If magnetically confined plasmas are to burn, producing energy by the fusion of light atomic nuclei, they must operate at high pressures, or more precisely at a high β, where β is the ratio of the plasma pressure to the magnetic-field pressure. Having a high β is crucial because the fusion power density varies as the square of the numerator, while the device’s costs and complexity increase with the denominator.
Throughout the 1990s, experiments conducted on tokamaks—popular, toroidally shaped magnetic “containers”—suggested that the achievable value of β was confined below a certain limit, although some runs showed that the plasma pressures could rise slightly above this limit, at least transiently. Now, researchers working at the General Atomics (GA) DIII-D tokamak in San Diego, California, have shown that, by rotating the plasma about an axis through the center of the torus and applying feedback to correct for imperfections in the magnetic field, they can attain a value of β that is twice the previous limit and close to the maximum one can expect for an ideal device. Stewart Prager of the University of Wisconsin views the work as a “beautiful experiment showing how you can surpass a fundamental limit.”
The DIII-D National Magnetic Fusion Facility is operated by GA for the Department of Energy. The research team came from GA, the Princeton Plasma Physics Laboratory, and Columbia University. Larry Johnson of PPPL announced the new results at the European Physical Society Conference on Controlled Fusion and Plasma Physics held in June in Madeira, Portugal. 1
The success of the rotation strategy was good news for all those working on magnetic confinement schemes that are subject to similar kinds of pressure limits. Those schemes include spherical toruses (see Physics Today, May 1999, page 19), advanced tokamaks, and reversed-field pinch configurations. The new results help validate the decision of many designers to build the capability of rotating a plasma into many new devices.
Masa Ono of the PPPL’s National Spherical Torus Experiment, which began operation in 1999, said his team plans to try rotating their plasma in about a year. Researchers at another new spherical torus, MAST, at the Culham Science Center in the UK, are just starting to explore the limits on β in their device. While designed to have a higher β value than the DIII-D tokamak, spherical toruses are at an earlier proof-of-principle stage.
The impact of the new work on stellarators is less clear because these devices have three-dimensional magnetic field configurations; they have no symmetric coordinate in their physical shape, and hence no natural direction of undamped rotation. However, a medium-scale stellarator experiment being proposed for PPPL is quasi-axisymmetric in a certain coordinate system and should allow rotation similar to that in a tokamak.
In a tokamak, coils are wound around a doughnut-shaped form to create a toroidal magnetic field, with field lines describing circular paths within the torus. A current inside the plasma then generates a poloidal field that wraps the short way around the torus, producing a net helical magnetic field that confines the plasma.
The upper limit on β is determined by the onset of instabilities—that is, distortions in the density profile of the plasma. The most troublesome instabilities in a tokamak are the “kink” modes, in which the plasma develops helical bulges; it then contacts the walls of the chamber and cools quickly because of the influx of material produced by interaction of the hot plasma with the wall.
The limiting pressures dictated by these instabilities were analyzed in the early 1980s by two groups of theorists, who used calculations based on ideal magnetohydrodynamics. 2,3 Although those groups used different approaches, both predicted that β would follow a certain scaling law, varying directly with the plasma current and inversely with the toroidal magnetic field and its linear cross sectional dimension. Experiments since then have largely followed this scaling law, with a constant of proportionality, known as the normalized β, or βN, that falls close to the value of 2.8 predicted by Francis Troyon and his coworkers at the Ecole Polytechnique Fédérale de Lausanne in Switzerland. 2
The value of βN that appears in the scaling law is also known as the “no-wall” limit because the theories assumed free boundary conditions. In reality, all magnetic fusion devices have walls. If such walls were perfect superconductors, they could suppress instabilities by resisting the associated changes in magnetic field, and one could get to a higher pressure before the instabilities arose. By assuming such ideal boundary conditions, Alan Turnbull of GA and colleagues calculated the limit on βN with an ideal wall, finding it to be about twice the no-wall value. 4
The resistive walls in most tokamaks can also suppress the instabilities, but only for a limited time—the time for wall currents to decay. After that, the instabilities are free to grow once more. The slowly growing instability is called the resistive wall mode, and its existence was confirmed at the DIII-D facility. 5 Most devices to date have not managed to get much beyond the no-wall pressure limit.
Strategies to stabilize the plasma
How then, experimenters asked, could they tame the instabilities enough to reach a higher βN? One possibility is to apply feedback to correct for deviations in the magnetic field caused by the instabilities. That’s essentially playing the role of a superconducting wall. Andrea Garofalo (Columbia), who is a member of the team that produced the recent DIII-D results, pointed out that feedback schemes are feasible because the resistive walls slow the growth time of instabilities from the microsecond to the millisecond range, just enough for a feedback system to detect and correct them. The DIII-D device is uniquely equipped with such feedback coils, but still the task is daunting.
Another route to higher βN is to spin up the plasma. Rotation should have the effect of continually refreshing the image currents in the wall, making it more like a superconductor. Although many theorists had looked at that idea, a particularly thorough treatment in 1994 suggested that rotation at a high enough speed could stabilize the plasma. 6
The DIII-D experimenters tested this prediction. They got the torque required to spin up the plasma from the high-energy beams of deuterium atoms that are sent tangentially into the plasma to heat it. The linear speeds of rotation can get as high as 300 km/s. With such fast rotation, the pressure was indeed above the no-wall limit, but not for long. Too soon, the rotations died out, to the team’s surprise and disappointment.
The DIII-D researchers showed that the rotational braking resulted from tiny imperfections in the magnetic field, which are amplified by the plasma. 7 These imperfections are at the 1 gauss level, or 1 part in 20‥000 of the toroidal field. The researchers decided to try a feedback scheme to suppress them. Using pickup coils both outside and, more recently, inside, the tokamak chamber, the DIII-D team sensed any perturbations in the field, both in the toroidal and the poloidal directions. These signals activated three pairs of external coils, which applied corrective fields that essentially pushed the plasma back into shape whenever it tried to bulge outward. Figure 1 shows an exaggerated view of the impact of the feedback loops.
In the set of experiments reported in Madeira, the DIII-D team preprogrammed a set of corrections for the active coils based on the feedback required in previous runs. The behavior was essentially the same as with active feedback.
Figure 2 summarizes the results of the rotating-plasma experiment. Early in the run (not shown), the plasma is formed and heated; around 1.2 s, its pressure has built up to just about the stability limit. Feedback is turned on at 1.3 s. The top panel shows that βN then rises to about twice the no-wall limit. As Richard Buttery of Culham points out, this value is much closer to the upper limit for an ideal conducting wall. So the GA-PPPL-Columbia team has found a way to span the gap between the two limits. The plasma, which had exceeded the no-wall pressure limit for only 0.2 s with no feedback, remains stable at pressures significantly above the no-wall limit for a full second with feedback. In other cases, the plasma has remained stable at high pressure for almost two seconds. Ron Stambaugh, DIII-D program director, asserts that this time is “enormously long compared to the 10-100 µs growth times of instabilities without a conducting wall.”
More work ahead
Stambaugh told us that, for the recent work, the device was not set to operate at its peak values for the no-wall limit; the research was more easily conducted at lower values of βN. Full exploitation of this result requires moving toward higher values. He and his coworkers have already begun such experiments and find essentially the same result: The feedback corrections maintain the rotation and improve stability against pressure-limiting kink modes. They also plan to try to use magnetic-field feedback alone, without rotation, to exceed the no-wall limit. Such research should provide important information for devices whose plasmas cannot be as readily rotated, such as some of the larger devices envisioned for the future.