Prompt Fission Neutron Spectrum Uncertainty Propagation Using Polynomial Chaos Expansion

The polynomial chaos expansion-stochastic collocation method (PCE-SCM) is demonstrated to be a computationally efficient approach for propagating nuclear data uncertainties evaluated for the prompt fission neutron spectra (PFNS) of n + ²³⁵U and n + ²³⁹Pu fission reactions through two fast neutron critical benchmark experiments. A principal component decomposition of the PFNS covariance matrices yields an efficient representation of the uncertainty in terms of two to four random variables. Both normal and uniform distributions are considered for these random variables, and the random output variables (angular flux and k-eigenvalue) are expressed in terms of Hermite and Legendre chaos expansions, respectively. Tensor product Hermite and Legendre Gauss quadrature sets, respectively, are used to relate the deterministic chaos expansion coefficients to solutions of independent transport k-eigenvalue problems, and the resulting polynomial chaos expansion provides a complete statistical characterization of the uncertainty in the output variables. Direct random sampling of the PFNS followed by repeated solution of the transport problem to create an ensemble of solutions is used to benchmark results obtained from the PCE-SCM implementation. Both direct random sampling and the PCE-SCM implementation yield comparable results where, for the Jezebel and Lady Godiva critical assemblies, the calculated uncertainties in k_eff resulting from the PFNS propagated uncertainties are found to be of the same order or larger than reported experimental measurement uncertainties, respectively. The PCE-SCM implementation results obtained require orders of magnitude less computational resources compared with the direct random sampling approach.