To describe the development capability of a fuel cycle, it can be useful to cal­culate the doubling time of a given system. It corresponds to the time needed to breed enough fissile element to start a new reactor. It can be defined by

Td(years)=-F— (П.3)

-FNa

0.99 0.98 0.97 0.96

where I is the inventory of the fissile element, 1 — ц the fraction of the elec­tricity produced which has to be used for the accelerator (ц = 1 for a critical system) and F the fission rate per year (around 1000kg/GWe depending on the thermal efficiency of the system).

An alternative definition of the doubling time can be the time which is needed by Nr reactors to double the installed power, with Nr very large. We denote this doubling time T“. In this condition, we can write that the fissile breeding during dt is NrFNadt, and the number of new reactors which can be built during dt is

which leads to

Nr = Nr(t = 0) exp ^FNa t

and

For a solid fuel cycle, the cooling time (around 5 years) has to be taken into account: one has to alternate two cores.[55] The fissile inventory is thus twice as large, and is around 15 tons in a fast lead cooled reactor of 2500 thermal GW. Considering ц = 0.9 and Na = 0.3, we find a doubling time of 55 years (T“ = 38 years). This is a typical doubling time for a fast- spectrum core.

The breeding rates can be improved using gas as coolant, which leads to a faster spectrum, as compared with lead cooled systems, and makes the fission of 232Th non-negligible (around 8% of the total fissions). The core can be surrounded by a large thorium blanket, in order to minimize neutron leakage and to optimize the captures on 232Th. The elements of this blanket have to be changed every 2 months, in order to avoid modifying the evolution of the reactivity. The 233U produced is then accumulated to start a new reactor. The 233U of the core is reprocessed, with all other actinides. Different subcriticality levels are obtained by playing on the proportion of fuel in the core. Figure 11.5 shows the annual growth factor of such a system, as a function of the multiplication factor, for two different blanket configurations. A doubling time TU of 40 years is obtained for k = 0.97 and 60 years for k = 1 (by extrapolation). With this the advantages of hybrid systems for development of fast thorium reactors can be quantified. Subcriticality can help for a deployment of the nuclear power on a few tens of

years at the scale of a single country, but appears not to be sufficient to consider a fast increase of the share of nuclear power in the world in 20 or 30 years.

At the end of this section we mention a scenario which associates fast — neutron reactors and molten salt thorium reactors, allowing a very fast growth of world nuclear energy.