Core Concept: Stabilizing turbulence in fusion stellarators vol. 114 no. 6 > Adam Mann, 1217–1219, doi: 10.1073/pnas.1618480113

In the earliest days of the Cold War, physicists on both sides of the Iron Curtain raced to harness energy from nuclear fusion, which could, in principle, provide nearly limitless electricity. Innovative devices with names like pinch machines, levitrons, and superstators flourished, and for most of the 1950s it was unclear which would eventually prove most promising. But in 1968, at the Third International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Soviet scientists announced that their tokamak—which confined a thermonuclear plasma within a donut-shaped magnetic field—had achieved temperatures 10 times higher than any other experiment (1).

The interior of the Wendelstein 7-X stellarator. Visible are the plasma vessel, one of the stellarator coils, a planar coil, part of the support structure, and the cryostat together with a lot of cooling pipes and power supply lines. Photo by Wolfgang Filser and image courtesy of Max Planck Institute for Plasma Physics.

Although the figure was initially met with shock and skepticism, it was quickly confirmed by British physicists (2). The tokamak has remained the dominant research avenue for pursuing fusion until today, with machines like the multibillion-euro International Thermonuclear Experimental Reactor (ITER), the world’s largest confined plasma physics experiment, currently under construction in France. But another invention, a close cousin of the tokamak called a stellarator, has lately begun to receive renewed attention. Despite their complexity, stellarators offer ways around many of the instabilities that plague tokamaks. “In simple words, the stellarator is just tamer,” says plasma physicist Thomas Klinger, codirector of the Wendelstein 7-X (W7-X) stellarator experiment in Greifswald, Germany. “It’s difficult to build, but easier to run.”

Researchers now think the advantages of stellarators might extend to one more area that’s crucial to any real-world fusion reactor: the management of turbulence.

Scientists have put enormous effort into creating supercomputer models that can correctly describe and predict the turbulent flows in tokamaks. Some of the same computer simulations have recently suggested that stellarators might have inherently more stable plasmas. At W7-X, which completed its initial run this year, researchers are keen to confirm these hints with experimental evidence. If the theoretical findings are borne out, stellarators could step out of the shadow of their more famous kin, offering a second pathway toward achieving the long-standing dream of fusion energy.

A Star on Earth
“The basic idea of fusion is to create a small sun on the Earth,” says physicist Frank Jenko of the University of California, Los Angeles. “That’s a bit poetic but, in other words, we want to mimic the processes that fuel the stars.”

Nuclear fusion requires atoms to be squeezed so close together that they overcome the powerful electrostatic forces repelling them. In the belly of the sun, the blistering temperature (15 million degrees Celsius) and crushing pressure (340 billion times greater than the Earth’s atmosphere) effectively converts, by a series of reactions, four hydrogen atoms into a helium nucleus. This unleashes colossal amounts of energy. On Earth, where such pressures are unachievable, engineers
“We’re gaining confidence that after decades we’re finally able to understand [turbulence].”
—Per Helander
instead turn up the temperature and smash hydrogen isotopes deuterium and tritium, which fuse through a more energetically efficient route. The blazing conditions strip the atomic nuclei of their electrons, generating an ionized gas called plasma.

In a star’s center, gravitational pressure keeps the fusion reaction confined. For experiments on Earth, the plasma must be caged inside a magnetic field. Not just any magnetic field arrangement will do. Tokamaks trap the plasma within a toroidal field resembling a donut. But this simple magnetic field has a slightly stronger pull on its inner edge, which would cause the ionized material to drift around and interact with the walls of a machine, cooling the plasma. So a second magnetic field is generated by inducing an increasing electric current in the plasma. The total resulting magnetic field lines wind helically around the donut’s perimeter, looking a bit like diagonal stripes painted from the inner hole to the outer edge, locking the plasma up completely.

The Constant Concern of Current
Tokamaks suffer from two main disadvantages, both related to the electric current induced in the plasma. Because a magnetic field appears only when the electric field is changing, the current must constantly be increased, and this escalation can’t be sustained forever. The longest pulses for most modern tokamaks last around 10 seconds, although ITER hopes to one day achieve pulses as long as 30 minutes. But the constant stopping and starting means that a tokamak chamber is heated and cooled over and over, causing deterioration similar to “bending a paper clip back and forth many times until it breaks,” says theoretical physicist Per Helander of the Max Planck Institute for Plasma Physics (IPP) in Garching, Germany.

In addition, temperature and pressure instabilities in the plasma can create huge alterations to its resistance. This creates an obstacle to the current, causing it to suddenly stop flowing and disrupting the magnetic field. “You lose the energy of the plasma and you transfer a significant fraction of the current into the metallic walls of the machine,” says plasma physicist David Campbell, Director of Science and Operations at ITER in France. Tokamak engineers must therefore design their devices to withstand such onslaughts, and any future power plant might have to take into account significant downtime from such interruptions.

Stellarators, on the other hand, shape their magnetic field into a winding Möbius-like ribbon that completely confines the plasma. This twistiness avoids the need to run a current through the plasma center, meaning the machine can theoretically be run indefinitely without the potential for violent disruptions, like in a tokamak.

