J. Leppänen.

*"Performance of Woodcock Delta-Tracking in Lattice Physics Applications Using the Serpent Monte Carlo Reactor Physics Burnup Calculation Code."*Ann. Nucl. Energy,

**37**(2010) 715-722.

and it has been shown to perform well with burnable absorber pins containing gadolinium.

However, discussions at UC Berkeley last week brought up a potential concern related to the performance of delta-tracking with other absorber types, specifically control rods containing boron. Unlike Gd-155 and -157, which are essentially thermal absorbers, boron-10 is a 1/v absorber, with a relatively high absorption cross section spanning a much wider energy range (see the attached figure). The fact that the combined DT/ST method works so well with thermal absorbers may be due to the fact that the performance is good at higher energies, where the neutron mfp's are also long. This is almost certainly not the case if the majorant cross section is clearly dominated by a 1/v absorber.

To test whether this is the case with some typical boron absorbers, I ran a set of calculations in two geometries:

1) a VVER-440 lattice calculation with a flux-trap control element containing boron steel

2) a BWR lattice calculation with a cruciform control rod containing boron carbide

The boron in both cases was of natural composition, with about 20% B-10. The atomic density of B-10 was 1.58921E-03 barn/cm3 in the first case and 1.51714E-02 barn/cm3 in the second case. I repeated the calculations in full surface-tracking, full delta-tracking and the combined mode, with and without the control rod. The running times (minutes) for the VVER case are:

Code: Select all

```
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with CR without CR
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Surface-tracking: 84.3 84.4
Delta-tracking: 32.4 (2.6x) 23.9 (3.5x)
Combined ST/DT: 29.9 (2.8x) 23.9 (3.5x)
------------------------------------------
```

Code: Select all

```
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with CR without CR
------------------------------------------
Surface-tracking: 82.4 69.0
Delta-tracking: 45.2 (1.8x) 40.4 (1.7x)
Combined ST/DT: 35.9 (2.3x) 32.7 (2.1x)
------------------------------------------
```