# Water-cooled fast neutron reactors

Can anyone explain why fast neutron reactor designs use sodium/lead/salt cooling, instead of water (heavy/light)?

Is that because neutron absorption by water would not allow to break even in fuel cycle? Will heavy water help here?

Or water slows neutrons so efficienly so that even if we reduce amount of water inside the reactor (by increasing flow speed) - it still will significantly lower neutron energy, while sodium does not slowdown neutrons at all?

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First question: Na for fast reactors

Sodium is better for faster reactors because it has a lower total cross section than water. Fast reactors still has some moderation and obviously all types have some neutron loss due to absorption from the moderator in addition to whatever other materials may be in the core. For numbers, I'm going to reference NIST:

Sum up all of the cross sections for all types of reactions, which is the total scattering + absorption from that link. You find $82 \text{b}$ for Hydrogen and $3.8 \text{b}$ for Sodium. For water you add Oxygen. Combine that with density and atomic weight information to get the macroscopic cross sections. For water, we have $3.45 cm^{-1}$ and for Na we have $0.115 cm^{-1}$. These numbers are from my reference.

A fast reactor primarily wants the moderator to do nothing. Indeed, without a coolant or moderator the reaction works just fine... aside from getting cooled. Even if a moderator wouldn't absorb any neutrons, it would muck with your intent, which is to get the fuel atoms (U, Th, Pu) to absorb fast neutrons from fission. The reason you want fast neutrons to hit the fuel atoms includes:

• to breed new fuel, for which the isotope chain is only neurotically favorable with fast neutrons
• some isotopes are only fissile at fast energies, and at lower energies will have small fraction fission, meaning you couldn't sustain the chain reaction ($k<1$) with a thermal spectrum

If you slow down the neutrons, these objectives will be thwarted.

Second question: D20 for thermal reactors

Heavy water is used in some designs because it is a superior moderator. For a single metric to give a figure of merit for moderation, my reference proposes:

$$\text{Moderating Ratio} = \frac{\xi \Sigma_s}{\Sigma_a}$$

To break this down, $\xi$ represents the lethargy gain per collision, which is the best metric for "how much relevant energy is lost per collision". Then the cross sections are the macroscopic scattering on top and macroscopic absorption on the bottom. If you imagine neutrons in a vacuum with only the moderator to hit, then the higher the moderating ratio is, the more will make it to thermal energies.

According to my reference, the moderating ratio for $H_20$ is $71$ and for $D_20$ is $5670$. The main reason for this is that Deuterium has a very low absorption cross section. Funny enough, Deuterium is actually vastly inferior to a simple proton on the basis of scattering cross-section as well as energy lost per collision, so the entire benefit comes from the lower absorption cross section. The following is my own calculation for the moderating ratio of $Na$.

$$\frac{\xi \Sigma_s}{\Sigma_a} = \frac{(0.0845)(3.28)}{(0.53)} = 0.52$$

Sodium is not a good moderator. It is 100 to 200 times worse than all the other common options, which include H, He, Be, and C.

Reference: Nuclear Reactor Analysis. James J. Duderstadt and Louis J. Hamilton.

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