Question

Explain how neutron diffusion theory is related to physical reality. Does this theory describe the actual phenomenon, or does it provide only approximation? If only an approximation, then explain what is being captured by this approximation and what is not. To get credit, you must justify your answer. State major assumptions and limitations of diffusion theory. Also, discuss potential application areas. Facilitate your discussion by providing appropriate examples

Answer 1

Long story short, relating neutron diffusion theory with reality and with it's practical application , it is found to be playing a significant role in designing nuclear reactors. The study of how neutrons would be distributed through the system of the nuclear reactor is of prime importance. Neutrons undergo various interactions in a nuclear reactor and the overall interaction  of the neutrons which undergo diffusion through the core can only be given as an approximated image like how gases interact with one another. Hence, the neutron diffusion theory.

The approximation is been explained with Fick's law, which states that in the nuclear reactor. Fick's law gives an image that neutrons flow in a way and behave as that of gases. It moves from higher density area to the lower density area. Thus greater collision occurs between neutrons in the area of higher neutron density and hence results with high flux in the neutron denser region. Hence Fick's states that the current density is always directly directly proportional to the negative gradient of neutron flux.

Fick's law is only given as an approximation and to some extent it is found that these limitations are valid practically in many reactors. The assumptions are as follows.

1. Ficks law assumes that the flux is independent of time.

2. The flux is large when neutron absorption is large. But usually there is only a  slow varying flux.

3. It is assumed that a uniform medium was used.

4. It is assumed that the variation of the flux is only from elastic scattering reactions.

5. The calculations of integration are always done with an assumption of an infinite medium but the flux contributions are very low beyond the boundaries of the diffusion medium

6.. Even though it is not true in general, here it is assumed that isotropic reactions take place at low energy level.

The Application of Neutron Diffusion theory can be mainly seen in the core design and specifications of various reactors where it provides detailed information about the neutron flux to design and thus by validating the above assumptions. design of reactors such as Boiling Water Reactors (BWR) and Pressurized Water Reactors (PWR) are the applications.

I hope the explanation helps. :)