Development of a Monte-Carlo based method for calculating the effect of stationary fluctuations
Paper in proceedings, 2015
This paper deals with the development of a novel method for performing Monte Carlo
calculations of the effect, on the neutron flux, of stationary fluctuations in macroscopic crosssections.
The basic principle relies on the formulation of two equivalent problems in the frequency
domain: one that corresponds to the real part of the neutron balance, and one that corresponds to
the imaginary part. The two equivalent problems are in nature similar to two subcritical systems
driven by external neutron sources, and can thus be treated as such in a Monte Carlo framework.
The definition of these two equivalent problems nevertheless requires the possibility to modify the
macroscopic cross-sections, and we use the work of Kuijper, van der Marck and Hogenbirk to
define group-wise macroscopic cross-sections in MCNP. The method is illustrated in this
paper at a frequency of 1 Hz, for which only the real part of the neutron balance plays a significant
role and for driving fluctuations leading to neutron sources having the same sign in the two
equivalent sub-critical problems. A semi-analytical diffusion-based solution is used to verify the
implementation of the method on a test case representative of light water reactor conditions in an
infinite lattice of fuel pins surrounded by water. The test case highlights flux gradients that are
steeper in the Monte Carlo-based transport solution than in the diffusion-based solution.
Compared to other Monte Carlo-based methods earlier proposed for carrying out stationary
dynamic calculations, the presented method does not require any modification of the Monte Carlo
group-wise macroscopic cross-sections