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**SODIUM GUARD BAND OVERVIEW:**

The function of the FNR Sodium Guard Band is to absorb all the neutrons that escape from the FNR blanket. The fundamental question from a practical reactor engineering perspective is: "How thick must this guard band be?"

Related questions are: "How thick must the the sodium guard band be for bio-safety?" and "How thick must the sodium guard band be to prevent neutron activation of nickel in the intermediate heat exchanger and in the primary sodium pool liner?"

An important technical issue that must be addressed to answer the aforementioned questions is: "What is the ratio of neutron random walk path length to guard band thickness?"

Neutrons diffuse through the guard band by scattering. At each scatter a neutron loses a small fraction of its kinetic energy. Between successive scatters the number of neutrons reduces due to neutron absorption. Our first concern is that 100% of the neutrons that escape from the reactor blanket must be absorbed in the liquid sodium guard band. Hence the neutron random walk path length in the blanket must be long enouch to ensure 100% neutron absorption.

One of the issues is that the average atomic weights of the blanket materials are large so that neutrons which manage to escape from the blanket still have much of their original kinetic energy.

As a neutron proceeds along its random walk path in sodium it gradually loses kinetic energy, so the neutron absorption cross section changes. Hence the neutron random walk path length in the liquid sodium guard band must take this change in absorption cross section into account.

The combination of the reactor core zone diameter, the reactor blanket thickness, the liquid sodium guard band thickness and the intermediate heat exchanger tube bundle thickness sets the reactor primary sodium pool dimensions, which in turn set the reactor cost. Thus from an overall system cost perspective the required liquid sodium guard band thickness is an important design constraint. This thicknesses is relatively independent of reactor power. Hence from a cost perspective it is not practical to make a very small FNR that meets the envisaged safety criteria of zero neutrons activating nickel in the intermediate heat exchanger and in the primary sodium pool liner.

The average concentration of Na-23 atoms in the liquid sodium guard band determines the rate of absorption of neutrons along the neutron random walk path.

**NEUTRON RANGE TO SCATTERING IN LIQUID SODIUM:**

The cross section for high energy neutron scattering in sodium is 2.62 b. Hence the distance Ls between successive high energy scatters in pure liquid sodium is given by:

Ls = 1 / [(2.62 X 10^-28 m^2 / atom) X (6.023 X 10^23 atoms / 23 gm) X (.927 gm / 10^-6 m^3)]

= 23 m / [ 2.62 X 6.023 X .927 X 10]

= .1572 m

In each scattering event total momentum is conserved.

Define:

Mn = neutron mass

Ms = scattering mass

Vn = neutron velocity

Vs = scattering mass velocity

Conservation of momentum gives:

Mn Vn = Ms Vs

or

(Vs / Vn) = (Mn / Ms)

The fractional loss of neutron kinetic energy in each scattering event is:

Ms Vs^2 / Mn Vn^2 = (Ms / Mn)(Mn / Ms)^2

= (Mn / Ms)

= 1 / (23)

Hence the neutron energy after a scattering event is (22 / 23) of its energy before the scattering event until the neutron kinetic energy reaches thermal energy.

(22 / 23)^2 = .9149338374

(22 / 23)^4 = .8371039268

(22 / 23)^8 = .7007429843

(22 / 23)^16 = .49104073

(22 / 23)^32 = .2411209985

(22 / 23)^64 = .0581393359

(22 / 23)^128 = .0033801824

Thus after about 128 scattering events a 3 MeV neutron has lost sufficient energy to drop to 10 keV.

Since scattering takes place in a 3 dimensional random walk the required thickness of liquid sodium required to provide this energy loss along a single axis is:

[(128 / 3)^0.5 X (.1572 m)] = **1.03 m**

For neutrons with energies of less than 10 keV the average sodium atom absorption cross section is 0.310 barns = 0.31 X 10^-28 m^2 and the scattering cross section is 122.68 barns.
Hence the probable number of scatters before absorption is 122.68 / .31 = **395.74**.

The density of liquid sodium is 927 gm / lit. The atomic weight of sodium is 23. Avogadro's number is 6.023 X 10^23 atoms / mole. Hence the range Ls between scatters in liquid sodium for neutrons with midrange energies less than 10 keV is given by:

Ls = 1 / [927 gm / lit X 1000 lit /m^3 X 1 mole / 23 gm X 6.023 X 10^23 atoms / mole X 122.68 X 10^-28 m^2 / atom]

= 23 m / [927 X 1000 X 6.023 X 10^23 X 122.68 X 10^-28]

= 23 m / [9.27 X 6.023 X 122.68]

= **.003357 m**

Hence the expected distance along one axis that a neutron travels before absorption is:

(395.74 / 3)^0.5 X (.003357 m) = **.0385 m**

However, after that distance there are still a lot of thermal neutrons. For thermal neutrons the scattering cross section is 3.090 b and the absorption cross section is 0.417 b.
Hence the average number of scatters before thermal neutron absorption is:

3.090 / 0.417 = 7.41 scatters.

The distance between thermal neutron scatters is:

Ls = 1 / [927 gm / lit X 1000 lit /m^3 X 1 mole / 23 gm X 6.023 X 10^23 atoms / mole X 3.090 X 10^-28 m^2 / atom]

= 23 m / [927 X 1000 X 6.023 X 10^23 X 3.090 X 10^-28]

= 23 m / [9.27 X 6.023 X 3.090]

= **0.1333 m**

Thus the expectation distance for thermal neutron travel along a single axis for a single scatter is:

0.1333 m / 1.732 = 0.07696 m

(N)^0.5 = 1.3 m / .07696 m

= 16.892

or

N = (16.892)^2 = 285.33

Assume that in 7.41 scatters the neutron flux is reduced by a factor of 2.71. Thus the neutron flux reduction factor is about:

exp (285.33 / 7.41) = exp(38.5) = 5.25 X 10^16

which is sufficient.

**Thus a 2.4 m wide liquid sodium guard band around the reactor is sufficient for absorbing all emitted neutrons.**

** To absorb these neutrons we need 2.4 m of sodium between the outside edge of the blanket and the reactor wall and the heat exchange bundles. This issue substantially impacts the overall sodium pool dimensions.**

The neutrons exiting the reactor blanket vertically can avoid the sodium between the tubes by travelling through the fuel tube plenums. Hence there must be 2.4 m of liquid sodium both above and below the fuel tubes.

**Hence the liquid sodium pool dimensions should be about:
20 m diameter X 15.0 m deep**.

This web page last updated October 20, 2019

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