DOESciDAC ReviewOffice of Science
FUSION
Supercomputing Boosts FUSION Research
Since the 1950s, scientists have believed that fusion—the nuclear reaction that powers our Sun—could one day be utilized to help meet humankind's ever-increasing demand for energy. But controlling the fusion reaction in order to cleanly and efficiently produce power is a complex and elusive endeavor. Researchers employing scientific computing have made great advances towards this goal, and as computational resources continue to grow and improve, the day when fusion power becomes a reality is drawing closer.

Today, more than 400 nuclear fission reactors operate in 31 countries, splitting heavy atomic nuclei to produce heat that drives steam turbines, which in turn produce the electricity humankind uses to power modern civilization. Generating next to no carbon, fission reactors contribute 6.5% of the world's energy and 15.7% of its electricity, according to the International Energy Agency. While reactor construction worldwide dropped over the two decades following the Three Mile Island accident in 1979, recent concerns about energy independence and global warming have rekindled investment in fission. But as populous China and India increase their standards of living and energy appetites, fission alone will not be able to meet the world's growing power needs. Even maintaining its proportionate contribution to world energy consumption would require construction of many more reactors—to replace decommissioned ones and meet increasing demand—as well as expanded solutions for dealing with radioactive waste. What's a world hungry for energy—and getting hungrier—to do?
Figure 1. Turbulence in a torus-shaped plasma manifests itself as electron density fluctuations. Dr. Ron Waltz and Dr. Jeff Candy used the General Atomics GYRO code to compute gyrokinetic turbulence, shown in this advanced simulation. Fluctuations are shown as red and blue magnetic field lines. The halo shows the region outside the boundary of the computational domain.
The near-term answer is likely to be a buffet of energy solutions including nuclear fission, as well as power from biofuels, photovoltaic batteries, solar panels, hydrogen, wind, and more. One offering farther out on the horizon may come from doughnut-shaped reactors called tokamaks. These toroidal devices produce energy from nuclear fusion—the process that releases energy from hydrogen bombs, powers the sun, and produces elements in stars. In fusion, nuclei join to form heavier nuclei. If the fusing nuclei are heavier than iron or nickel, energy gets absorbed when they merge. But if the nuclei are lighter than these elements, energy gets released upon fusion.
Fusion power plants would produce far less radioactive waste than fission plants, and none of it would be long-lived.
Fusion reactors are fueled by isotopes of the lightest element, hydrogen. The isotopes are deuterium, isolated by distillation from sea water, and tritium, bred from plentiful lithium bombarded with neutrons from the fusion reactors themselves. The hydrogen isotopes combine at high temperatures to make isotopes of helium and neutrons. The neutrons carry the energy away, and lithium blankets outside the reactor wall capture it. In a future commercial reactor, the trapped energy would heat water to make steam to drive electric turbines. The process generates no greenhouse gases.
Fusion power plants would produce far less radioactive waste than fission plants, and none of it would be long-lived. Fusion reactors would contain only enough fuel to sustain a reaction on the order of minutes without added feed, whereas fission reactors hold several years' worth of fuel. Runaway reactions inside a fusion reactor are impossible because they would cause the hydrogen fuel—which takes the form of a hot, ionized gas called plasma—to come into contact with the reactor wall, immediately cooling the plasma and stopping the fusion process.
Plasma is often referred to as the fourth state of matter, beyond the more familiar states—solid, liquid, and gas. Plasma forms when gases are heated to temperatures so high that electrons get energized and fly off their atoms (figure 1). The process turns formerly neutral atoms into charged particles called ions.
While plasma fills outer space and makes up stars, here on Earth it takes the form of lightning bolts, auroras, and even mercury vapors in fluorescent light bulbs. Plasmas easily conduct electric currents and can be held in place by magnetic fields. The fundamental equations describing plasma were well understood by the mid-1800s, but the physics of plasmas is enormously rich. That makes solving equations related to plasmas moving through fusion reactors complicated and extremely difficult, even for high-performance computers.
Plasma forms when gases are heated to temperatures so high that electrons get energized and fly off their atoms.
To get a significant rate of fusion reactions, the plasma with a density of nuclei (n) must be heated to a very high temperature (T) of about 10 kiloelectron volts, or 100 million degrees centigrade—more than five times hotter than the core of the sun. The energy put into the plasma to heat it must be confined for a time (τ) before it leaks away to the wall and cools the plasma. In a tokamak reactor, magnetic field lines keep the plasma contained away from the wall (sidebar "The Evolution of Tokamaks," p22). The measure of progress for any fusion reactor concept is the "fusion product," denoted nTτ. This is essentially the same as the performance, Q, of a fusion device: fusion power out divided by heating power in.
For tokamaks, the physics and technology for heating the plasma with radio-frequency waves (similar to those in microwave ovens) or with external neutral beams (as in particle accelerators) are well in hand. So too are the science and technologies for controlling the gross mechanical stability of the plasma, called magnetohydrodynamics. The main challenge from the beginning of magnetic fusion research has been confining the plasma long enough to keep it hot. It has been said that containing plasma with magnetic field lines is like holding up a blob of Jell-O with a net of strings—a lot of Jell-O leaks through.

