Very qualitatively then, safety can be said to penalize the breeding ratio. If one designed for a large Doppler coefficient by having a softer spectrum with more resonances below 10 keV playing a significant role, then the breeding ratio would decrease.

Fortunately, however, other considerations also demand a softer spec­trum. The ceramic fuel required to increase the fuel lifetime, the coolant required to remove heat, the cladding for support and containment, and the fertile material in the core to reduce the reactivity swing during burn — up—all these degrade the spectrum and give rise to a reasonable Doppler coefficient anyway.

However, one would like to soften the spectrum a little more to increase the Doppler coefficient and gain an extra safety margin. This has to be done while keeping strict account of the resultant breeding ratio. If there were a particular need to enhance the Doppler feedback, then one could soften the spectrum and improve the Doppler coefficient by:

(a) Choosing a low molecular weight fuel with moderating atoms. Metal fuel gives the smallest Doppler coefficient and this is improved successively by changing to carbide, nitride, and then oxide fuels.

(b) Adding beryllium oxide to the core.

(c) Using boron and not tantalum rods for control, although then more boron would be required for the control required.

(d) Using a relatively low temperature and using the jT dependence of the Doppler coefficient. This solution is not available in a power producing system.

(e) Making sure that the plutonium and uranium isotopes are intimately mixed in the fuel. The point here is to keep the uranium that gives the negative contribution to the Doppler coefficient in close association with the plutonium where the neutrons are produced by fission and where, otherwise, only a positive Doppler coefficient would result. In fact, because the plutonium and uranium tend to migrate away from each other at high burn-ups, the Doppler tends to be delayed as a function of burn-up and could also be reduced if the separation were sufficient to cause spectrum changes.

The other coefficient of great interest in the sodium-cooled system is the sodium void coefficient. This too can be affected by the design.

Figure 1.15 shows the neutron worth (adjoint flux) as a function of energy plotted against the background of a fast spectrum. An increase in

the mean neutron energy clearly results in an increase in reactivity. This is the main effect of voiding the center of a sodium-cooled core where leakage has very little effect, so that design changes seek to alleviate this effect by flattening out the worth curve or by moving the mean neutron energy lower to a positive slope of the worth curve.

Several design choices will accomplish this effect:

(a) Add a nonvoidable moderator such as beryllium oxide.

(b) Use NaK rather than sodium in the first place. It is a poorer mod­erator and thus its removal makes less difference to the neutron energy (but the use of NaK would also reduce the Doppler coefficient).

(c) Use dilute fuel to soften the spectrum as for the Doppler effect above.

(d) Use clean 239Pu with no higher isotopes which have a greater worth in neutrons produced per fission.

(e) Use 233U as the fissile species and so flatten the worth curve above 1 MeV.

(f) Use a higher core pressure to maintain a higher vapor density after voiding with a consequent slightly softer spectrum.

(g) Increase the sodium inventory in the core to make the spectrum much softer initially.

Then one can also use design to increase the leakage effect:

(h) Use a pancake or modular core to increase the leakage.

(i) Power flatten and decrease the core size and so increase the effect of leakage. This would not help at the center where the power is of course always flat.

However voiding effects are not necessarily all important; time effects may be more important in particular accidents and, of course, the avoidance of accidents in the first place, by providing a reliable system, is the primary objective of safety engineering.