Sensitivity Analysis and Uncertainty Quantification of Neutron Multiplicity Statistics using Perturbation Theory

It is frequently important to estimate the uncertainty and sensitivity of measured and com- puted detector responses using simulations of experiments. These uncertainties arise from the physical construction of the experiment and from uncertainties in the transport pa- rameters. In particular, the solution is geometrically sensitive to the fission neutron yield distribution. Perturbation theory enables sensitivity analysis and uncertainty quantification (SA/UQ) on integral quantities like detector responses. The aim of our work is to apply SA/UQ to subcritical neutron multiplicity counting distributions. Current SA/UQ methods have only been applied to mean detector responses and the k-effective eigenvalue. For mul- tiplicity counting experiments, knowledge of the higher order counting moments and their uncertainties are essential for a complete SA/UQ analysis. We are applying perturbation theory to compute the sensitivity of neutron multiplicity counting moments of arbitrarily high order. Each moment is determined by solving an adjoint transport equation with a source term that is a function of the adjoint flux of lower order moments. This formulation enables moments of arbitrarily high order to be sequentially determined, but it also shows that each moment is sensitive to the uncertainties of all the lower order moments. This work will produce a new technique to adjust the evaluated values of nuclear parameters using subcritical neutron multiplicity counting experiments, and it will enable a more de- tailed sensitivity and uncertainty analysis of subcritical multiplicity counting measurements of special nuclear material.