability has dramatically increased our progress in developing large-scale computing applications for fusion research.”

Fusion, the energy that powers the sun and stars, is a long-term energy source that could provide an environmentally acceptable alternative to fossil fuels. Achieving fusion energy requires that the fuel, heavy isotopes of hydrogen, be heated to hundreds of millions of degrees, much hotter than the sun. The atoms in matter at such temperatures are torn apart into electrons and ions to form a “fourth” state of matter called plasma (which makes up over 99% of the visible universe). The fuel particles and their energy must then be confined by magnetic fields for a long enough time to produce more energy by fusion reactions than was needed to establish the plasma.

“A great challenge is to understand the physics of how plasma and plasma energy leak out of the carefully constructed magnetic fields used for confinement,” says Batchelor. “The dominant transport process in most cases is turbulent motion due to plasma instabilities.”

Ben Carreras of FED and Vickie Lynch of ORNL’s Computational Science and Engineering Division are carrying out massively parallel computations on the Cray T3E and IBM supercomputers at NERSC and the IBM RS/6000 SP supercomputer at ORNL. These calculations simulate the evolution of certain instabilities that occur in plasma devices, resulting in turbulent fluctuations and greatly increased transport of energy away from the plasma center.

“We are finding that turbulent transport is not following traditional laws of diffusion or heat conduction,” says Carreras. “We find that evidence of a non-linear process called self-organized criticality exists and that transport may be described by more complicated integro-differential or ‘fractional’ differential equations. We are also applying these techniques to fields outside fusion. Methods of self-organized criticality can provide insight into the very timely topic of vulnerability of complex systems such as power grids or communication networks.”

The design of very complex, nonsymmetrical magnetic systems to minimize plasma losses in fusion devices is another area in which FED scientists are using supercomputers. ORNL supercomputers are being used in the analysis and design of a new type of magnetic fusion device called the Quasi-Poloidal Stellarator (QPS); see the Review, Vol. 34, No. 2, 2001, Modeling a Fusion Plasma Heating Process and Stellarator, for more details. This device may result in a much smaller and more economically attractive fusion reactor than existing stellarators and would eliminate the potentially damaging plasma disruptions that plague conventional research tokamaks. It is hoped that QPS will be built at ORNL starting in 2003.

With the help of ORNL supercomputers and new funding from DOE’s Scientific Discovery through Advanced Computation (SciDAC) Program, Batchelor, Fred Jaeger, and Lee Berry, all of FED, and Ed D’Azevedo of ORNL’s Computer Science and Mathematics Division are investigating the heating of plasmas to the astronomical temperatures needed for fusion by electromagnetic waves. “Besides heating the plasma in the way that a microwave oven heats food, experiments show that radio waves can drive electric currents through the plasma and force the plasma fluid to flow,” says Batchelor. “These waves have even been seen to improve the ability of the applied magnetic field to hold the energetic particles and plasma energy inside the device.”

“In 2000 we had a very significant breakthrough in developing a computational technique we call the all-orders spectral algorithm in two dimensions,” says Jaeger. “This algorithm eliminates a number of restrictive mathematical approximations to the theory that were previously necessary. Simultaneously, it enables us to study essentially arbitrarily small-scale wave phenomena, limited only by the size and speed of the computer, not the approximations in the theory.”

Using 576 processors on the IBM SP computer at ORNL, FED researchers obtained the first converged wave solutions in 2D for an important wave process in fusion called fast wave to ion Bernstein wave mode conversion. According to Berry, “As soon as we heard about the SciDAC award, we pressed ahead as rapidly as possible to implement a three-dimensional version of the all-orders spectral algorithm.”