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.

中文翻译：

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蒙特卡罗 k-特征值问题的有效无网格裂变源收敛指标

摘要 在蒙特卡罗 k 特征值问题中，在每个裂变循环后计算裂变位点分布的熵，并检查其在整个裂变循环中的演变。在这里，一旦裂变源分布收敛，熵演化就达到平衡。不幸的是，标准熵计算需要空间离散化，并额外努力将裂变位点分配到空间箱中。此外，选择空间 bin 数量的决定是主观的，并基于代码用户的经验。因此，提出了一致的无网格收敛指标作为传统熵指标的替代方案。该指标利用了裂变位点分布的傅立叶级数展开的基模系数。还，它消除了为熵计算的目的而对空间网格划分的用户规范的需要。本文进行的数值测试表明，新指标与传统熵指标一样可靠，能够指示源分布收敛的情况。