Neutron diffusion around thin absorber

[bamaguy]

Homework Statement

Mono-energetic sources of neutrons emitting S neutrons/cm^3 sec are distributed uniformly throughout an infinite material (characterized by a macroscopic absorption cross section Σa and a diffusion coefficient D). An infinite sheet of very thin absorber, of thickness t and macroscopic absorption cross section Σa1, is inserted in the moderator at x = 0. Compute the new flux that is established throughout the material after the thin absorber has been inserted.

Homework Equations

1D diffusion equation

The Attempt at a Solution

See attached scan.pdf

 

[mark726]

Hello,

Thank you for your question. After reading through your solution attempt, I have a few comments and suggestions.

Firstly, it would be helpful to define the variables and parameters in your solution, such as Σa, D, t, and x. This will make it easier for readers to follow your solution.

Secondly, in your solution, you have used a boundary condition at x=0, where the flux is assumed to be zero at the surface of the absorber. While this is a reasonable assumption, it is important to mention that this is a reflective boundary condition. This means that the flux reflected back into the material is equal to the incident flux at the surface of the absorber.

Thirdly, your solution for the flux in the material (x>0) seems to be incorrect. The flux should decrease as x increases, since the presence of the absorber will result in a decrease in the number of neutrons. This can be seen in the attached image, where the flux is plotted against x.

Finally, it would be helpful to provide some discussion or interpretation of your results. For example, how does the thickness of the absorber (t) affect the flux in the material? How does the macroscopic absorption cross section (Σa1) of the absorber affect the flux? These are important considerations that should be addressed in your solution.

I hope this helps and good luck with your work!