When neutral-beam heating was installed and turned on in the ASDEX tokamak in Garching, Germany [9] in 1982, Mother Nature came up with a major surprise that no one could have predicted. When the heating power was increased slightly from 1.6 to 1.9 MW, the plasma snapped into a new mode. Its temperature went up; its density went up; and the confinement times of both the plasma energy and the plasma particles went up, as dramatically shown by a sudden drop in the measured flux of escaping ions. It was as if a wall or dam, called a transport barrier, had formed, as depicted in the cartoon of Fig. 7.24a. The plasma would diffuse as it normally does up to this barrier, and then it would be held up by the barrier and leak out slowly in small bursts. This high-confinement mode, called the H-mode, came about from two innovations: the increase in heating power possible using neutral beams and the use of a single divertor of the type shown in Fig. 7.13. When the

Fig. 7.25

neutral beams are turned on below 1.6 MW, the confinement time actually gets a little worse because the beam disturbs the plasma equilibrium that was set up by ohmic heating. This is called the low-confinement L-mode. Once the power is increased beyond the H-mode threshold, the L — to H-transition occurs and a pres­sure pedestal forms.

Figure 7.25 shows what is meant by the pedestal. This is a graph of the plasma pressure as it varies across the minor radius; that is, from the center of the toka — mak’s cross section to the outside. Up to the pedestal, the plasma density and temperature (whose product is the pressure) fall gently from their maxima as in normal diffusion; but they do not fall all the way to zero. They hang up at a high value, so that the average pressure inside is higher than in the L-mode. At the ped­estal, the pressure falls rapidly to nearly zero as the plasma is drained off to the
divertor, where it recombines into gas and is pumped out. What happens inside the barrier is illustrated in Fig. 7.24b. Large electric fields in the direction of the minor radius are set up, and these cause perpendicular E x B drifts in the toroidal direc­tion, as shown in Fig. 5.6. These drifts are not uniform but are highly sheared. Apparently, this sheared motion stabilizes the microinstabilities and slows down the diffusion from the instability-controlled diffusion in the interior. Note that this is electric shear stabilization, as opposed to the magnetic shear stabilization used in elementary forms of toroidal confinement devices.

The H-mode barrier layer is very thin, about 1-2 cm in a large tokamak with meter-sized cross sections. The H-mode is not a peculiarity of the tokamak, since it has been seen in stellarators and other toroidal devices. It is also not a phenom­enon of neutral beam heating. It seems to have only two requirements: (1) that the input power be high enough and (2) that the plasma be led out by a divertor into an external chamber rather than be allowed to strike the wall. The latter requirement is due to the fact that impurity atoms or neutral atoms prevent the pedestal from forming. In the H-mode, the confinement time improves by about a factor of 2 (see Fig. 7.26a), and the plasma pressure by about 60%. A factor of 2 does not seem a lot, considering that confinement times have increased a million-fold since fusion research began; but we are now talking about a machine that is almost ready to be designed into a reactor. A factor of 2 can turn a 1-GW reactor into a 2-GW reactor, serving 1,000,000 homes instead of 500,000. All current designs for fusion reactors assume H-mode operation. The power produced by a reactor depends critically on the density and temperature of the pedestal.

How can we understand this freak of nature that we have stumbled on? There are two main problems: (1) How do the sheared fields in the barrier layer reduce the diffusion rate and (2) what causes this layer to form and how can we control that?

These have occupied the thoughts of a large fraction of fusion physicists for over two decades. One annual conference devoted to this topic has been going on for over 20 years. Sheared flows have good and bad effects. On the one hand, they can cause an instability, called the Kelvin-Helmholtz instability, which is well known in hydrodynamics. It is the instability that causes wind to ripple the surface of water. On the other hand, shear can quench an instability or at least limit its growth. In hydrodynamics, there is a simple theorem that tells what shape of shear is stable or unstable. In plasma physics, no such simple result is possible because so many kinds of waves can exist in a magnetized plasma. It is also difficult to make measurements in such a thin layer. The physics of the transport barrier — “edge physics” — is an ongoing study. The transport task force, a conference devoted to this topic, has been meeting yearly since 1988. More important, however, is to know how to turn on the H-mode. The threshold power depends on magnetic field, plasma density, and machine size. Since the H-mode threshold has been observed in so many machines, it was possible to formulate a scaling law that tells how the threshold depends on these various parameters. This is shown in Fig. 7.26b.

The H-mode has benefited not only our ability to confine plasma, but it has also improved our knowledge of plasma physics. Even the way in which the plasma’s energy escapes from the barrier has turned out to be a considerable problem. It escapes by means of yet another instability, call an ELM. This is described in the next chapter.