Hot Prospect, Big Challenge
Strong magnetic fields can confine plasmas for longer periods of time than weaker ones. But there is a technological limit to the strength of magnetic fields. Because it takes longer to cool a large object (or plasma) than a small one, scientists just make the plasma bigger. But that makes the tokamak required to contain the larger plasma more expensive. How big must the tokamak reactor be before the heat loss is slow enough (and the confinement time long enough) to get a steady and nearly self-sustained (large Q) plasma core burning its nuclear fuel? This question makes the development of fusion power different from any previously developed advanced technology, such as powered flight, fission reactors, or computers, all of which can be made to work on a small scale. A process of trial and error to optimize what works among those technologies is not expensive, and scaling up is not risky. Not so with fusion. It is as if the Wright brothers had to build a 747 just to get off the ground. To minimize the risk in scaling up laboratory tokamaks (which do not produce net power) to commercial tokamak reactors (which must produce net power to be useful), forefront fusion science must try to predict, as accurately as possible, the rate of heat transport across the confining magnetic field lines to the wall of the tokamak. That turns out to be much more difficult than fusion pioneers in the early 1950s imagined.
Plasmas carry electric current along magnetic fields by a well-understood "classical" collision process, with fast electrons colliding with slower ions and the resulting resistance heating the plasma. In fact, the first plasmas were heated by induced toroidal currents in the tokamak plasma, a process similar to currents running through toaster wires heating a slice of bread.
It turns out, however, that the heat energy put into the tokamak plasma gets transported across the confining magnetic field lines to the cold wall by a much harder to predict turbulent transport process—about one hundred times faster than the simpler collision process. Even in an unmagnetized and neutral fluid like the air in a room, the transport of heat (or smoke) occurs through a turbulent transport process with small-scale eddy, or vortex, motions. A curlicue of smoke rising from a burning cigarette is one example. If the smoke molecules had to rely on collisions with molecules of still air, it would take a long time to smell a cigarette lit just across the room. Turbulence in the air speeds the transport. Turbulence in ordinary fluids like air and water has been experimentally and mathematically studied for a hundred years and has been called the greatest unsolved problem of classical physics. Turbulence in magnetized plasmas has small eddy motions not only in the plasma "fluid" itself, but also in the electric and magnetic fields.
The main challenge from the beginning of magnetic fusion research has been confining the plasma long enough to keep it hot.
Figure 5. Progress in tokamak fusion performance rivals progress in computer-chip technology as measured by Moore's Law, which states the number of transistors that can be packed onto a microprocessor doubles every 18 to 24 months.
However, "many fusion scientists now believe that with the advent of ever more powerful high-performance computers, we are getting very close at long last to a predictive understanding of turbulent plasma transport, at least in the hot plasma core of a tokamak," says Dr. Ron Waltz (sidebar "Biography in Brief: Dr. Ronald E. Waltz," p23), a theoretical physicist at General Atomics, a San Diego firm founded in 1956 to harness the power of nuclear technologies.
But the fight for deep scientific insight is far from over. It turns out much of the confinement time in a high-performance tokamak is controlled by an even more complicated plasma edge layer close to the cold wall. "Accurately predicting edge performance from first principles of plasma physics will take even longer," Dr. Waltz says.

