Appendix 1 Fast Spectrum Reactor Neutronic Considerations

Fast spectrum reactors can be used with either the U238/Pu239 cycle or the Th232/U233 cycle.1 The breeding ratio with the Th232/U233 cycle is somewhat lower than with the U238/Pu239 cycle. Nonetheless, as was mentioned earlier, there are some situations where the Th232/U233 cycle would be preferred such as in India, where there is relatively little naturally occurring uranium but abundant thorium. As a result, the Indians plan to initiate their LMFBR program using enriched uranium as the fissile material, but switch once they have accumulated sufficient U233 to support the Th232/U233 cycle. Their initial reactors will be fueled with fairly highly enriched uranium mixed with thorium to breed U233. The Th232/U233 cycle is also considered to have a lower non-proliferation potential since the U233 is highly radioactive and must be handled remotely. Although there has not been much analytic work on the subject, the Th232/U233 cycle may also have lower sodium void reactivity and therefore be attractive from that perspective.

There is a price that must be paid if fast neutrons are to be used in a fission reactor: the concentration of the fissile material must be much greater. The cross section for fission in a fast reactor is much lower than in a thermal reactor. While the cross section for fission of the U235 in a LWR is about 550 barns, the fissile component in a LMFBR will typically have a fission cross section in the 1.5-2.0 barn range, depending on the spectrum. As a result, the neutron flux tends to be much higher and it is necessary to raise the enrichment of fissile isotopes to a higher level than is required in LWRs. Whereas LWRs are typically fueled with uranium enriched to 2½-4% in U235, a large fast breeder may have Pu239 in the 15-30% range. Even with the higher concentration of fissile material in the core, the neutron flux will be at 20-100 times greater in a LMFBR than in a LWR. As a consequence, radiation damage of structural materials becomes a greater concern and must be dealt with in the design.

Because of the excellent heat transfer properties of sodium, the core tends to be much smaller and is somewhat pancake shaped. A large breeder reactor core may be just 3 ft. in height but 15 ft. or more in diameter.

Since core neutron energy is maintained high, there is no xenon or samarium poisoning of the reactor as is the case with thermal spectrum reactors. The accumulation of fission products in the core does insert negative reactivity but most of the neutron spectrum is well above the resonance region avoiding resonance captures of the type typified by xenon and samarium. While the average cross section of fission products in a thermal reactor is about 75 barns, that number is orders of magnitude lower in a fast reactor.

Burnable poisons cannot be used to extend core life as is sometimes done with LWRs. It is also not practical to poison the coolant with a material that can be readily removed as is routinely done on PWRs. Because of the spectrum, there is no convenient burnable poison material. Moreover, the use of a poison for this purpose would be a sink for neutrons and would conflict with the objective of breeding.

In addition to there being essentially no resonance region, there are no materials that exhibit high neutron capture cross sections such as hafnium that would be suitable for use as a control material. The best candidate for control material is boron, which exists in nature in two stable isotopes, B10 and B11. B10 is the better fast neutron absorber and represents about 20% of naturally occurring boron. If natural boron turns out to be inadequately absorptive, it will be necessary to enrich the boron in the B10 isotope. The operative reaction is B10 (n,α) Li7.

For those readers who are familiar with the four factor formula used with thermal spectrum reactors, K∞ = ηεpf, the terms ε and p, fast fission factor and resonance escape probability have no meaning in fast reactors. The term f, thermal utilization, would need to be redefined as the quotient of captures by the fuel and captures by all core materials. We can call it “neutron utilization” since there is no term for this factor that has wide spread usage in the nuclear community. If we were to retain the term “f” for this “neutron utilization”, then for fast reactors, K∞ = ηf.

The delayed neutron fraction, β, in fast reactors is comparable to thermal reactors, however since plutonium is the preferred fissile material in fast reactors and since β is lower for plutonium than for U235, the delayed neutron fraction is lower. Prompt neutron lifetimes are two to four orders of magnitude shorter in fast reactors than in thermal reactors. The smaller β and shorter prompt neutron lifetimes increase the burden on the control system. More is said on this subject in Appendix 2A where the fuel form is discussed and Section 10 on control systems.

The concept of spectral hardening and softening is somewhat unique with fast reactors.2 The term applies to the energy spectrum of the neutrons in the core. In any fast reactor, the spectrum will be softer, i.e. have lower energy than a fission energy spectrum since there will inevitably be neutron collisions with structural materials and the coolant. Even more important are the collisions with U238. About 80% of the non-absorptive neutron collisions with U238 are inelastic, meaning the neutron is briefly absorbed then re-emitted at a significantly lower energy followed by a gamma emission from the excited U238 nucleus. Most of the remaining 20% of the non-absorptive U238 collisions result in fission. Small metal fueled reactors with high Pu239 enrichment will tend to have the hardest, i.e. highest energy spectrum while large oxide fueled reactors with lower Pu239 concentrations will have a softer spectrum. All other things being equal, it is preferable to have a hard spectrum since the neutron reproduction is greater at higher incident neutron energy. Thus, a harder spectrum leads to a higher breeding ratio. However, all other things are not equal as will be discussed in Appendix 2A on the fuel form appearing next.

Spectral hardening plays an important role in safety analyses of fast sodium cooled reactors.  All other things being equal, increasing the coolant temperature decreases collisions with the coolant resulting in spectral hardening.  Since this would lead to reactor instability, this phenomenon must be compensated for with some other effect such as Doppler.  Importantly, sodium voiding accompanying boiling also hardens the spectrum thereby inserting positive reactivity.


1 As will be shown in the section on actinide burning, other cycles involving artificial isotopes can also be used.

2 The concept of over- and under-moderation in thermal spectrum reactors is related.  LWRs typically are designed with a small amount of under moderation so that a coolant temperature rise with resulting coolant density decrease causes further under moderation, thus inserting negative reactivity and enhancing reactor stability.