SCALE 6: KENOVI in adjoint mode

[SCALE Software Coordinator]

This topic has been migrated from the SCALE 6 notebook.

Date: Mon Dec 6 13:54:12 2010

 

Dear users and developers!

I have some questions regarding KENOVI in the adjoint mode.

1. In the table summarizing the results of the calculations at the end of the output files, all quantities except for the k-effective ("system nu bar", "system mean free path", "Energy of average lethargy of Fission") differ from the ones got in the forward calculation for the same input, sometimes with orders of magnitude. Is there a description somewhere of what these are exactly in the adjoint mode?

2. KENOVI in the adjoint seems to converge strangely, the k-effectives from cycle to cycle can differ greatly. First I noticed it in my inputs for a fast system, that even at the end of the calculation the values vary between 0.6 and 1.5-1.6 (sometimes reaching even 2.1), and I also got lots of warning messages about too few independent fission point generation (k6-132). Then I took a look at the outputs for the sample problems where the same behavior can be seen, though the range of the k-effectives is a bit smaller. This of course causes high variance and bad statistics, and usually the chi square test to fail (that's the case for the adjoint calculation in the 2nd Tsunami-3D-K6 sample as well). I also experienced that running my problems with more generation doesn't change this behavior at all, what's more, sometimes the chi square test is met with lets say a 1000 generations, but fails at 2000 generations or more (though at least the results are the same within variance).

I'd appreciate any comments on why this is.  

Best regards,   

Danny Lathouwers

 

[SCALE Software Coordinator]

The only documentation is F11.4.26, which doesn't say much. These are calculated the same way in adjoint mode as they are in forward mode. Since the adjoint spectrum will likely be very different than the forward spectrum, there is no reason to expect these to be the same as the forward values. Because these values don't have a good, real world physical meaning we have been considering suppressing them for adjoint problems.

 

There are at least 2 significant factors contributing to increased variance with the adjoint calculation. First, the transfer array no longer sums to some sort of scattering cross section from the group, but is the sum of transfers to the group. This means the cross sections for a group in the adjoint mode do not balance. The second factor is the interchange of chi and nu*sigma fission in the adjoint mode. chi is essentially zero over a significant part of the energy range for all nuclides, which means that no fissions occur over that range in the adjoint mode. Further, nu*sigma fission peaks strongly for most important nuclides in that same range, which means that neutrons are created in an energy range where they cannot cause fission.   Especially for fast systems, this leads to many source neutrons not causing any fission, which increases the variance. Thermal systems will generally have smaller variances for a given number of histories than fast systems. Increasing the number of histories per generation is usually more effective at reducing the variance than increasing the number of generations.