Supercomputing Boons
Fusion for peaceful purposes has been in development for more than half a century (sidebar "The Pope of Plasma Physics"). Yet, predicting turbulent transport from reactor core to edge remains one of the greatest scientific challenges of our time. That said, and despite the running joke that fusion is always 30 years away, the field has made steady technological progress toward becoming a commercial reality. Fusion progress in tokamaks is comparable to that of processing progress in computer technology as measured by Moore's Law, which states that the number of transistors that can be packed onto a microprocessor doubles every 18 to 24 months (figure 5).
Are progress in computers and progress toward fusion intertwined? Dr. Waltz thinks so (sidebar "Fusion Sparks Supercomputing," p26). "In the past, we could say fusion research has long been at the forefront of computational science and drove progress in high-performance computing. In the future, it just may be the other way around."
Fusion research is mainly an experimental and laboratory science, and will be for some time to come, Dr. Waltz points out. But scientists increasingly design tokamak experiments based on theoretical understanding and scientific discovery from advanced computing, such as that supported through the DOE SciDAC program.
"When I came to General Atomics more than 30 years ago, predictions for tokamak confinement time were based solely on empirical global scaling laws," Dr. Waltz recalls. "The fundamental equations were known, but computers were not up to simulating the microscale turbulence with these equations. Theorists developed 'back-of-the-envelope' models and formulas based on highly-approximated equations, then fitted these formulas to the confinement-time data. Many of these early drift wave models were just crazy, but in the end, some versions applied in combinations gave a good phenomenological description of the many tokamak confinement regimes. Most importantly, the formulas helped to develop 'simplified fluid' model equations which could be solved (or simulated) on the previous generation of computers, first in two dimensions, then three."
Scientists increasingly design tokamak experiments based on theoretical understanding and scientific discovery from advanced computing.
By the mid-1990s, scientists used single-processor supercomputers to create even more realistic electrostatic simulations of so-called gyrofluid models, in which ions and electrons spiraling around drifting magnetic field lines create turbulence in plasma. The simulations made use of E × B, a vector that indicates the drift of electron- and ion-scale eddies as they react to an electric field E and its perpendicular magnetic field B.
"From these three-dimensional gyrofluid simulations, we learned that the small-scale E × B velocity shear in the small-scale radial electric field fluctuations actually stabilize and limit the turbulent transport," Dr. Waltz says. "These small-scale radial electric field fluctuations are driven nonlinearly by the unstable modes which transport the energy, so the turbulence is self-regulating. We also learned that steady and long-scale E × B velocity shear from toroidally spinning the plasma could actually quench the turbulence. Many scientists believe this was the most important thing learned in the mid-1990s since it explained how improved confinement could result from spinning the plasmas with injected beams."
Experiments have amply verified such physical mechanisms, he says. In essence, the shear in these small- and large-scale E × B velocities shave big eddies into smaller ones that transport less energy.
In the last five years, multiprocessor, high-performance computers have enabled physically comprehensive simulations using the gyro-kinetic-Maxwell equations, which characterize the motions of ions and electrons in turbulent matter. Simulated transport flows match experimental flows within error bars, Dr. Waltz says.

