Use of finite-difference diffusion Monte Carlo method to generate Shannon entropy of the fission distribution in a nuclear reactor core

Abstract

Monte Carlo criticality calculation is an iterative process which requires a guess fission distribution to start the simulations. It is important to assess when the fission source has converged, so that a sufficient number of the initial batches are discarded prior to beginning of the Monte Carlo (MC) tallies. Shannon entropy has been highly effective in characterizing convergence of the fission distribution in a reactor core. To compute Shannon entropy, transport-based MC code usually requires additional binning of the geometry along with the use of algorithms to get the distribution of fission source in these bins. This binning is done by superimposing a grid kind of structure over and above the geometry defined for transport simulation. The entropy computation in transport-based MC code thus involves additional computational efforts. In this paper, we have used finite-difference (FD) difference based diffusion MC method to calculate Shannon entropy. In this method, problem is divided into regular meshes. Shannon entropy is estimated in these mesh structures without any additional computational efforts. Shannon entropy for 3D PHWR benchmark is estimated by this method and is compared with Transport MC Code PATMOC and 3D Space Time Kinetics Code KINFIN and the results are found to be in good agreement.