Equation 1.25 shows three effects of a change in density of a non­fissile isotope: a “moderating” effect due to the change in £sg^g<, a “capture” effect due to the change in Esg, and a “scattering” effect due to the change in Dg. There is a fourth “self-shielding” effect, which is shown in equation 1.40: if is changed all the group cross-sections for the resonant isotopes, such as £cg in equation 1.38, are altered. For lead-bismuth or gas coolant all these effects are small but not so for sodium. The various components of the sodium temperature coefficient of reactivity are as follows.

An increase in temperature reduces the density of the sodium and this reduces £cg giving an increase in reactivity and a positive capture contribution to the temperature coefficient, but it is a small contribution because the sodium does not capture many neutrons in the first place.

The reduction in has the effect of hardening the spectrum — that is of shifting the peak in ф shown in Figure 1.7 to a slightly higher energy. Figure 1.7 also shows that in a plutonium-fuelled reactor the peak occurs in the range where ф* increases with energy, so there is a gain in reactivity. Because sodium is an effective moderator this posit­ive moderating contribution to the sodium temperature coefficient is large.

As Ss decreases Scg decreases because ф* in equation 1.38 increases more than J. There is a similar effect on S f but, as in the case of a change in the fuel temperature explained later, in a breeder reactor the capture effect from 238U is greater than the fission effect from 239Pu and 241Pu so the reactivity increases, giving another small positive contribution to the sodium temperature coefficient.

These three components, due to the capture, moderating and self­shielding effects, are contributions to the фф term in equation 1.25, so they all depend on position in roughly the same way. They are greatest at the centre of the core and smaller at the edges. The effect of scattering is quite different, however. A decrease in the scattering cross-section increases the diffusion coefficient Dg and this results in a decrease in reactivity, depending this time on V фg — Уф*. It is therefore zero at the centre and reaches a maximum in the outer parts of the core.

Table 1.4 shows the effect of increasing the coolant temperature uniformly throughout the core of a small sodium-cooled breeder. In this case the resulting reactivity change is the small difference between two large quantities and is just positive, giving a small overall positive sodium temperature coefficient.

The effect of a local change in sodium temperature or of a local loss of sodium may, on the other hand, be positive or negative depending on where in the core it happens. Figure 1.26 shows the effect of loss of coolant from various points on the axis of the core of a larger breeder

Table 1.4 Components of the sodium
temperature coefficient of reactivity of
a small fast reactor

Component dk/д T (K 1)

reactor. Near the centre moderating, capture and self-shielding domin­ate and the reactivity change is positive, but towards the edges leakage becomes more important and it is negative.

Chapter 5 describes extreme hypothetical accidents in which the sodium is lost completely from all or part of the core. The reactivity

increase due to complete loss of coolant from the whole core of the small reactor of Table 1.4 would be 4 x 10-5, but if coolant was lost only from the part of the core where the sodium coefficient is positive it would be as high as 7 x 10-3. For a large 2500 MW (heat) reactor the effects are more positive, and the gain in reactivity might be 0.017 for complete loss of sodium and 0.020 if it was lost only from the central region.