Coupling Small and Big Eddies
Understanding turbulent plasma transport in tokamaks is critical to designing a full-scale commercial reactor in the future. Working with General Atomics computational physicist Dr. Jeff Candy, Dr. Waltz used the supercomputers at the National Center for Computational Sciences (NCCS), a DOE Office of Science (SC) user facility at Oak Ridge National Laboratory (ORNL), and the National Energy Research Scientific Computing (NERSC) Center, a DOE SC user facility at Lawrence Berkeley National Laboratory (LBNL). They used these powerful resources to simulate both large, ion-gyroradius-scale and small, electron-gyroradius-scale turbulent transport in the core of a tokamak. If scientists can predict the temperature at the reactor's edge, they will be able to easily predict the core temperature from such simulations, Dr. Waltz says.
At the NCCS, the team used the Phoenix Cray X1E (figure 7, p26) supercomputing resources to create simulations of confined plasmas (sidebar "GYRO Code Cracks Gyrokinetic-Maxwell Equations to Predict Microturbulence in Plasmas," p27). Access to the NCCS supercomputers was granted through a program called Innovative and Novel Computational Impact on Theory and Experiment (INCITE), launched in 2003 by DOE Under Secretary for Science Dr. Raymond Orbach.
Figure 7. Fusion researchers Dr. Waltz and Dr. Candy used the Phoenix Cray X1E supercomputers at the NCCS to create simulations of confined plasmas. Visiting dignitaries, including President George Bush and former Vice President Al Gore, have signed the supercomputer cabinets.
Turbulent eddies driven by the free energy in plasma temperature gradients have two size scales, Dr. Waltz says. Ion-temperature-gradient (ITG) turbulence, which mainly transports ion energy and cools the ions, has larger eddies on the scale of a dozen ion gyroradii. An ion gyroradius of about 0.3 centimeters is less than half a percent of the plasma radius of current tokamaks (about 0.6 meters). Electron-temperature-gradient (ETG) turbulence, which mainly transports energy stored in the electrons, has eddies more than 60 times smaller than those of ITG turbulence (figure 10, p28).
In the last five years multiprocessor, high-performance computers have enabled physically comprehensive simulations using the gyrokinetic-Maxwell equations, which characterize the motions of ions and electrons in turbulent matter.
While it is the large ITG eddies that transport most of the energy, before the two-year INCITE project, which concluded in December of 2007, it was controversial how much the small ETG eddies were contributing to the overall energy transport. Because the larger-scale ITG transport can be quenched by the shear in the large-scale E × B velocity, the remaining smaller ETG transport can end up controlling the net transport in good confinement regimes.
It was also unclear how much the large ITG eddies and the small ETG eddies interacted. "We were trying to bridge the different spectra and couple them together," says Dr. Mark Fahey, an NCCS computational scientist and INCITE liaison who optimizes the performance of the fusion code on Phoenix.
Handling this computational challenge meant dealing with a huge Reynolds number, an important parameter in ordinary fluid dynamics, a field addressing flows in the atmosphere and oceans or around an airfoil. The Reynolds number indicates the range of size scales of eddies in a turbulent system.
Figure 10. In the left panel, large simulation box with small ETG eddies coupled to (or embedded in) large-scale ITG eddies. In the inset box on the left and the panel on the right are decoupled small-scale ETG eddies in a simulation box too small to contain large ITG eddies. In the left panel, the yellow has a slightly electric potential high and the blue a low. The E × B velocity or motion circulates clockwise around highs and counterclockwise around lows. The mathematical physics of these drift wave turbulent eddies is similar to the way cyclonic (or anticyclonic) wind circulates around high- (or low-) pressure zones on weather maps, and in fact climatologists studying geostrophic turbulence in oceans and atmosphere commonly use equations developed by plasma physicists Akira Hasegawa and Kunioki Mima in the 1980s. It turns out the spinning Earth's Coriolis-force vector is analogous to the B-field vector.
The researchers found that when the large and small scales are both unstable, the coupling is not that strong. The surprising result was that when the small electron gyroscales were stable, large, unstable ion gyroscales could drive electron energy transport at the small scales. This kind of cross-coupling effect had never been seen before. "This new knowledge will be important in improving the models," Dr. Waltz says.
Before Phoenix came into play, calculations of large and small scales of plasma turbulence separately taxed even the best high-performance computers.
Figure 13. This cutaway of a tokamak shows a D shape, a promising design for heating plasma.

