4.1 The chain reaction

Although the binary fission of a nucleus by an im­pinging neutron would no doubt be of academic interest, it would in itself be of little significance in the context of large scale power production. It is the accompanying release of neutrons which makes power production possible in that the neutrons may induce further nuclei to fission and thus lead to a chain reaction. Figure l. tl shows a rapidly diverging chain reaction.

Figure 1.11 is unrealistic because it presumes 100% fissionable material with no scattering events and no loss of neutrons by capture events or by leakage of the neutrons out of the system. However the figure is useful to illustrate the principle of a chain re­action and also for the need to ‘measure’ what is happening.

4.2 The multiplication constant к

The development of a chain reaction may be mea­sured by the multiplication constant (or reproduction factor) which is defined to be к = (number of neu­trons arising from the chain reaction in one genera — tion)/(number of neutrons arising from the chain reaction in the previous generation).

For simplicity it is advantageous at this stage to retain the presumption implicit in Fig 1.11 that there is no loss of neutrons out of the system; that is, the system — the nuclear reactor — is assumed to be of infinite size. The symbol is now used for the multiplication constant, the subscript infinity (®) being a reminder of the imposed condition of an infinite sized nuclear reactor. From the definition of the multiplication constant it is clear that:

• If kcc>l the chain reaction is diverging and the nuclear reactor is said to be ‘supercritical’. As the power produced is related to the number of fission events taking place, this is the condition for power raising. The larger the value of k«, the quicker is the rate of power rise.

• If ke = 1 the chain reaction is self-sustaining and the reactor is said to be ‘critical’. A nuclear power station producing power at a steady rate for per­haps months and years — a base load power station —■ is therefore critical. The word is unfortunate but understandable when it is recalled that the term ‘critical’ dates back to 12 December 1942. On that day Enrico Fermi and his colleagues first achieved a self-sustained chain reaction, an achievement which had aspects of uncertainty and peril for the participants.

• If к»< 1 chain reaction is converging and the reactor power is decreasing. As before, the rate of power decrease is determined by how much less than unity is the value of k®.