To illustrate the effects of various design options on the flux and importance spectra, in the following paragraphs comparisons are made with the “reference core” described in Table 1.1, which is a simplified representation of a 2500 MW (heat) breeder reactor. The “absorber” component represents the effect of the control rods when the fuel is

Table 1.1 Reference reactor core specification Dimensions Circular cylinder Height 1m Diameter 2 m Buckling 18 m-2 Composition Coolant 50 v/0 Fuel 30 v/0 Structure 19 v/0 Absorber 1 v/0 Materials Coolant Sodium Density 840 kgm-3 Structure Stainless steel “ 7900 kgm-3 Absorber 10BeO2 “ 2000 kgm-3 Fuel (U, Pu)O2 Overall density 8900 kgm-3

new or of the accumulated fission products at the end of its irradiation life. The stainless steel structure is assumed to be 74% Fe, 18% Cr and 8% Ni. The overall density of the fuel material is 80% of the theoretical density of the oxide, allowing for porosity incorporated to accommodate fission products (as explained in Chapter 2). The spectra are derived from a fundamental mode calculation based on the ANL 16-group cross-section data (Tamplin, 1963). The enrichment E, defined as Pu/(U+Pu), is adjusted to make the reactor critical.

Figure 1.7 shows the spectrum of the flux in the reference core com­pared with the spectrum of neutrons as they are born in fission of 239Pu. (The fission spectrum for other isotopes is very similar.) The energy of the fission neutrons is reduced by scattering so that the peak is at around 0.3 MeV, and below this energy the flux falls off steeply until there are hardly any neutrons with energies less than about 1 keV. The spectrum in a fast reactor is very different from that in a thermal reactor.

At high energies, above about 0.5 MeV, inelastic scattering in 238U and to a lesser extent in 56Fe and 23Na is very important. Excitation of the lowest energy level of the 238U nucleus reduces the energy of a neutron by 45 keV and the corresponding values for 56Fe and 23Na are 845 and 439 keV respectively, so the effect of inelastic scattering is

Figure 1.7 Neutron flux and importance in the reference core.

very marked. At lower energies it is elastic scattering that reduces the energy of the neutrons and the lightest nuclei such as 23Na, 16O and 12C are the most important moderators. Many collisions are needed, however, to reduce the energy, and the chance that the neutron will diffuse out of the core or be absorbed is large, so the flux declines steadily with decreasing energy. A few of the neutrons are captured in 23Na or 56Fe but most are absorbed in 238U.

The neutron importance, also shown in Figure 1.7, increases with energy. Above 1 MeV it is high because of the possibility of fission in 238U. At low energies, below 3 keV, (not shown in Figure 1.7) it

rises with decreasing energy because the fission cross-section in 239Pu rises more rapidly than the capture cross-section in 238U, so the lower its energy the more likely a neutron is to cause fission and therefore contribute to the reactivity. It should be remembered that a neutron captured in 238U is lost as far as maintaining the chain reaction is concerned even though it causes the generation of a new fissile nucleus.

Fuel Material. The effect of replacing oxide fuel in the reference core by carbide or metal is shown by comparing the spectra in Fig­ure 1.8. (The overall densities are 10900 and 14300 kg m-3 respectively,

both 80% of theoretical.) Fewer moderating atoms are present in (U, Pu)C than in (U, Pu)O2 and even though a carbon nucleus is lighter than oxygen there is less moderation so the mean neutron energy is higher, as indicated by the fact that the peak in the spectrum is at a higher energy. This is usually called a “harder” spectrum. At the peak of the spectrum neutron importance increases with energy so the harder spectrum resulting from a change from oxide to carbide fuel allows fissile material to be replaced by fertile. As a result of this, and the higher fuel density, the enrichment is lower and there are more captures in the fertile material in the core. The importance is higher above 1 MeV because the enrichment is lower and more 238U is present, and it is lower at lower energies because the ratio of fissile material to absorbers is lower.

Similar, but greater, changes result if oxide is replaced by metal as the fuel material.

