Reaction rates

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1

Hi,

I have several questions about calculation of reaction rates.

I am running an eigenvalue calculation of a simple PWR core, and calculating fission and absorption tallies for both U235 and U238.

According to the manual, units of these tallies are reactions per source particle.

Since I have several filters (space, energy), I sum over all the filters, and multiply by number of neutrons (10^6 in my case).

This is what I get:
U235:

  • absorption: 4158.198
  • fission: 3348.738
    U238:
  • absorption: 1913.277
  • fission: 250.258

I have now several questions:

  1. Are the tallies taken in a single batch, or are they averaged over all previous (active) batches? If single, why aren’t these numbers integers?

  2. The numbers above add up to ~10^4, out of 10^6 source particles (~1% of all particles). Does this mean that the rest of the particles had different scores? In general, if I tallied and summed over all filters and all scores, would the numbers sum up to the total number of source particles?

  3. The system is thermal, still U238 fission is not negligible. Any ideas?

Thanks,
Shai

2

Hi Shai,

  1. Tallies are averaged over all active batches. Even if they weren’t, you generally won’t see integer numbers because these reaction rates are calculated probabilistically using tracklength estimators. That is to say, OpenMC doesn’t actually count the number of reactions that occurred but instead estimates it by multiplying the flux by the expected number of reactions that would occur each time the neutron moves. Have a look at the theory and methodology guide section on tallies as it explains this in more detail.

  2. The tally results tell you what the expected number of reactions are per source particle. For example, if OpenMC gives you an absorption rate of 0.5, this means that on average a source particle would be absorbed 50% of the time. The tallies are always normalized to the number of (active) particles that are simulated and you generally shouldn’t need to multiply by the number of particles. Using more particles will just give you better statistics (lower standard deviation).

  3. Contrary to popular belief (and what may be taught in classes), U238 has a non-zero cross section even at thermal energies, so you will still see a non-zero fission rate for U238 even for thermal systems.

Hope this helps.

Best,
Paul

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