Ever since the early days of tokamak research, it has been noticed that the plasma density could never be raised above a certain limit. Sometimes this limit was blamed on a loss of confinement via an unspecified instability, sometimes on exces­sive energy loss by radiation, and sometimes the plasma suffered a disruption. In 1988, Greenwald et al. [28] put together the data from different machines to see what the density limit depended on. They came up with a surprisingly simple answer: roughly speaking, the density limit depended only on the tokamak current per unit area! For those who would rather have a formula, the one for the Greenwald density nG2 is given in Note 8 hrs.8 This limit has been found to be obeyed in all tokamaks regardless of what mechanism causes the problem at high densities. No one has yet found a theory that explains this; the Greenwald limit is purely empirical. Figure 8.18 shows how well the Greenwald limit is obeyed in two large tokamaks. In almost all shots, the measured density cannot be raised above the straight line,

which is the Greenwald limit. This unexplained law is so universal that it is used in the design of future machines. The design would be to achieve, say, 85% of nG, or 95%, depending on how adventurous one wants to be.