4.3 Reactor design considerations

Section 4.4.2 of this chapter indicated that a value for кgreater than unity may theoretically be pos­sible in a reactor design in which natural uranium fuel is combined with a moderator material where the elastic scattering collisions convert fast neutrons of the fission events into thermal neutrons. However it is not clear at this stage how to proceed further with specifying the reactor design to ensure k« > 1 or indeed if к» > 1 is achievable in any real practical design. The designer will need to know, for example, how much moderator is needed relative to the fuel; how should the fuel be dispersed in the moderator and what effect the option of slight fuel enrichment may have on the design.

In other words, an understanding is required of what factors determine the value of k® in order to optimise these factors and hence maximise k®.

4.4 The neutron life cycle

The infinite multiplication factor k® is a measure of the number of neutrons in one generation of the chain reaction relative to the number in the previous generation. In order to gain an understanding of the factors that make up the overall value of k® it is therefore sensible to ‘observe’ a generation of neu­trons until they have been replaced by the next gen­eration of identical neutrons; that is, to study the neutron life cycle.

It will be seen that the neutron life cycle may be regarded as comprising four distinct stages. A mea­sure of the ‘efficiency’ of each stage is useful and this is done by dividing the number of neutrons at the end of a particular stage by the number at the beginning of that stage. The four stages of the neutron life cycle are illustrated in Fig 1.13.

The mathematical analysis of the neutron life cycle of Fig 1.13 can be referred to in the literature; never­theless it is useful to consider qualitatively each of the four stages. As it is a cycle it is not imperative to ‘start* at aiiy particular stage — let us here start with Пі thermal neutrons in the moderator.

To clarify matters further, numerical values are given in the brackets for the number of neutrons at each stage (n 1 = 1000) and for the four factors. These values do not represent any particular reactor design.