The achievement of reversed shear led to an even more important discovery: internal transport barriers or ITBs (another acronym that I shall avoid). These are like the H-mode pedestal but can be created inside the plasma, away from the walls. They effectively stop the fast transport of plasma to the walls caused by instabilities and turbulence. At the radius where the q profile is at a minimum, the shear in both the poloidal magnetic field and the poloidal E x B drift is so strong that most instabili­ties are quenched, and anomalous diffusion comes to a stop, as if there were a wall in the middle of the plasma. This is another unexpected benefit discovered only by painstaking experiment on large tokamaks. Figure 7.28 shows how an internal transport barrier should be designed. If it is placed close to the axis (dashed line), the hot, dense plasma will be limited to the small volume inside the barrier. Furthermore,

it turns out that a barrier placed further out, as shown by the solid lines, is more consistent with the current profiles achievable with bootstrap current. The width of the barrier also makes a difference. It has to match the size of the turbulent eddies to be suppressed. Since the large eddies are more dangerous, the barrier should not be too narrow.

To create a good internal barrier, the current profile has to be manipulated so that it does not peak at the center, as it tends to do. This is done by adjusting the current in the ohmic heating coils and using waves to drive additional currents (noninduc­tive current drive). The wave used is primarily the so-called lower-hybrid wave, but electron cyclotron waves are also used. The radial location of the currents driven by waves can be adjusted by changing their frequencies. In the most intense discharges produced to date, the bootstrap current can make a significant contribution. Internal transport barriers have been produced in all four of the largest tokamaks in operation: the ASDEX Upgrade in Germany; the DIII-D in General Atomics of San Diego, California; the JT-60U in Japan; and JET, the European tokamak in England. A fifth large machine, the TFTR in Princeton, New Jersey, has been decommissioned and scrapped as a result of budget cuts by the US Congress. The example shown here is from the DIII-D [11].

In the following example, a double barrier was actually achieved, consisting of an H-mode edge barrier in addition to an internal barrier. The q profiles are shown in Fig. 7.29, one with the internal barrier alone and one with a double barrier. In neither case does the q-value drop below the Kruskal-Shafranov limit of 1.

The effect of the barriers on the plasma is shown in Fig. 7.30. Both curves show the high temperatures and density inside the internal barrier, and the solid curve shows the large increase in temperature when the edge barrier is added.

That the transport barriers dramatically reduce the losses and increase the energy containment in a tokamak is shown in Fig. 7.31. What is shown is the radial variation of the thermal diffusivity % (chi) of ions and electrons; that is, the rate at which their energies are being transported outwards at each radius in the discharge. A low value is good; a high value is bad. The dotted curves show % when there are no transport barriers. As before, the dashed curves show the case with an internal barrier alone and the solid one with both barriers. These dip well below the barrier-less curve inside the barriers. At the bottom of the % plot, are thin lines showing what % should be according to neoclassical theory; that is, if there were no instabilities. Normally, the turbulence level from microinstabilities makes % much larger than the ideal theoretical value. Here, we see that the internal barrier has brought % down to the ideal level for the first time, at least in the inside part of the plasma.

These results were obtained in a powerful tokamak, with 1.3 MA (megamperes) of toroidal current, a toroidal field of 2 T (20,000 G), and a bootstrap-current frac­tion of 45%. For best barrier formation, it was found that it was better to heat the

plasma with neutral beams injected opposite to the direction of the tokamak current than along it, as in the usual case. This could be done without moving the large beam injectors by simply reversing the polarity of the current in the ohmic heating coils. In the larger JET tokamak, running with DT instead of pure deuterium, ion temperatures up to 40 keV, maintained for almost 1 s, were achieved with an inter­nal transport barrier. The magnetic field there was 3.8 T, and the plasma current was 3.4 MA [12]. Taken together, the data from the large tokamaks, especially those with large bootstrap fraction, give credence to the hope that the Advanced Tokamak scenarios can be used in the design of a practical reactor.

Although the possibility that reversed shear and internal transport barriers could reduce the plasma loss rate was predicted theoretically [13, 14], turning the idea into reality depended on the availability of machines large enough to produce this effect and on hands-on twiddling of these machines to attain the right conditions. The diagnostics needed to quantify these results with detailed measurements inside the plasma also required major equipment and advanced technique. For instance, to get the q(r) profiles a sophisticated method called Motional Stark Effect was used which actually measures the pitch of the field lines at every radius.

Fusion has suffered from the reputation that it is always promised to be available in 25 years. This was because the difficulties were not initially known. They have been overcome, but it took time and funding to build the necessarily large research machines, to train a generation of plasma physicists, and to develop the diagnostic tools to be able to see what we are doing. The underlying physics is now understood well enough that more accurate estimates of what it takes to make magnetic fusion work can be made. Thousands of dedicated physicists and engineers labored for decades to bring fusion within the foreseeable future. There are still a few physics problems to be solved, as described in the next chapter. Engineering is another matter. What has to be done to make fusion reactors practical is the subject of Chap. 9.

Notes

1. Courtesy of Roscoe White.

2. An acute reader would ask, “Why don’t we just let those non-gyrating particles go and con­fine the rest?” The reason is that those particles which have leaked out would be quickly regenerated by the plasma in what is called a velocity-space instability. It is another of a plas­ma’s tricks to bring itself to thermal equilibrium without waiting for collisions to do so.

3. A nice treatment of this is given by Jeff Freidberg, in Plasma Physics and Fusion Energy, Cambridge University Press, 2007.