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A mesh-input-free on-the-fly source convergence indicator is proposed for Monte Carlo source iterations by the power method. This indicator consists of two step computations of source particle centers. In the first step, the geometric center of all source particles is computed. The spatial domain is then divided into eight subdomains by the xy, yz, and zx planes that intersect at the geometric center. In the second step, a new geometric center is computed for the source particles in each of the eight subdomains. Therefore, nine centers are obtained at each cycle of source iterations and the distances to the corresponding centers at the initial cycle are computed, yielding the nine center-distances sum (NCDS). NCDS was compared against entropy indicators defined on a fixed mesh. Visual inspection reveals that the overall trend of NCDS is as sound as the entropy indicators. The feasibility of NCDS is shown by the step-refined on-thefly convergence diagnosis with Wilcoxon rank sum.

A mesh-input-free method is not yet established for particle population diagnosis in the power distribution calculation by the Monte Carlo source iteration method. To approach this issue, the Euclidean minimum spanning tree (EMST) in the graph theory was applied to the source particles. A characteristic volume that one particle covers was defined to be the cubic power of the average edge length of EMST. Thirty and one hundred times of the characteristic volume were proposed as weak and strong requirements, respectively, for a minimum tally cell volume since ten particle characteristic volumes can be accommodated within the tally cells producing one-third and 10% of average power density. These requirements were examined against a three-dimensional full-core model of a 1,100 MWe pressurized water reactor. The comparison with the population diagnosis with a mesh in Nucl. Sci. Eng., 158, 15 (2008) shows a lot of promise of the EMST-based approach. Further developmental issues are identified concerning computational time and output fitting. In addition, a practically useful result was obtained as follows. If the three-dimensional uniform tally cells have volume larger than the quarter fuel bundle unit, the EMST-based approach yields a less conservative diagnosis than fissile volume per source particle.

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