The most familiar application of fast reactors is as breeders, designed to turn fertile material into fissile. A simple performance indicator for a breeder reactor is the Breeding Ratio B, defined by

B = (rate of production of fissile material)/

where ^cfertiie is the macroscopic cross-section for neutron capture in fertile material and £afissile for absorption in fissile. The sums run over all energy groups and the integrals over the entire reactor including the breeder region.

B is widely used as a measure of the effectiveness of a breeder reactor, but it suffers from the major disadvantage that it does not take account of the differences between the isotopes. It counts an atom of 241Pu as being equivalent to an atom of 239Pu, whereas in fact the fission cross-section of 241Pu is higher and its capture cross-section is lower, so it is more valuable as a reactor fuel. A better measure of breeding is the “Breeding Gain” introduced by Baker and Ross (1963). This is based on an assessment of the values of the various isotopes as contributors to reactivity using perturbation theory in a simplified form involving a single energy group.

If there is only one neutron energy group we can see from equa­tions 1.27 and 1.30 that neutron flux and importance, ф and ф*, are proportional. If equation 1.25 is then rewritten for a single group we have

Sp a 5 (v £ f — £ f — £ c ф2 + SD (Уф)2 dV (1.42)

R

because £r = £f + £c, and the scattering terms are no longer signi­ficant. The macroscopic cross-sections are averages over the whole energy range weighted with фф*. Thus, for the fission cross-section,

£ f = £ Ntaft, (1.43)

І

where the subscript i represents the nuclides of which the reactor is composed, Ni is the number of nuclei of i per unit volume, and a fi is the average microscopic fission cross-section of i. The average is taken over the entire neutron energy range, weighted with фф*; i. e.

п TO I г — TO

a fi = a fi(E )ф(Е )ф* (E )dE ф(Е )ф* (E )dE, (1.44)

where ф (E) and ф* (E) are the fundamental mode flux and importance.

It follows from equation 1.42 that, if the effect of scattering is neglected, the reactivity increase when an atom of i is created is pro­portional to wi, where

Wi = va fi — a fi — a d. (1.45)

wi is the “worth” of an atom of i and measures its usefulness for building a new reactor of the same design. The “Breeding Gain”, G, is then defined as the net increase in worth (summed over all the nuclides present in the reactor) divided by the worth of the nuclides destroyed. It is still rather artificial because it assumes that the changes are distributed throughout the reactor in proportion to the numbers of nuclides present. (Thus fissile nuclides generated outside the core in a breeder region are assigned the worth they would have if they were in the core.) It nevertheless indicates the rate at which new cores, of the same specification, could be assembled when all the core and breeder fuel is reprocessed.

It is clear from the way they are defined that G & B — 1, but there is no algebraic way to show this to be the case.