FLUKA: Why Does Neutron Flux Increase When Passing Through a Moderator?

[mudmucker]

TL;DR Summary

I am modeling a neutron beam passing through a carbon block. The strange thing is that when I give the beam energy a large energy spread (Gaussian FWHM set to 10) I am calculating that 3,462% of the neutrons that enter the block exit and 2,851% are reflected. n, 2n reactions are conceivable but not that much. Either I am setting up the simulation wrong or I am processing the data incorrectly.

I have been banging my head against this for a few weeks now; tweaking the simulation, adjusting my calculations, and searching around the web to try to find an answer. I can't post questions on CERN's Fluka help forum so this seemed like the best option. I really appreciate any help you can give.

I am using Fluka (via Flair) to model a 2 MeV neutron beam passing through a carbon block with the goal of looking at the percent of neutrons that pass through and the percent that are reflected. I have set up 3 USRBDX planes to count the one way neutron flux.

1. The first plane is between the beam origin and the carbon block
2. The second plane is at the far end of the carbon block where neutrons would exit
3. The last plane is behind the beam origin to measure reflected neutrons.

These planes are very large compared to their separation from each other, but its possible for some neutrons to escape out the sides without being counted. The carbon block is surrounded by the standard void in Fluka, there are no other objects to interact with the neutrons (The USRBDX planes are the interfaces between regions that are "filled" with vacuum).

I looked at 3 scenarios

• The first is with no energy spread on the beam. The results look plausible: 12% of neutrons exit and 83% are reflected.
• The second is with a Gaussian beam energy spread with the full width half maximum is set to 1. 94% of neutrons exit and 166% are reflected.
• The third scenario is where there is a big problem. With a Gaussian beam energy spread with FWHM is set to 10. The table of the results is attached, but to summarize:
  • 3,462% of neutrons exit and 2,851% are reflected. It's conceivable that there are some n, 2n reactions but these numbers seem unrealistically high.
  • I also looked at the cumulative neutron flux from the sum.list file and the numbers are lower but still too high; 1,186% exiting and 677% reflected.

I am using the numbers from the sum.lis file to get a neutron count and calculate the percent of neutrons exiting versus reflected. I am taking the width of each energy bin for the flux, multiplying the flux times the bin width for all bins, and then adding up the results. Honestly I'm not exactly sure what the different is between the "Flux (Part/GeV/cmq/pr)" and "Cumul. Flux (Part/cmq/pr)" data in the sum.lis file, and I'm clearly not processing either correctly.

Attached are the .flair and .inp from Fluka/Flair (I had to add .txt file extensions to be able to upload the files, you should just be able to delete that), the spreadsheet with my calculations, and I have also attached the graphs of the USRBDX output for each of the 3 beam scenarios.

Thank you!

 

[Alex A]

I know precisely one thing about fluka, so this interpretation could be wildly wrong. The natural unit of energy for the program is GeV. Have you asked it for a 2MeV beam with a 10 GeV FWHM?

 

[mudmucker]

That is an interesting point about the base units, but I think that the 2 MeV value is f-max on the image below on the Y axis and the "10" is X2-X1 on the X axis. I'm not sure of the units on the X axis though, some count of the number of neutrons.

 

[Alex A]

I would interpret that as a histogram, with f(x) being the frequency of occurrence of a particle with energy x, and x2-x1 as the Full energy Width at Half Maximum occurrence. It's commonly used to express the resolution of an energy dispersive spectrometer, where it can be given directly or as a percentage of the peak energy.

I have no experience with this program and the online manual I checked did not say, but since you appear to be getting spallation and you shouldn't be...

Edit,
I also don't understand why you would multiply the flux by the energy bin width. That does not seem a meaningful quantity.

 

[Astronuc]

With respect to the question, "Why Does Neutron Flux Increase When Passing Through a Moderator?", is one referring to the flux buildup in the thermal energy range?

In mixed spectrum cores/systems (e.g., graphite or water moderated systems), one sees a peak population in the fast energy (MeV) range and a peak in the lower (thermal or epithermal) energy (eV) range. The peak in the fast energy range reflects the source(s) while the peak in the thermal energy range represents the results of neutrons down scattering into those low energies, which is the purpose of a moderator. Remember, slowing down of fast neutrons to thermal energies happens in milliseconds.

At an energy of 2 MeV, there should be no n,2n reactions. The threshold for such a reaction should be great than 2 MeV, more like 8 MeV. Think of the binding energy of the last neutron.

Regarding the difference between "Flux (Part/GeV/cmq/pr)" and "Cumul. Flux (Part/cmq/pr)", the former is per unit energy, while the latter would be integrated over the energy range (bin). I've seen similar representation from MCNP output. One would multiply the flux/energy by the mean energy in the bin rather than the bin width.

Looking at the FLUKA manual, I find the following confusing/puzzling.

Soon after, the cumulative fluence distribution as a function of energy is also given:

**** Cumulative Fluxes as a function of energy ****
**** (integrated over solid angle) ****

The manual mentions fluence, then flux(es). Fluence is cumulative, i.e., flux integrated over time.

Lastly, 'reflected' has a connotation of recoiling in the opposite direction, and it is more appropriate to refer to 'scattered' and 'unreacted' or 'uncollided/unscattered or non-scattered', or 'forward scattered'. Depending on the thickness of the block, one will find exiting neutrons, and they will most likley have scattered at least once or twice, and the neutron energy spectrum will be spatially dependent and will be different from the incident face to the exiting face of the carbon block.

I'm not very familiar with FLUKA, but I'm aware of the concepts, and I have used the results of calculations of others.

 

[mudmucker]

@Astronuc thank you for your help, that got me closer, somethings still not right. When multiplying flux by the mean energy of the bin the result is close to the the cumulative flux numbers, so I'm guessing that I can use either one. However the results still don't make sense to me.

When I multiply flux by the mean energy of the bin I get that the unreacted and forward scattered neutrons are 1,546% of the original neutrons, and the backward scattered neutrons are 1,041%. The results when I use cumulative flux is 1,186% unreacted and forward scattered and 677% backward scattered.

As you point out the energy is too low for n, 2n reactions so I'm not sure why we're getting almost 18 times more neutrons out of the system than we put in.