Tying Plasma Knots
Princeton astrophysicist Lyman Spitzer first came up with the innovation behind stellarators in 1951, bending a torus into a figure-eight knot to trap the plasma within (3). But plasma particles prefer to flow through perfectly symmetric fields, like the donut shape in tokamaks. The asymmetry in Spitzer’s stellarator meant that the particles tended to drift out of the magnetic cage and carry away heat, making it difficult to sustain the high temperatures needed for fusion. When the Soviets demonstrated the superiority of their tokamak in the late-1960s, laboratories all over the world abandoned stellarator research, some even converting their machines into tokamaks.

It wasn’t until the 1980s that researchers had a better understanding of 3D nonlinear plasma flows and discovered the right equations to deal with them (4). Using the powerful calculating abilities of supercomputers that became available around the same time, physicists could optimize the magnetic field in a stellarator specifically to prevent the plasma particles’ escape.

“It was a paradigm shift in the way you design a stellarator,” says physicist David Gates of the Princeton Plasma Physics Laboratory in New Jersey. “You could now design the magnetic coils around the plasma shape you wanted.”

W7-X is one of the world’s first such optimized stellarators. Rather than a torus, the device has a pentagon-like structure when seen from above, with five helical twists in its ring. Construction of the 1-billion-euro machine began in 2004 and took a decade to complete. Engineers had to achieve millimeter-scale precision when placing each of its 3.5-meter-high, 6-ton magnetic coils. “The accuracy borders on the amazing,” says computational physicist Pavlos Xanthopoulos of IPP in Germany.

Operations began at W7-X last December, and on February 3 German Chancellor Angela Merkel pressed a button to ignite the first hydrogen plasma in the reactor chamber, achieving temperatures of between 10 and 100 million degrees Celsius for a tenth of a second. Helander says this initial run was not intended to conduct experiments, but mainly to check the control systems and diagnostics before the device is upgraded to its full potential. The first scientific operational phase is scheduled to begin in the middle of 2017.

Taming Turbulence
Turbulence is among the many issues that W7-X will investigate. Optimistic scientists in the 1950s thought that fusion would be relatively easy to achieve based on back-of-the-envelope estimates that assumed simple particle collisions would carry away most of the heat. “Since then it’s become clear for tokamaks that turbulence is the dominant mechanism for heat lost in the plasma,” says plasma physicist Gabriel Plunk, also of IPP. “And with the modern stellarator, turbulence is one of the major factors with the performance of the device.”

Because it has been such a long-standing problem in tokamaks, researchers have built powerful computer codes to simulate turbulence in magnetically confined plasmas. Those same models have been applied to more-complicated stellarator plasmas in only the last few years, but the results have so far been promising.

In 2012, Helander and his colleagues showed that the curving twists inside a stellarator should make them automatically immune to a particular type of turbulence arising when electrons become magnetically trapped in certain regions of a tokamak’s field (5). And this year, Xanthopolous and his colleagues published a paper suggesting that the 3D geometry of stellarator plasmas provides “speed bumps” to the build-up of another type of turbulence, making them inherently more stable than tokamak plasmas (6). “This seems to be there by sheer magic,” says Xanthopolous. “The finding was established only after being able to run these complicated simulations, because nobody predicted it before.”

Helander says, “We’re gaining confidence that after decades we’re finally able to understand [turbulence].”

The next step is to move these results from the virtual to the physical. “Numerical codes have their uncertainties,” says Klinger. “It’s a good custom in the turbulence business to trust only codes which have been benchmarked against reality.” Diagnostic instruments are being developed for W7-X’s reactor chamber that will examine the turbulent flows in the plasma and determine how stable they are compared with tokamaks.

Whereas the reactor types are competitors in a sense, most people who work on them tout the complementarities and cross-fertilizations that have resulted from studying both. “I think Wendelstein will be a very interesting physics experiment in its own right,” says Campbell. “If it pays off, it’ll give us confidence that we have two really good options for the future of fusion theory.”

↵ Artsimovich L, et al. (1968) Paper CN24/B1. Procedures of the Third International Conference on Plasma Physics and Nuclear Fusion (International Atomic Energy Agency, Vienna)..
↵ Peacock N, et al. (1969) Measurement of the electron temperature by Thomson scattering in Tokamak T3. Nature 224(5218):488–490.. CrossRefWeb of Science
↵ Spitzer L (1951) A Proposed Stellarator, US Army Environmental Command Report no. NYO-993 (PM-S-l)..
↵ Nuhernberg J, Zille R (1988) Quasi-helically symmetric toroidal stellarators. Phys Lett A 129(2):113–117..
↵ Proll JH, Helander P, Connor JW, Plunk GG (2012) Resilience of quasi-isodynamic stellarators against trapped-particle instabilities. Phys Rev Lett 108(24):245002–245006.. Medline
↵ Xanthopoulos P, et al. (2016) Intrinsic turbulence stabilization in a stellarator. Phys Rev X 6(2):021033–021038..