Second-Order Correction for Statistical Bias in Monte Carlo Depletion Calculations

Esthem Bouvet; Benoit Forget; Dean Price

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arXiv · 2610.24932

Second-Order Correction for Statistical Bias in Monte Carlo Depletion Calculations

Esthem Bouvet·Benoit Forget·Dean Price

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Abstract

Depletion analyses are often driven by Monte Carlo neutron transport methods that introduce uncertainty into the transmutation matrix used to evolve a material composition. The nonlinearity of the matrix exponential applied to this transmutation matrix causes the uncertainty to introduce a systematic bias in the computed isotope vectors. This work derives a second-order correction for this bias that can be computed with quantities obtainable from typical Monte Carlo transport routines. An augmented Bateman system is formulated to evaluate these quantities and an adapted Chebyshev rational approximation method uses transmutation matrix factorizations for efficient evaluation of the second-order correction. Then, the correction is demonstrated using a ten-nuclide verification problem, an ITER port-plug activation problem, and a 9-pin boiling water reactor lattice containing self-shielded gadolinium-bearing fuel.

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Esthem Bouvet, Benoit Forget, Dean Price. 2026-10-18. Second-Order Correction for Statistical Bias in Monte Carlo Depletion Calculations. https://arxiv.org/abs/2610.24932

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