In systems using solid fuels as small a variation of kx as possible between two refuelling events is sought. From equations (3.133), (3.134) and (3.135) it is

(a) (b)

Figure 3.9. Model fuel evolution in a Th-U hybrid system. The fast neutron flux is 4 x 10 n/cm /s. The evolution of the concentrations of U and fission fragments (F. F.) with respect to 232Th are shown in (a), the evolution of in (b).

seen that the value of k1{t) depends on the initial concentration of the fissile element. An initially breeding value of this concentration induces an increase of k1(t) with time. This increasing trend may be more or less exactly com­pensated by the decrease of k1 caused by the increase of the concentration of fission products. Rubbia et al. [76] have shown that such a compensation was possible over long periods of time. To illustrate the mechanism of this compensation, we use our simple three-component model where we choose representative values of the cross-sections for a fast reactor using the thorium cycle. Thus, referring to table 3.2, the capture cross-section of the fertile nucleus is taken to be 0.45 barns and the fission cross-section of the fissile nucleus to be 2.75 barns. The average capture cross-section for fission products was taken to be 0.15 barns, according to recent calculation results.[25] Starting from a state without any fissile component, figure 3.9 shows the evolution of the fissile part, of the fission product part (a), and that of the multiplication factor k1 (b). The evolution of k1 shows a maximum after about 7 years, starting from zero concentration of 233U. After 3 years, the concentration of 233U is close to 0.135. Starting with this concentration the value of k1 is reasonably found to be constant for at least 5 years, as shown in figure 3.10(b). The maximum value of кж shows that the neutron economy for a critical reactor would be difficult since only 6% of the neu­trons are available for sterile captures and leakage. This point will be dis­cussed later, in more realistic terms. In figure 3.10(a) we show the evolution of k1 when the fissile component initial load noticeably exceeds the equilibrium value. Here there is a fast and continuous decrease of the reactivity. This means that solid fuel hybrid reactors would not be a good choice for incinerating without regenerating a highly fissionable nucleus like 239Pu, for example.

Figures 3.11(a) and (b) are equivalent to figures 3.9(b) and 3.10(b), but for a thermal reactor with the same specific power corresponding to a flux of 4 x 1014 n/cm2/s.[26] One sees that, if the neutron economy is slightly improved (higher value of kx at maximum), kx is stable only for a very short time, less than 1 year. This difference between fast and thermal systems was stressed by Rubbia et al. [76]. Figure 3.11(a) also shows that the electro-breeding^ of 233U is much faster for thermal reactors than for fast reactors. This is a reflection of the fact that the equilibrium concentration of 233U is seven times smaller for thermal reactors.

(a) (b)

Years Years

Figure 3.11. Variation of kx for a thermal system using the Th-U cycle. (a) Starting with no U present in the system at time 0. (b) Starting with an initial concentration of U slightly below the equilibrium value.