Fission source convergence of Monte Carlo criticality calculations in weakly coupled fissile arrays

Anomalous fission source convergence in a Monte Carlo criticality calculation for a weakly coupled array of two fissile material units are demonstrated. Introducing coupling coefficients among array units, it is quantitatively explained that this anomaly is caused by an insufficient restoring force to the true distribution and its large statistical uncertainty, especially, in a symmetric system. A new approach for estimating the fission source intensity ratio in an array is proposed by obtaining the eigenvector of a coupling coefficient matrix. This method also gives the uncertainty of the ratio as well as the ratio, which is available for evaluating the accuracy of the obtained ratio. The correlation between a calculated k(eff) and the fission source intensity ratio is formulated. It is illustrated theoretically and empirically that there is no significant correlation in a symmetric two-unit array system. In general, care should be taken that a calculated k(eff) may be biased by an incorrect fission source distribution, especially, in a slightly asymmetric system. A regionwise weight adjustment method is developed such that the fission source intensity ratio is forced to converge to a predetermined ratio. Using this method, a satisfactory convergence can be achieved. A larger number of neutrons per generation is recommended for a Monte Carlo criticality calculation of a weakly coupled array of units.