Lecture 11 Moderation

Objectives In this lecture you will learn the following We shall understand the essence of the slowing down process. Then we shall look at the mechanism of elastic . We shall conclude that lighter materials are better moderators. Then we shall identify the common moderators. Lecture 11 Neutron Moderation

Moderation

The process by which the energy of neutron is decreased is called moderation. As discussed in our previous lecture, the for neutron reactions can be assumed to vary approximately as 1/v, where v is the speed of the neutron. We also learnt that the average energy of the fission neutron is about 2 MeV, where as a neutron in thermal equilibrium with the 300 K environment is 0.025 eV.

Thus the ratio of the speed is approximately 104 and hence the probability of a average energy neutron is 104 times less than the thermal neutron.

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The Process of Moderation

Moderation occurs in the nuclear reactor by collision process with the material present in the system. This process is called scattering. There are two kinds of scattering process, viz. Elastic scattering and Inelastic Scattering.In inelastic scattering is not conserved as the target nucleus gets into excited state consuming energy.

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Elastic Collision Process

We had shown in previously that it is enough to consider Newtonian Mechanics and relativistic effects need not be considered, if the neutron travels at speeds less than 1/10 of the speed of light. For all practical purposes with neutron reactions in reactors this is valid. From mechanics we can write that , p, and kinetic energy E as

Consider the elastic collision process

The momentum conservation can be expressed by the vector diagram shown

Here p, p' and pA are the momenta of the incident neutron, scattered neutron and the recoil nucleus respectively.

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From Triangle Law of vector addition, we can write

This can be rewritten as

In the above equation E, E' and EA are the kinetic energies of incident neutron, scattered neutron and the recoil nucleus respectively.

Dividing both sides by 2 and invoking kinetic energy conservation, E = E' + EA, We can write

Dividing by E, we get a quadratic in

The solution of the above quadratic equation is

Only positive sign will be considered for physically realisable solution.

Till now the treatment is rigorous. From here on we make simple approximations to get some general results. These results can be shown to hold using more rigorous arguments in a next level course. If we assume that angle θ = 0, often referred as gracing collision, we can write Thus, the energy after collision is same as before and there is no energy loss.

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General Observations

If we take θ = 180, which is often referred as head on collision, we can write

Thus, the minimum energy a neutron can have after collision is αE. Note that if A = 1, which is true for hydrogen nucleus, α = 0 and thus a neutron can be brought to rest in one collision. Further, if A >>1, then α ~ 1 and thus, there is no energy loss. Thus for the moderator to be effective, A should not be large. If we assume that every angle is equally likely, then the mean energy of neutron after collision is

Thus the mean energy loss is

We can construct the following table

Element A α H 1 0 0.500 D 2 0.111 0.444 Be 9 0.640 0.180 C 12 0.716 0.142 U 238 0.983 0.008

H as H2O and D as D2O are used as most common moderators. cooled reactors use C as the moderators.

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Choice of Moderator

We can construct the following table illustrating the choice of the elements as moderator.

Element Atomic No Comment H 1 Good moderator, but absorbs and hence a reactor needs enriched fuel D 1 Good moderator and can be used with natural U He 2 Noble Gas and hence not used Li 3 Not used as it has high absorbtion cross section Be 4 Difficult to machine and used only in research reactor B 5 Strong Absorber, hence not used C 6 Good moderator, can use Natural U

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Estimation of Number of

To understand the effectiveness of a moderator, we can estimate the average number of collisions to reduce the energy from 2 MeV to 0.025 eV. The average energy of neutron after one collision is

The average energy after two collisions shall be

The average energy after n collisions shall be

Thus for a given En, Eo and α, n can be estimated.

The number of collisions required to reduce the energy from 2 MeV to 0.025 eV is given in the following Table.

Element A α (1+α)/2 n H 1 0 0.500 26.2 D 2 0.111 0.555 30.9 Be 9 0.640 0.820 91.7 C 12 0.716 0.858 118 U 238 0.983 0.9915 2132

As the number of collisions increase, the size of the reactor also has to be increased to ensure less leakage.