1.7.1 Neutron Economy

To ensure the safety of a reactor it is essential to control the reactivity in such a way that it does not become supercritical and generate excessive amounts of heat. This may be easier if the reactor is designed to remain subcritical, so that criticality is not possible at least in normal operation. The advantages of this approach are discussed in Chapter 5.

A subcritical reactor is a multiplying assembly with ke < 1 that is driven by a neutron source. The relationship between power P, source-strength S and ke is of the form

P a S/(1 — ke).

The neutrons might come from spontaneous fission of curium isotopes (see section 1.4.1), or the 9Be(a, n)12C reactions in a radium-beryllium assembly, but for a power reactor a controllable source is required, such as can be provided by a particle accelerator. Such a system is known as an “accelerator-driven reactor” (ADR) or “accelerator — driven system” (ADS). In most cases it involves an accelerator (a linear accelerator for example or a cyclotron) that delivers a beam of high-energy protons to a spallation target consisting of material with high atomic weight located in the subcritical core. The target produces a cascade of high-energy neutrons that drive the reactor. An ADR can be seen as a device for producing neutrons that can be used for a variety of purposes — breeding fissile material such as 233U from thorium, transmuting radioactive nuclear waste (either fis­sion products or higher actinides) to reduce its hazard, or generating power.

The subcritical assembly acts to multiply the neutron output of the spallation source, and the multiplying factor depends on its ke. Figure 1.29 shows the neutron economy of an ADR. It is greatly simplified but illustrates the important aspects.

This simplified analysis shows that n + S = 1 + L + C, where, for each fissile nucleus destroyed, n = v/(1 + a), where a = af /(af + ac) is the number of fission neutrons generated; S is the number of source neutrons injected into the assembly; L is the number of neutrons lost by being captured in structure, coolant, shielding, etc.; and C is the number of neutrons available for use. In addition since the chain reaction produces n new neutrons from n + S neutrons, ke = n(n + S), so, after rearranging the terms,

S

C=it-m -1 — L (149)

For a critical reactor S = 0 and ke = 1, and

C = n — 1 — L.

If the ADR is operated as a breeder, C is the breeding ratio. If it is operated as a consumer of higher actinides account must be taken of the capture events in the fissile fuel, each of which may lead to the production of a new higher actinide nucleus, so the net reduction in the number of higher actinide nuclei is C — ac/(ac + af) = Ca(1 + a) per fuel atom destroyed.

As explained in the Introduction for a critical reactor L is in practice around 0.2, mainly because neutrons are captured in control absorbers. However it may be possible to control an ADR by means of varying the neutron source strength, in which case control rods may be unne­cessary. This might allow L to be reduced to around 0.1.