What happens when you shoot one of the coldest materials into the hottest environment on earth? The answer may help solve the world’s energy crisis.

Imagine that there is a large chamber in hell that’s shaped like a doughnut, and that you’d like to shoot a series of hailstones into that chamber so that as they melt, the water vapor penetrates as deeply as possible and disperses as evenly as possible throughout the chamber. Setting aside for a moment the question of why you would want to do that, consider the multitude of how questions: Should you shoot in the hailstones from outside the ring of the doughnut or from inside the hole? What size hailstones should you use? At what speed and angle should they enter the chamber?

This strange scenario is actually an analogy for one of the questions facing fusion energy researchers: how to refuel a tokamak. A tokamak is a machine that produces a toroidal (doughnut-shaped) magnetic field. In that field, two isotopes of hydrogen—deuterium and tritium—are heated to about 100 million degrees Celsius (more than six times hotter than the interior of the sun), stripping the electrons from the nuclei. The magnetic field makes the electrically charged particles follow spiral paths around the magnetic field lines, so that they spin around the torus in a fairly uniform flow and interact with each other, not with the walls of the tokamak. When the hydrogen ions (nuclei) collide at high speeds, they fuse, releasing energy. If the fusion reaction can be sustained long enough that the amount of energy released exceeds the amount needed to heat the plasma, researchers will have reached their goal: a viable energy source from abundant fuel that produces no greenhouse gases and no long-lived radioactive byproducts.

High-speed injection of frozen hydrogen pellets is an experimentally proven method of refueling a tokamak. These pellets are about the size of small hailstones (3–6 mm) and have a temperature of about 10 degrees Celsius above absolute zero. The goal is to have these pellets penetrate as deeply as possible into the plasma so that the fuel disperses evenly.

Pellet injection will be the primary fueling method used in ITER (Latin for “the way”), a multinational tokamak experiment to be built at Cadarache in southern France (Figure 10). ITER, one of the highest strategic priorities of the DOE Office of Science, is expected to produce 500 million thermal watts of fusion power—10 times more power than is needed to heat the plasma—when it reaches full operation around the year 2016. As the world’s first production-scale fusion reactor, ITER will help answer questions about the most efficient ways to configure and operate future commercial reactors.

Figure 10. Cutaway illustration of the ITER tokamak.

However, designing a pellet injection system that can effectively deliver fuel to the interior of ITER represents a special challenge because of its unprecedented large size and high temperatures. Experiments have shown that a pellet’s penetration distance into the plasma depends strongly on how the injector is oriented in relation to the torus. For example, an “inside launch” (from inside the torus ring) results in better fuel distribution than an “outside launch” (from outside the ring).

In the past, progress in developing an efficient refueling strategy for ITER has required lengthy and expensive experiments. But thanks to a three-year, SciDAC-funded collaboration between the Computational Plasma Physics Theory Group at Princeton Plasma Physics Laboratory and the Advanced Numerical Algorithms Group at Lawrence Berkeley National Laboratory, computer codes have now reproduced some key experimental findings, resulting in significant progress toward the scientific goal of using simulations to predict the results of pellet injection in tokamaks.

“To understand refueling by pellet injection, we need to understand two phases of the physical process,” said Ravi Samtaney, the Princeton researcher who is leading the code development effort. “The first phase is the transition from a frozen pellet to gaseous hydrogen, and the second phase is the distribution of that gas in the existing plasma.”

The first phase is fairly well understood from experiments and theoretical studies. In this phase, called ablation, the outer layer of the frozen hydrogen pellet is quickly heated, transforming it from a solid into an expanding cloud of dense hydrogen gas surrounding the pellet. This gas quickly heats up, is ionized, and merges into the plasma. As ablation continues, the pellet shrinks until all of it has been gasified and ionized.

The second phase—the distribution of the hydrogen gas in the plasma—is less well understood. Ideally, the injected fuel would simply follow the magnetic field lines and the “flux surfaces” that they define, maintaining a stable and uniform plasma pressure. But experiments have shown that the high-density region around the pellet quickly heats up to form a local region of high pressure, higher than can be stably confined by the local magnetic field. A form of “local instability” (like a mini-tornado) then develops, causing the high-density region to rapidly move across, rather than along, the field lines and flux surfaces—a motion referred to as “anomalous” because it deviates from the large-scale motion of the plasma.

Fortunately, researchers have discovered that they can use this instability to their advantage by injecting the pellet from inside the torus ring, because from this starting point, the anomalous motion brings the fuel pellet closer to the center of the plasma, where it does the most good. This anomalous motion is one of the phenomena that Samtaney and his colleagues want to quantify and examine in detail.

Figure 11 shows the fuel distribution phase as simulated by Samtaney and his colleagues in the first detailed 3D calculations of pellet injection.7 The inside launch (top row) distributes the fuel in the central region of the plasma, as desired, while the outside launch (bottom row) disperses the fuel near the plasma boundary, as shown in experiments.

Figure 11. Time sequence of 2D slices from a 3D simulation of the injection of a fuel pellet into a tokamak plasma. Injection from outside the torus (bottom row, injection from right) results in the pellet stalling and fuel being dispersed near the plasma boundary. Injection from inside the torus (top row, injection from left) achieves fuel distribution in the hot central region as desired.

Simulating pellet injection in 3D is difficult because the physical processes span several decades of time and space scales. The large disparity between pellet size and tokamak size, the large density differences between the pellet ablation cloud and the ambient plasma, and the long-distance effects of electron heat transport all pose severe numerical challenges. To overcome these difficulties, Samtaney and his collaborators used an algorithmic method called adaptive mesh refinement (AMR), which incorporates a range of scales that change dynamically as the calculation progresses. AMR allowed this simulation to run more than a hundred times faster than a uniform-mesh simulation.

While these first calculations represent an important advance in methodology, Samtaney’s work on pellet injection is only beginning. “The results presented in this paper did not include all the detailed physical processes which we’re starting to incorporate, along with more realistic physical parameters,” he said. “For example, we plan to develop models that incorporate the perpendicular transport of the ablated mass. We also want to investigate other launch locations. And, of course, we’ll have to validate all those results against existing experiments.”

This pellet injection model will eventually become part of a comprehensive predictive capability for ITER, which its supporters hope will bring fusion energy within reach as a commercial source of electrical power.

Research funding: FES, SciDAC
Computational resources: NERSC
This article written by: John Hules