Coolant. The choice of coolant has a great effect on the neutron flux and the performance of the reactor mainly because it occupies such a large fraction of the core volume. The effect is mainly due to differences in the inelastic scattering at energies above about 1 MeV. Figure 1.9 shows the spectra for reference cores cooled by sodium, lead-bismuth eutectic (54.5%Pb, 45.5%Bi) and carbon dioxide. Lead- bismuth eutectic and carbon dioxide are much poorer moderators than sodium (lead-bismuth because the atoms are heavier, carbon dioxide because it is much less dense), so in both cases the flux spectrum is harder. The fission-neutron spectrum peaks at around 2 MeV (see Figure 1.7). Strong inelastic scattering in 238U and iron scatters many of these neutrons down to around 0.7 Mev, causing the sharp peaks in the lead-bismuth and carbon dioxide spectra. However elastic scattering in sodium is particularly strong at this energy so this peak is “smoothed out” in the sodium spectrum.

Although lead-bismuth is a poor moderator it has a high macro­scopic scattering cross-section, whereas that of a gas coolant is very low. As a result the former leads to a lower critical enrichment than

sodium and the latter to higher. Largely as a result of this the neutron importance curve is steeper for lead-bismuth and shallower for carbon dioxide.

Core Size. Figure 1.10 shows what happens if the core of the reactor is made smaller. It compares the spectrum for reference cores with — B2 = 18 m-2 (a cylinder 1 m high and 2 m in diameter) and — B2 = 28 m-2 (0.9 m high and 1.2 m in diameter). The difference is that 47% of the fission neutrons leak from the smaller core whereas only 32% leak from the larger. As a result the spectrum is harder and, as in the

case of a gas-cooled core, the importance curve is shallower because the critical enrichment is higher.

Plutonium Composition. These comparisons have been made assuming the fissile material in the core is pure 239Pu, but this is in prac­tice very unrealistic. The plutonium is most likely to originate from the reprocessing of irradiated thermal reactor fuel. In the thermal reactor higher plutonium isotopes are formed by successive neutron capture reactions, and the longer it is irradiated — i. e. the higher the burnup — the more of them there are. For example plutonium from AGR fuel irradiated to 20000 MWd per tonne consists of Pu-239, 240, 241 and

Figure 1.11 The effect of the thorium cycle.

Table 1.2 Neutron balances Ref. Core Metal Fuel Carbide Fuel Pb/Bi Coolant Gas Coolant Small Core AGR Plut. Thorium Cycle Enrichment (%) Neutron Production 25.8 14.6 20.1 22.2 28.0 34.7 30.8 26.8 Fissile Nuclides 0.904 0.836 0.875 0.913 0.902 0.922 0.813 0.982 Fertile Nuclides Neutron Consumption 0.096 0.164 0.125 0.087 0.098 0.078 0.187 0.018 Absorption in Fuel 0.488 0.538 0.514 0.513 0.462 0.444 0.486 0.519 Capture in Coolant 0.001 0.001 0.001 0.005 0.000 0.000 0.001 0.001 Capture in Structure 0.012 0.010 0.011 0.014 0.010 0.009 0.012 0.011 Capture in Absorbers 0.125 0.093 0.115 0.147 0.098 0.083 0.126 0.106 Leakage 0.374 0.358 0.359 0.321 0.430 0.464 0.375 0.363 Breeding Ratio 1.08 1.34 1.17 1.02 1.19 1.19 1.26 0.94

233U and 232Th. The flux spectrum is harder in the thorium case because there is less inelastic scattering at high energy. The enrichment is higher (27% compared with 23%) because the fission cross-section of 233U is lower than that of 239Pu in the 0.1-1.0 MeV range where the flux peaks. However there is a very significant difference in the importance spectra, which for the thorium reactor is almost completely flat. This is because the fission cross-section of 233U is significantly higher than that of 239Pu at lower energies.

Neutron Balance. Table 1.2 shows the sources and fates of the neut­rons in these cores and illustrates the effects of the different spectra. As compared with a thermal reactor, fast fission in 238U, and in the cases where they are present, 232Th, 240Pu and [1]Pu, is a more significant source of neutrons, and loss of neutrons by capture in the coolant or the structure is quite insignificant. In contrast many neutrons leak from

Figure 1.12 The effect of enrichment zones on the radial distribution of power.

the core, but these are not necessarily lost because they can be made use of if the core is surrounded either by a breeder containing fertile material or by waste materials to be eliminated by transmutation.

An oxide-fuelled thorium-cycle reactor with this specification would not breed because the capture cross-section of 232Th is lower than that of 238U in the keV energy range, but a higher breeding ratio can be attained with carbide fuel.