The colorful language of plasma physics cannot compete with the charmed and colored quarks of high-energy theory, but we have so far had bananas, sawteeth, and ELMs. We now have fishbones. These arise from their oscilloscope traces, not from the hunger for better funding. Fishbones were first seen in the PDX tokamak at Princeton during neutral-beam injection [21]. Recall that the most powerful way to heat a plasma is to inject beams of high-energy deuterium atoms. Since the atoms are not charged, they can penetrate the magnetic field and get inside the plasma. Once there, they are rapidly ionized by the electrons and become a beam of deuterium ions of 50-keV energy. Oscillations in the plasma could be seen with several different

diagnostics, and they look like those in Fig. 8.14. Fishbones often occur on the q = 1 surface where the sawtooth oscillations (Chap. 7) occur, and sometimes they can excite the sawteeth and appear simultaneously with them. The bad news is that fishbones cause injected ions to be lost before they have transferred their energy to the plasma. As much as 20-40% of the energy can be lost, greatly reducing the efficiency of this primary heating method.

Beams are notorious in exciting plasma instabilities. As usual, the plasma finds a way to come to thermal equilibrium rapidly by generating an instability. Theorists had no problem in finding a suitable instability for this. Initially, there were two somewhat different theories [22, 23], each having to do with an internal kink mode. In Chap. 6, we described the kink instability that occurs to the whole plasma when too large current is driven through it. A localized current can also drive a kink inside a plasma, and this is what happens in the sawtooth region in the presence of a current of fast injected deuterium ions.

The theories could predict the frequency of the oscillations and the conditions when they would occur. Computations of the nonlinear behavior gave traces very much like the experimental ones in Fig. 8.14b. Subsequent work has cleaned up many of the details of the fishbone instability.

The fact that fast ions can be lost via instability is worrisome not only because of the loss of heating power, but even more so because of the fast helium ions (the “ash”) that are generated in fusion. The helium has to remain in the plasma long enough to give up their energy to keep the plasma “burning.” Fortunately, the theorists can tell us not to worry. Roscoe White et al. [24] have found that there is a regime in a fusion-quality plasma in which neither sawteeth nor fishbones will occur, and this parameter regime is actually larger at higher temperatures and with more fast particles. This has yet to be tested, but there is another mitigating factor. In the next generation of tokamaks, starting with ITER, the plasma will be much larger than the widths of the banana orbits. Since the fast ions are lost with a step size of the order of the banana width, it will take many steps for them to reach the wall. Though not finished, the physics of fishbone instabilities is far enough advanced to tell us that this is not a big problem.

Disruptions

No picturesque name here, because this is a really serious problem. Tokamak discharges are known to disrupt themselves, suddenly stopping and releasing all the energy put into them into the containment chamber. Unless we can stop disruptions from occurring, the entire structure of the tokamak, especially the divertors, would have to be beefed up to absorb all that energy. This is not the kind of accident that can happen in fission, because in fusion no energy is released that has not already been put in; it is just that we do not want it to come out all at once and melt or otherwise harm the tokamak structure. The problem is so serious that a large experimental data base has been accumulated on numerous tokamaks, even in the interim between the two ITER planning documents, the ITER Physics Bases of 1999 [25] and 2007 [26].

To get a DT plasma to fuse, we need to heat it to temperatures of the order of a half-billion degrees. The amount of heat in a large experiment like ITER will be about 400 MJ, the energy of 100 pounds of TNT. The poloidal magnetic field created by the tokamak current will hold another 400 MJ of energy. Fortunately, the toroidal mag­netic field energy, which is much larger, is not released in a disruption unless the toroidal field coils are damaged. Normally, the plasma energy escapes slowly into the divertors, which are designed to handle that heat load; and when the plasma is turned off, the current decays slowly, and the poloidal field energy goes back into the coils that drove the current. In a disruption, all this energy sprays out in a matter of 10 milli­seconds and is hard to handle. What happens to the plasma in a disruption has been caught by the M. I.T.7 group working with the intermediate-size Alcator-C tokamak. In a typical elongated D-shaped tokamak, the plasma has to be kept from drifting up or down with specially shaped coils. When an instability causes a disruption, the plasma moves vertically, as shown in Fig. 8.15, shrinking as it loses its energy and current. In this case, it moves downward toward the divertor, but it could as well move upwards. The time scale shows that the whole event took less than 4 ms.

The damage caused by a disruption can be divided into three parts: thermal quench, current quench, and runaway electrons. In thermal quench, the plasma’s heat is deposited in the walls, vaporizing them in spots. This influx of impure gas raises the resistivity of the plasma, and the tokamak current decays. Even if most of the plasma outflow is channeled into the divertor, there is no time for the heat to be conducted away, and the refractory materials in the divertor — tungsten and carbon — will be vaporized also. In current quench, the fast decrease of the toroidal current will drive a counter-current, by transformer action, in the conducting parts of the confining vessel. Since this counter-current is located inside the strong DC toroidal magnetic field, it will exert a tremendous force on the vessel, moving or deforming it unless it is made sturdy enough. As plasma shrinks toward the divertor, it will drive a “halo current,” shown by the dark arrows in Fig. 8.15, flowing through the conducting parts of that structure. The halo current can be as much as 25% of the original tokamak current; and since that current was flowing along helical field lines, the halo current will try to find a helical path through the conducting parts around the divertor.

