10.73. The conditions under which breeding is feasible will be developed shortly, but for the present it is sufficient to state that a breeder will usually consist of a core, containing both fissile and fertile species, surrounded by a blanket initially containing only the fertile species. Fissile nuclei are then produced from the fertile nuclei in the core and also in the blanket by neutrons which have escaped from the core.

10.74. Bearing the foregoing in mind, the breeding ratio defined by equation (10.10) can be represented by

І ф2?г1і1е dV + І ф2£егШе dV

. J core./blanket

BR (at a given time) = ————- ^———————————— , (10.13)

ф(2г + 2c)fissile dV

J core

where and are the macroscopic fission and capture cross sections, respectively, for the indicated species, and dV is a volume element. (The destruction of fissile nuclei in the blanket is neglected.) By integrating over the core and blanket volumes, the breeding ratio is an average over the whole reactor system. It is to be understood that the neutron spectra are different in the core and blanket systems. As noted earlier, equation (10.13) refers to a particular time, at which the values of ф and S are applicable.

10.75. It will now be assumed that all the neutrons leaking from the core will eventually be utilized for breeding by capture in the blanket. This assumption is fairly reasonable since some neutrons are formed by fission in the blanket to compensate for neutrons lost in parasitic (nonbreeding) processes and by escape. If the total breeding ratio is divided into two

since T) is equal to v/(l + a) by equation (2.57).

10.76. The fission cross section ratio does not vary significantly with neutron energy; hence, an indication of the effect of neutron energy on the potential for external breeding (or conversion) is given by the corre-

sponding value of r| — 1. Approximate data for several energy ranges are quoted in Table 10.1, and general trends (omitting fine structure) are shown in Fig. 10.8. It is seen that only in a comparatively fast neutron spectrum (>0.1 MeV) is t) — 1 sufficiently greater than unity to make plutonium — 239 breeding practical. Breeding of uranium-233 from thorium-232 should be theoretically possible, although with a smaller efficiency, in a thermal spectrum as well as in a fast spectrum.

10.77. The internal (or core) breeding ratio is given by

ф^егШе dy

where 1/(1 + a) = t]lv by equation (2.57). It is seen from Table 2.9 that the highest values of ті/v arise in a fast-neutron spectrum for all three fissile species. Hence, the internal breeding ratio is largest in such a spectrum. Apart from its contribution to the total breeding ratio, internal breeding has an important bearing on fuel-cycle costs since fissile material produced in the core can be utilized directly without the necessity of going through reprocessing and fabrication stages. It is apparent from equation (10.15) that the internal breeding ratio for a given fertile-fissile nuclide system depends on the core composition, since this determines the macroscopic cross-section ratio. For example, an increase in the ratio of fertile to fissile atoms in the core would lead to an increase in the internal breeding ratio. There is a general decrease in breeding ratio as the core is diluted with inert material because of spectral softening which results in a greater par­asitic capture of neutrons in inert diluents.