In every tokamak discharge, there is a magnetic surface where q = 1. Inside that surface, where q is less than 1, the plasma is unstable to kinks, according to the Kruskal-Shafranov limit. Therefore, it is turbulent and a jumble of oscillations, and

there is no magnetic confinement. Only when plasma gets outside the q = 1 surface and enters the nested magnetic surface and island structure, does it get restrained by the magnetic field and diffuse slowly to the wall.

Very early in tokamak research, experimenters using a synchrotron-radiation method to detect changes in electron temperature observed regular oscillations near the q = 1 surface. These were observed in all tokamaks and always had a sawtooth shape, rising slowly and falling sharply each time, as seen in Fig. 7.5. Since the current is largest inside the q = 1 surface, near the center, the plasma gets hotter there. Higher temperature means less resistivity, and that makes the current even larger and more peaked. When the shape of the current profile changes, so does the whole island structure, as seen in Fig. 7.3. Finally, the magnetic structure is so disturbed that the steady state can no longer be maintained, and the plasma has to change. What the tokamak does is to eject the overly hot plasma in outward bursts, thus cooling the center back to normal. This explanation was for a long time only a conjecture, but recent advances in instrumentation have enabled actual movies of these sawtooth bursts to be taken in real time. These movies show that the tempera­ture actually oscillates several times before the big crash, when hot plasma is shot out and replaced by cooler plasma. Still frames from the movie by H. K. Park of the Princeton Plasma Physics Laboratory are shown in Fig. 7.6, but they do not do justice to the actual product [3].