An effective mesh-free fission source convergence indicator for Monte Carlo k-Eigenvalue problems

Abstract

In Monte Carlo k-eigenvalue problems, the entropy of the fission site distribution is calculated after each fission cycle and its evolution over the entire fission cycles is examined. Here, the entropy evolution equilibrates as soon as the fission source distribution converges. Unfortunately, the standard entropy calculation requires space discretization with an additional effort to assign the fission sites into the space bins. Plus, the decision on choosing the number of spatial bins is subjective and based on code users’ experience. Therefore, a consistent mesh-free convergence indicator is proposed as an alternative to the conventional entropy indicator. The indicator utilizes the fundamental mode coefficient of the Fourier series expansion of the fission site distribution. Also, it eliminates the need for user specification on spatial meshing for the purpose of entropy calculation. The numerical tests conducted in this paper indicates that the new indicator is as reliable as the conventional entropy indicator and able to indicate the instance where the source distribution has converged.