The COE depends on some factors that are independent of the power core and others that are specific to fusion. These factors appear in the following formula for COE,

which at first seems rather daunting. However, it is not necessary to know what the formula means in detail; it is used here just as a convenient way to show what affects the cost. The COE is proportional to the quantities in the parenthesis times those in the

rL Л °’6 1

AJ <5pe0A bN4 n03 denominator of the fraction following it. Inside the parenthesis, r is the discount rate, a financial factor similar to interest rate that will be explained later. L is a learning factor which takes into account that the first of a kind is always more expensive than the tenth one made. L starts at 1 and gets smaller with learning, so COE drops. A is the availability, which is the fraction of time the plant is running rather than shut down for repairs. Larger A means lower costs. The fusion reactor designs have A’s ranging from 60 to 80%.

The first two quantities in the denominator at the right have to do with the whole plant, and the last two concern the quality of the plasma in the tokamak. Eta — thermal (pth) is the efficiency of converting heat into electricity. Pe is the size of the plant in terms of electrical power produced. The larger the better because of econ­omy of scale. Beta-normalized (BN) expresses the efficiency with which the plasma current can confine a large amount of hot plasma by creating the right amount of twist in the magnetic field. Finally, N is the ratio of the plasma density to that pre­dicted by Greenwald limit (Chap. 8) for a stable plasma. In the different reactor models, r varies from 5 to 10%, L from 0.5 to 0.7, A from 0.6 to 0.8, Hth from 35 to 60%, Pe from 1 to 2.5 GW, and N from 0.7 (safe) to 1.4 (speculative). Most impor­tantly, BN varies from 2.5 to 5.5, representing the progression from well-established data to hopefully achievable advanced tokamak operation. Figure 9.42 shows the COE predicted from the PPCS models A-D as a function of the learning factor L.

As an example of how sensitive the COE is to assumptions made in the models, Fig. 9.43 shows how the availability factor A changes with the lifetime of the materials

in the first wall and blankets. The lifetime is expressed as the neutron fluence that the materials stand before they have to be replaced. The fluence is measured in years at an equivalent neutron energy flux of 1 MW/m2. The shorter the lifetime, the more often the blankets will have to be replaced, and hence the lower the availability. This then increases the cost (the higher blue points at the left).