The third deleterious effect of disruptions is the generation of “runaway” elec­trons. In Chap. 5, we showed that a hot plasma is almost a superconductor because fast electrons do not make many collisions. The faster the electron, the farther it will go before it collides with an ion. This distance is its free path. If there is a large electric field pushing the electron, its free path can increase faster than the electron is going, and it never makes a collision! It is a runaway and can get up to MeVs of energy before it loses confinement. Of course, this depends on the number of scat­tering centers; namely, on the plasma density. Normally, runaway electrons occur during the startup of the plasma. If the electric field is turned up too high before the density is high, runaways can occur. Machine operators know how to prevent this. In a disruption, however, there is no control. If the density falls below a critical value while a strong toroidal electric field is still on, a horde of runaway electrons will be created, amounting to 50-70% of the original tokamak current. When these hit the wall, they will certainly cause damage. In ITER, the tokamak current will be 15,000,000 A. By comparison, household circuits carry only 15-20 A.

The obvious questions are then: What causes disruptions? How often do they occur? Can they be eliminated? It turns out that disruptions mostly occur when we try to push the envelope. There are known limits to the plasmas that a tokamak can confine. There is a density limit, called the Greenwald density, which we will describe shortly. There is a pressure limit called the Troyon limit. And there has to be enough shear stabilization, as specified by the quality factor q, which has to be above 2 at the edge. When the plasma is pushed too close to one of these limits, a disruption is likely to occur. Exactly how it occurs is not entirely clear. Sometimes two island chains with different numbers of islands can lock onto each other and merge. If there is a detected precursor, this locking can be avoided by setting the plasma into rotation. Sometimes this change in magnetic geometry brings a bubble of cold gas in from the periphery, disrupting the whole plasma. When the density or pressure limits are approached, known instabilities can occur. These are the ideal MHD instability, called the Rayleigh-Taylor instability in Chap. 5, and the neoclassical

tearing mode, which is triggered by finite resistivity, as described in Chap. 6. Here, “ideal” means that no resistivity has to be considered for the instability to occur, and “neoclassical” means that banana orbits are considered in the calculation. Figure 8.16 shows a computer simulation of how an instability can bring cold plasma in from the edge, thus cooling the core.

Up to now, tokamak discharges have been pulsed and not run continuously as in an eventual reactor. An average over all tokamaks shows that 13% of these pulses have suffered a disruption. This would be an unacceptable rate, but these are experi­ments meant to probe the stability of a plasma. In long pulses, lasting many seconds in the large tokamaks such as TFTR and JET, the disruption rate is less than 1% because the machine is run conservatively. In the experimental stage, much depends on the experience of the machine operator. He learns the settings on various controls that will produce a stable discharge. For instance, the currents on the various magnetic coils have to be turned on at the right time and increased at the right rate, and the heating power from various sources have to come on at the right time. Operator experience is valuable in the use of almost any machine; snow plows, cranes, and ordinary cars, for instance. Even in the use of a toaster, one sets the darkness level intuitively depending on the dryness of the bread. Nonetheless, in a reactor even one disruption would be disastrous, and methods must be found to eliminate them.

This task is being tackled on three fronts: avoidance, prediction, and ameliora­tion. As already shown in experiment, disruptions can be avoided if the plasma parameters are not pushed close to the instability limits. As shown in Fig. 8.17, these limits have been extensively tested, and the occurrence of disruptions from this cause is predictable. The quantity BN is a measure of the plasma pressure, and stable discharges are all below the theoretical limit, with disruptions occurring when the limit is exceeded. Prediction of imminent disruption can be obtained from many sensors, for instance of magnetic precursor signals; and neural net­works have been successfully used to integrate these signals to give a definite warning of an oncoming disruption. After many trials, these networks can be

trained to suppress false positives. To stop a disruption from occurring, automatic controls can change such parameters as the plasma density, the toroidal current, or the plasma elongation; but this response may be too slow. A faster method would be to drive electron current with electron cyclotron waves in order to change the current profile, and thus the q profile, to a more stable shape. Once an unavoidable disruption starts, there are still ways to ameliorate the damage. For instance, a massive injection of a gas such as neon or argon can reduce the halo currents by 50% and the electromagnetic forces by 75% [26]. Raising the plasma density by about two orders of magnitude this way would also suppress runaway electrons. As tokamaks get larger, the damage from disruptions can be expected to get worse, because the energy released varies as the cube of the radius (i. e., the volume), whereas the energy has to be absorbed by the surface area, which varies only as the square of the radius. On the other hand, the disruptions will evolve more slowly, giving more time to control them.

For tokamaks, the problem of disruptions is receiving a great deal of attention because of its importance. However, tokamaks may not be the machines ultimately chosen for fusion reactors. Stellarators, which do not need large currents, do not suffer from disruptions. The reason that tokamaks are now prevalent is that they gave the best initial results, and there has not been enough money to study other toruses to the same extent. The next generation of tokamaks — the ITER — will allow

us to study a burning plasma, one in which the helium products can be used to keep the plasma hot. After that, we still have a choice; we are not stuck with the tokamak if disruptions continue to be a problem.