On the fusion triple product and fusion power gain of tokamak pilot plants and reactors

The energy confinement time of tokamak plasmas scales positively with plasma size and so it is generally expected that the fusion triple product, nTτE, will also increase with size, and this has been part of the motivation for building devices of increasing size including ITER. Here n, T, and τE are the ion density, ion temperature and energy confinement time respectively. However, tokamak plasmas are subject to operational limits and two important limits are a density limit and a beta limit. We show that when these limits are taken into account, nTτE becomes almost independent of size; rather it depends mainly on the fusion power, Pfus. In consequence, the fusion power gain, Qfus, a parameter closely linked to nTτE is also independent of size. Hence, Pfus and Qfus, two parameters of critical importance in reactor design, are actually tightly coupled. Further, we find that nTτE is inversely dependent on the normalised beta, βN; an unexpected result that tends to favour lower power reactors. Our findings imply that the minimum power to achieve fusion reactor conditions is driven mainly by physics considerations, especially energy confinement, while the minimum device size is driven by technology and engineering considerations. Through dedicated R&D and parallel developments in other fields, the technology and engineering aspects are evolving in a direction to make smaller devices feasible.