What Have We Accomplished?

A controlled fusion reaction requires holding together for a long enough time a plasma that is hot enough and dense enough. These critical conditions can be quan­tified by the triple product Tut, a modification of the Lawson criterion explained in Chap. 5. Here, Tis the temperature of the ions, the reacting species; и is the density of either the ions or the electrons, since the plasma is quasineutral; and t (tau) is the energy confinement time, a measure of how fast (or slowly) energy must be applied to keep T constant. Over the years, over 200 tokamaks have been built, and the value of Tut achieved in each has been calculated. Some of these are plotted in Fig. 8.1 as a function of time. This measure of success has increased over 100,000 times in four decades, recently doubling every two years.

Most of this increase has come from the confinement time. The first experimental machines suffered from hydromagnetic instabilities such as the Rayleigh-Taylor and the kink instabilities described in Chap. 5. These can take the plasma to the wall at the speed of a field line wiggle called an “Alfven wave,” which limits the confine­ment time t to microseconds. Once these were controlled, t increased a thousand-fold to several milliseconds, at which point microinstabilities were the limiting factor. After years of understanding banana orbits, magnetic islands, ballooning modes, and connection lengths, these instabilities were minimized; and t increased another thousand times to the present value of several seconds.

The rate of progress in fusion can be compared with that in the development of computer chips, the famous Moore’s Law. Gordon Moore had predicted that the number of transistors on a chip would double every two years, an unbeliev­able rate which was actually followed almost exactly. Figure 8.2 shows how this growth compares with a range of doubling times. The fusion figure of merit in Fig. 8.1 keeps pace with Moore’s law, now also doubling every two years. Both of these outstrip Livingston’s law for particle accelerators; where the energy doubling time is three years.

‘Numbers in superscripts indicate Notes and square brackets [] indicate References at the end of this chapter.

F. F. Chen, An Indispensable Truth: How Fusion Power Can Save the Planet,

DOI 10.1007/978-1-4419-7820-2_8, © Springer Science+Business Media, LLC 2011

Fig. 8.2 Moore’s Law for semiconductors compared with doubling rates

Here are pictures of the four large tokamaks which provided the points at the top of these graphs (Figs. 8.3—8.6).1

As you can see, or cannot see, the tokamak itself is hidden behind a jumble of equipment which includes the neutral-beam injectors, power feeds to the coils, the support structure, and diagnostic instrumentation. To show the size of these machines, Fig. 8.7 is an inside view of the vacuum chamber of DIII-D when it is opened up to air.