The q(r) profile of a tokamak discharge is perhaps its most important characteristic. It controls the stability of the plasma, where the magnetic islands form, and other essential features. An example of how the quality factor q varies with minor radius is shown in Fig. 7.2. It typically increases from 1 at the core to some number between 3 and 9 at the edge. Remember that q is the reciprocal of the rotational transform, so the twist of the magnetic field lines decreases gradually from the center to the edge of the plasma’s cross section. The changing degree of twist pro­vides the shear stabilization of instabilities. To increase the amount of shear would require q(r) to change over a wider range than 1-9. However, q cannot be too large, because then the twist would be too weak to cancel the particles’ vertical drifts; and q cannot be smaller than the Kruskal-Shafranov limit of 1, because, as we saw in Chap. 6, kink instabilities would occur. An obvious solution to this dilemma would be to make the twist change its angle several times, which would increase the shear without exceeding the bounds on q. This idea was never taken seriously earlier because there was no way to produce tokamak currents that would have to vary with radius in a screwy way. But now, all the large tokamaks have been able to produce “hollow” current profiles that are not peaked at the center but at some radius half­way out, as shown in Fig. 7.27. This generates a q(r) that is large at the center, falls to a minimum somewhere inside, and then rises again to a normal value at the edge.

Physically, the twist of the magnetic lines is very small near the center, gets tighter halfway out, and then gets gentle again near the edge. The twist angle changes more rapidly with radius, thus increasing the shear. A lower turbulence level is observed as well as a corresponding increase in confinement time.

Initially, hollow current profiles were produced transiently by a combination of ramped neutral beam heating (increasing the power in a prescribed way) and aux­iliary heating. This would not work for a reactor, which has to run in steady state; but by a fortuitous circumstance, bootstrap current can create hollow current profiles. This is yet another of Mother Nature’s gifts. With the large bootstrap fractions in reactor-level machines, it is theoretically possible to design an “Advanced Tokamak” scenario in which the pressure profile leads to a bootstrap current profile that produces reversed shear, and the resulting reduced diffusion rate is consistent with the pressure profile! This sounds like a pipedream, but, as we shall see, much of this has already been accomplished in experiment.