MCNP keff > 1.0 depletion question

[Caden]

TL;DR

What does MCNP do with extra neutrons when keff > 1.0?

I am running some depletion calculations and have noticed odd behavior when keff is much greater or lower than one in the number of absorption's taking place on the outside the reactor. MCNP seems to be deleting the neutrons after it has reached the number of fissions required for the power level.
To test this I made an unrealistic reactor with a keff of 1.4 and a near infinite neutron capture blanket. I caught 70% of the neutrons created. By dropping keff to 1.0 in the same geometry by reducing the amount of fuel, I caught 100% of the neutrons created.
To me this implies that when keff > 1.0 any extra neutrons that would cause fissions in the fuel are deleted making it appear as though I am capturing less neutrons at higher keff.

If anyone can confirm what is going on that would be helpful.

Thanks

 

[DEvens]

It's curious. Can you post a short sample input file that shows this? And maybe show your work a little?

When keff is exactly one, it means that on average, each neutron produces one neutron in the next generation. So on average, enough neutrons find a fissionable nucleus and induce a fission, so the next generation has the same number of neutrons as the current generation.

Now $\nu$ is typically 2.3 approximately. That means a fission, on average, releases about 2.3 neutrons. You should be able to find the value in your output. It will be different for different fissile materials and for different configurations because you will have a different spectrum.

That means you need, on average, about 1/2.3 of the neutrons produced to be used up by finding a nucleus and fissioning. That's about 40%, roughly. A few will be captured in the fissile material. The rest will escape.

So if you are finding that 100% of the neutrons produced are escaping the fissile material, there is something wrong. At keff=1 you should be getting no more than 60% or so. And that is neglecting whatever fraction get captured inside your fissile material. That last might be a valid approx if it's small.

Generically, the main effect of a high or low keff for a kcode calculation will be that the neutron energy spectrum is a little weird. With very large keff it means you are getting more neutrons directly from fission. With low keff you are getting more that have had a long time to scatter and so lose energy. There is some more to it than that, but that's the main thing. It may also mean you lose more to capture events at low keff.

Also, you can count neutrons using an F1 tally. You don't need to use a capture blanket. But that's a secondary item.

 

[Caden]

DEvens

My experience with MCNP is lacking. Copied some of the MCNP output from a simple core that has fuel in a hexagonal formation shown below surrounded by water.
I put F1 and F2 tallies on the top and bottom planes as well as the surrounding cylinder.

The output from the the F1 tally looks like:

surface 1
energy
1.0000E-14 0.00000E+00 0.0000
3.1600E-14 0.00000E+00 0.0000
1.0000E-13 0.00000E+00 0.0000
3.1600E-13 0.00000E+00 0.0000
..... ..... ...
5.0000E+02 0.00000E+00 0.0000
1.0000E+03 0.00000E+00 0.0000
total 2.58606E-02 0.0051
and the output from the F2 tally is
surface 1
energy
1.0000E-14 0.00000E+00 0.0000
3.1600E-14 0.00000E+00 0.0000
1.0000E-13 0.00000E+00 0.0000
..... ..... ...
1.0000E+02 0.00000E+00 0.0000
5.0000E+02 0.00000E+00 0.0000
1.0000E+03 0.00000E+00 0.0000
total 1.58076E-06 0.0068
The first column is the energy bins defined in the input file. What are the units of the second and third columns. How do I determine how many neutrons are passing through surface 1? This would help me figure out how to provide you with a better output to answer my previous question.

 

[DEvens]

An F1 tally is current integrated over a surface. It gives you particles counted per particle started. You normalize it by using the number of particles started. You also need to tell MCNP the area of the surface, unless it's a very simple surface which it can calculate itself. You use the SD card to do that. You can also read up on use of the FS card to segment the tally into sub-surfaces. And you can only use a surface that forms part of a cell to do F1 tallies.

An F2 tally is the flux over a surface. That's particles/cm^2 per particle started. Same remark about SD card.

The total for your F1 tally is 2.58606E-02 0.0051

The second number, 0.0051, is the fractional error. Pretty good, it's 0.51%. Usually the guidance is anything less than 10% is acceptable, so you are pretty good. That's a "one sigma" type error.

The first number is particles per particle started. So you figure out the number of neutrons that went through the surface by multiplying by the number your kcode created. You multiply active cycles times particles per cycle.

Normalizing to actual reactor power is a bit more involved. One way to do that (not the only way) is to use an F7 tally to get the total fission energy per neutron started. Then use the total reactor power to convert that to the total number of neutrons per second. Total reactor power divided by fission power per neutron is neutrons per second. Watch those units, the F7 tally reports MeV/gram. You need to gather up all the F7 values for all the parts of the reactor, and multiply each one by their corresponding mass. You can do that using the SD card also.

Then neutrons per second times your F1 tally is the number of neutrons per second that pass the surface. Neutrons per second times your F2 tally is the number of neutrons per second per square cm through that surface.

You should also be looking in your output file for the summary table.