14.4% of the reactions will be capture reactions, leading to the formation of U-236.

There are some additional sources of fast neutrons:

• Fission of Pu-239 by thermal neutrons
• Fission of U-235 by fast neutrons (low probability)
• Fission of U-238 by fast neutrons (low probability)
• Fission of Pu-239 by fast neutrons (low probability)

If the reactor is assumed to have not produced much Pu-239, then these additional sources add only about 2% more fast neutrons.

What is the fate of these 2.10 fast neutrons?

• Some leak from the reactor – these are lost.
• A significant fraction of the remaining fast neutrons undergo thermalization – but some don’t, and remain fast neutrons.
• Some of the newly produced thermal neutrons are captured by various nuclei, and thus are lost. Some are captured by the construction materials of the reactor, some by the control rods, some by the water coolant/moderator, and some by certain fission products (called poisons).

The remaining thermal neutrons face the following reaction choices:

• Capture by U-238 (forming Pu-239). Note, fast neutrons are also captured by U-238, producing Pu-239.
• Reaction with U-235, either capture of fission, repeated the cycle.
• Reaction with Pu-239, either capture or fission.

• Increase the U-235 to U-238 ratio. That is, enrich the fuel.
• Improve the thermalization process – use a light isotope.
• Remove reactor poisons.

The number of collision required to thermalize a fast neutron are:

H (in H₂O): 16

D (in D₂O): 29

C: 91

The moderation ratio is defined as proportional to the neutron KE lost per collisions multiplied by the ratio of elastic scattering to neutron capture. The values are:

H (in H₂O): 1/16 x 38/0.333 = 7.1

D (in D₂O): 1/29 x 7/0.00053 = 455

C: 1/91 x 4.8/0.0036 = 14.7

The ranking is: D₂O (heavy water) >> C (graphite) > H₂O (light water).

Heavy water "wins" because it doesn’t capture thermal neutrons. Graphite is somewhat better than light water. However, water has the advantage of also being a coolant. If loss of coolant occurs, the fission process should shut down.

C = B = rate of production of fissile nuclei/ rate of consumption of fissile nuclei

Some values are:

• Small C: "burner"
• 0.7£ C£ 1; "converter"
• C>1: "breeder"

Reactors that use graphite (carbon) as the moderator tend to have higher conversion ratios than water moderated reactors. This occurs because:

• It takes many collisions with carbon to thermalize the neutrons (see below). Thus, the fast neutrons hang around longer, and can be captured by U-238, leading to Pu-239.
• There is less capture of thermal neutrons by carbon compared to water. Thus, there are more thermal neutrons to undergo capture (and fission) reactions.

There is also more conversion if the fuel is not enriched in U-235. Then the neutrons have more opportunity to react with U-238 (and be captured and form Pu-239) than to react with U-235.

In decreasing number of reactors, the types of nuclear reactors are as follows:

• PWR: pressurized water reactor. The coolant is light water, the moderator is light water, and the fuel is enriched uranium (~ 3% U-235).
• BWR: boiling water reactor. The coolant, moderator, and fuel are the same as for the PWR.
• PHWR: pressurized heavy water reactor. The coolant is heavy water, the moderator is heavy water, the fuel is natural (not enriched) uranium. The heavy water, being a superior moderator permits criticality to be attained with natural uranium. Canadian technology.
• GCR: gas-cooled graphite reactor. The coolant is CO₂, the moderator is graphite, originally natural uranium was used, now enriched uranium is used. British technology.
• LGR: light-water cooled graphite reactor. The coolant is light water, the moderator is graphite, the fuel is enriched uranium. Former Soviet Union. Chernobyl reactor.
• LMFBR: liquid metal fast breeder reactor. The coolant is liquid sodium (since thermalization of the neutrons must be avoided – there is no moderator). This reactor converts U-238 to Pu-239. A few exist.
• HTGR: high temperature gas cooled reactor. The coolant is helium, the moderator is graphite, and the fuel is enriched uranium. The high temperature improves the cycle. One was build in the US in Colorado, though is no longer operating.

The nuclear fuel cycle consists of the following steps:

• Mining the uranium ore.
• Processing the uranium ore.
• Enriching the uranium. In the USA, this is accomplished by converting the uranium into gas and separating the U-235 and U-238 isotopes by a gas diffusion process.
• Fabricating the uranium pellets and fuel rods.
• Using the uranium in the reactor, producing electrical energy.
• Removing the "spent" fuel (which contains FPs and unused fuel), and storing it under water at the reactor site until it cools and the water decay has considerably slowed. This may be followed by temporary storage in canisters at the reactor site.
• Or re-processing of the spent fuel to remove and use the fissile material in reactors. This is not done in the USA.
• Long-term storage (final deposition) of the spent fuel – not yet significantly practiced in the USA.