10.67. The conversion ratio is applicable to thermal reactors in which the fuel is natural or slightly enriched uranium. In deriving an expression for the conversion ratio, the formation (and consumption) of plutonium — 241 will be neglected since it is relatively small, at least initially, except in reactors employing recycled plutonium.

10.68. In a thermal reactor, plutonium-239 is produced as a result of
the capture by uranium-238 of thermal and resonance neutrons, formed by the slowing down of fast neutrons generated in fission. The rate of production of fission neutrons from a given fissile species in a thermal flux ф is фМгатіє, where N is the concentration of fissile nuclei, ua is the thermal — neutron absorption cross section, y is the number of fast neutrons produced per neutron absorbed in fissile nuclei, and в is the fast-fission factor (§3.143).

10.69. Of the fast neutrons produced, a fraction of Pt reaches the res­onance energy region, where Рг is the nonleakage probability in slowing down into the resonance region. If p is the resonance escape probability (§3.110), the fraction 1 — p of the neutrons in the resonance region is captured by uranium-238 to form plutonium-239. Hence,

Rate of formation of Pu-239 = ф{А238ст238 + [єР^І — р)2(Мтатп)]}, (10.11)

where а238 is the capture cross section of uranium-238 for thermal neutrons. The two terms on the right give the rates of production of plutonium-239 from uranium-238 by capture of thermal and resonance neutrons, respec­tively; the summation in the second term includes both fissile species, uranium-235 and plutonium-239. Soon after reactor startup with uranium (not recycled) fuel, the plutonium-239 concentration is zero; the rate of destruction of fissile nuclei is then фА235а235. The initial conversion ratio, as defined by equation (10.10), can thus be represented by

10.70. As the reactor operates and plutonium is generated, fissions (and captures) occur in plutonium-239 as well as in uranium-235; this tends to decrease the conversion ratio, mainly because of the large capture cross section of plutonium-239 for thermal neutrons (Table 2.8). Furthermore, fission products and heavy nuclides, including plutonium-239, compete with uranium-238 for resonance neutrons; this also results in a decrease in the conversion ratio. However, a large value of the initial ratio generally in­dicates a high conversion efficiency throughout the operating period of the reactor. A large conversion ratio is desirable because the fissile plutonium — 239 formed slows the decrease in the overall reactivity as the uranium-235 is consumed. As a result, the fuel burnup is extended.

10.71. It is evident from equation (10.12) that the conversion ratio can be increased by decreasing the resonance escape probability, i. e., by in­
creasing the resonance capture. One way whereby this may be achieved is by hardening the neutron energy spectrum (§2.102) so that the flux in the resonance region is increased. In a water-cooled reactor, a decrease in the moderator-to-fuel ratio, e. g., by closer fuel spacing, causes the neutron spectrum to be hardened. On the other hand, neutron leakage is increased, and fuel of a higher enrichment is needed to maintain the burnup, i. e., ДГ235/ДГ238 js increase(j These two consequences of spectral hardening have opposite effects on the conversion ratio.

10.72. In commercial water-cooled reactors, the fuel spacing is such that the initial conversion ratio is approximately 0.6. Of the plutonium formed, somewhat more than half undergoes fission during the normal fuel lifetime, and roughly one-sixth is lost by neutron capture. About one-third of the heat produced in a commercial LWR arises from the fission of plutonium-239 and plutonium-241.