The triple product plotted in Fig. 8.20 contains the energy confinement time te, which is how long each amount of energy used to heat the plasma stays in there before it has to be renewed. The plasma energy is lost through three main channels: radiation, mostly in the form of X-rays, and escape of ions and electrons to the wall, carrying their heat with them. The first two of these, radiation and ion loss, follow theory and can be predicted, but electrons escape faster than can be explained. The energy loss by electrons can be measured, but it cannot be predicted. It would be

Fig. 8.21 Data from 13 tokamaks showing that the energy confinement time as measured follows an empirical scaling law12 impossible to design a new machine accurately without knowing what te would be, but fortunately the over 200 tokamaks that have been built were found to follow an empirical scaling law. This formula12 gives the value of te in terms of the size and shape of the tokamak, the magnetic field, the plasma current, and other such fac­tors. The result is shown in Fig. 8.21.

This empirical scaling law is the basis on which new tokamaks are designed. It can­not be derived theoretically, but it is followed in a massive database from a variety of tokamaks. This “law” is given in mathematical form in footnote 12. Most of the dependences are consistent with our understanding of the physics. For instance, te increases with the square of the machine size. The strength of the toroidal field does not matter much because the size of the banana orbits depends on the poloidal field. The poloidal field indeed enters in the linear dependence on plasma current. The wonder is that only eight parameters are needed to make all tokamaks fall into line. As seen in Fig. 8.21, the data cover over a factor of 100 in te. To design ITER, the scaling had to be extrapolated by another factor of 4.