In a fusion reaction, energy is released when two hydrogen isotopes are fused together to form a heavier nucleus, helium. To achieve high enough reaction rates to make fusion a useful energy source, hydrogen contained inside the reactor core must be heated to extremely high temperatures—more than 100 million degrees Celsius—which transforms it into hot plasma. Another key requirement of this process is magnetic confinement, the use of strong magnetic fields to keep the plasma from touching the vessel walls (and cooling) and compressing the plasma to fuse the isotopes.
So there’s a lot going on inside the plasma as it heats up, not all of it good. Driven by electric and magnetic forces, charged particles swirl around and collide into one another, and the central temperature and density are constantly evolving. In addition, plasma instabilities disrupt the reactor’s ability to produce sustainable energy by increasing the rate of heat loss.
Fortunately, research has shown that other, more beneficial forces are also at play within the plasma. For example, if the pressure of the plasma varies across the radius of the vessel, a self-generated current will spontaneously arise within the plasma—a phenomenon known as the “bootstrap” current.
Now an international team of researchers has used NERSC supercomputers to further study the bootstrap current, which could help reduce or eliminate the need for an external current driver and pave the way to a more cost-effective fusion reactor. Matt Landreman, research associate at the University of Maryland’s Institute for Research in Electronics and Applied Physics, collaborated with two research groups to develop and run new codes at NERSC that more accurately calculate this self-generated current. Their findings appear in Plasma Physics and Controlled Fusion and Physics of Plasmas.
“The codes in these two papers are looking at the average plasma flow and average rate at which particles escape from the confinement, and it turns out that plasma in a curved magnetic field will generate some average electric current on its own,” Landreman said. “Even if you aren’t trying to drive a current, if you take the hydrogen and heat it up and confine it in a curved magnetic field, it creates this current that turns out to be very important. If we ever want to make a tokamak fusion plant down the road, for economic reasons the plasma will have to supply a lot of its own current.”
One of the unique things about plasmas is that there is often a complicated interaction between where particles are in space and their velocity, Landreman added.
“To understand some of their interesting and complex behaviors, we have to solve an equation that takes into account both the position and the velocity of the particle,” he said. “That is the core of what these computations are designed to do.”
Evolving Plasma BehaviorThe Plasma Physics and Controlled Fusion paper focuses on plasma behavior in tokamak reactors using PERFECT, a code Landreman wrote. Tokamak reactors, first introduced in the 1950s, are today considered by many to be the best candidate for producing controlled thermonuclear fusion power. A tokamak features a torus (doughnut-shaped) vessel and a combination of external magnets and a current driven in the plasma required to create a stable confinement system.
In particular, PERFECT was designed to examine the plasma edge, a region of the tokamak where “lots of interesting things happen,” Landreman said. Before PERFECT, other codes were used to predict the flows and bootstrap current in the central plasma and solve equations that assume the gradients of density and temperature are gradual.
“The problem with the plasma edge is that the gradients are very strong, so these previous codes are not necessarily valid in the edge, where we must solve a more complicated equation,” he said. “PERFECT was built to solve such an equation.”
For example, in most of the inner part of the tokamak there is a fairly gradual gradient of the density and temperature. “But at the edge there is a fairly big jump in density and temperature—what people call the edge pedestal. What is different about PERFECT is that we are trying to account for some of this very strong radial variation,” Landreman explained.
These findings are important because researchers are concerned that the bootstrap current may affect edge stability. PERFECT is also used to calculate plasma flow, which also may affect edge stability.
“My co-authors had previously done some analytic calculations to predict how the plasma flow and heat flux would change in the pedestal region compared to places where radial gradients aren’t as strong,” Landreman said. “We used PERFECT to test these calculations with a brute force numerical calculation at NERSC and found that they agreed really well. The analytic calculations provide insight into how the plasma flow and heat flux will be affected by these strong radial gradients.”
From Tokamak to Stellarator
In the Physics of Plasmas study, the researchers used a second code, SFINCS, to focus on related calculations in a different kind of confinement concept: a stellarator. In a stellarator the magnetic field is not axisymmetric, meaning that it looks different as you circle around the donut hole. As Landreman put it, “A tokamak is to a stellarator as a standard donut is to a cruller.”
First introduced in the 1950s, stellarators have played a central role in the German and Japanese fusion programs and were popular in the U.S. until the 1970s when many fusion scientists began favoring the tokamak design. In recent years several new stellarators have appeared, including the Wendelstein 7-X (W7-X) in Germany, the Helically Symmetric Experiment in the U.S. and the Large Helical Device in Japan. Two of Landreman’s coauthors on the Physics of Plasmas paper are physicists from the Max Planck Institute for Plasma Physics, where W7-X is being constructed.
“In the W7-X design, the amount of plasma current has a strong effect on where the heat is exhausted to the wall,” Landreman explained. “So at Max Planck they are very concerned about exactly how much self-generated current there will be when they turn on their machine. Based on a prediction for this current, a set of components called the ‘divertor’ was located inside the vacuum vessel to accept the large heat exhaust. But if the plasma makes more current than expected, the heat will come out in a different location, and you don’t want to be surprised.”
Their concerns stemmed from the fact that the previous code was developed when computers were too slow to solve the “real” 4D equation, he added.
“The previous code made an approximation that you could basically ignore all the dynamics in one of the dimensions (particle speed), thereby reducing 4D to 3D,” Landreman said. “Now that computers are faster, we can test how good this approximation was. And what we found was that basically the old code was pretty darn accurate and that the predictions made for this bootstrap current are about right.”
The calculations for both studies were run on Hopper and Edison using some additional NERSC resources, Landreman noted.
“I really like running on NERSC systems because if you have a problem, you ask a consultant and they get back to you quickly,” Landreman said. “Also knowing that all the software is up to date and it works. I’ve been using NX lately to speed up the graphics. It’s great because you can plot results quickly without having to download any data files to your local computer.”
Top Photo: A section of the W7-X plasma vessel. [Image: Max Planck Institute for Plasma Physics]