Buildup of Plutonium in a Natural Uranium Reactor

In deriving an expression for the conversion ratio, account has to be taken of both thermal and epithermal capture of neutrons by the fertile material. Considering a reactor where the fissile material is and the fertile the rate of thermal neutron capture per unit volume in is simply S28 5 where S28 is the thermal macroscopic absorption cross section of and (j the thermal neutron flux. (In the present chapter, we use the standard convention of specifying isotope cross sections by where m is 

Equation (4.5) may be put in another form by introducing the neutron balance condition for the critical reactor. The production rate of thermal neutrons, which is given by the product rjaL25 P is equal to the thermal neutron loss rate due to absorption in U , moderator, and fission product poisons, and to leakage. Hence, 

It is readily apparent from equation (4.7) why the best conversion ratio is obtained for a fast reactor system. Apart from the more favorable value of rj at high energies (see Fig. 4.1), the fast fission factor can rise to a value as high as 1.3 in a fast reactor spectrum. In addition, the third factor on the right-hand side is reduced owing to the absence of moderator. Consequently, values of C greater than unity can be readily achieved for a fast reactor. 

It is of interest to consider the way in which Pu builds up in a thermal reactor originally fueled with with as fertile material. We assume that the initial number densities of and are N2s(0) and zero, respectively. N2S, the number density of U , is assumed to remain constant, since its destruction over the life of the fuel charge is small in comparison with the total quantity present. To simplify the calculation, we ignore the capture of neutrons in the intermediate products and Np (see Fig. 4.2) and assume that Pu is produced directly from U , an assumption which is reasonable in view of the relatively short half-lives of its precursors. 

The rate of formation of Pu from capture of thermal neutrons in U is N2 02z4 - The resonance absorption is given by an expression similar to the second term in the numerator of equation (4.5), with a corresponding term having to be added to include the fast neutron source from Pu, once this has built up enough to be a significant factor. If we assume that e is the same for and Pu, the resonance production of Pu is then 

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