Nearly all operating tokamaks and all those currently on the drawing board have a D shape.
Fusion Research Heats Up
Work like Dr. Waltz's is energizing the field. "Fusion, not unlike space travel, has been a dream for the future going back to the 1950s," he says. "Now in 2007, one era has ended and another has just started. Many of the grandfathers of fusion are now passing on, but there is a younger generation of physicists hopeful that the recently initiated International Tokamak Experimental Reactor project will succeed with a burning plasma demonstration in the next decade."
That goal is a reason the SciDAC program has long supported development of complex fusion models. Support for advanced simulations exemplifies DOE's role in enabling high-risk/high-rewards research at government, academic, and industrial institutions. Currently Dr. Waltz's company, General Atomics, carries out the largest fusion program in private industry and since the late 1980s has operated an advanced tokamak called DIII-D. The name derives in part from viewing a slice through the tokamak, a squished-doughnut configuration that confines the plasma like a D instead of an O (figure 13). Scientists at General Atomics long advocated the D-shaped tokamak based on its theoretical magnetohydrodynamic stability properties. DIII-D was the first tokamak to be built in this form. Nearly all operating tokamaks and all those currently on the drawing board have a D shape.
"ITER is a bridge between today's plasma physics studies and tomorrow's commercial fusion power plants."

DR. RON WALTZ
General Atomics
DIII-D, the largest currently operating U.S. tokamak, is one of about 18 tokamaks (including small ones) now in operation worldwide. With an outer radius of 5.6 feet (1.7 meters), it is the third-largest operating tokamak in the world, after the Joint European Torus (JET) in the United Kingdom and the slightly smaller Japan Torus (JT-60U) in Japan. Three more tokamak projects are planned. One, the ITER megacollaboration to build a tokamak with an outer radius of about 16 feet (five meters), eclipses all others (sidebar "ITER: Sun in a Box to Light Up the Earth," p29) The project's name, ITER, formerly stood for International Tokamak Experimental Reactor before the acronym was adopted as its official title.
Scientists hope ITER will put out ten times more energy than they will need to put in to light the reactor. That Q of 10 would be good enough for a commercial reactor, Dr. Waltz says. It is conceivable that ITER could achieve a Q of infinity, which means the burning plasma would be self-sustaining without any power input, he says. With a Q of 1 being the "breakeven" point, the currently operating JET and Princeton's previously operated Tokamak Fusion Test Reactor (TFTR), both of which used a deuterium/tritium mix for fusion, each achieved a Q about half this. For now, the world record to beat is that set in 1998 by Japan's JT-60 all-deuterium-burning tokamak, which achieved a deuterium/tritium-equivalent Q of 1.25. Years of hard work remain.
"ITER is a bridge between today's plasma physics studies and tomorrow's commercial fusion power plants," Dr. Waltz says. Expected to cost $13 billion and last 30 years, the project will take unprecedented multinational cooperation. Investment of an average of about a billion dollars a year is within the magnitude of research into other methods of power generation, ITER supporters say. The project's name—iter is Latin for "the way"—connotes a journey undertaken by a global community that, rather than curse the darkness, endeavors to light the world's brightest candle.
Contributor: Dawn Levy, science writer at the National Center for Computational Sciences

Further Reading
General Atomics
http://www.ga.com/index.php

NCCS
http://nccs.gov

ITER
http://www.iter.org

sidebar
Oil Prices and Fusion Research

 
Published by IOP Publishing in association with Oak Ridge National Laboratory, for the US Department of Energy, Office of Science. Copyright © 2008 by IOP.