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4th-Order-SENS: A Software Module for Efficient and Exact 4th-Order Sensitivity Analysis of Neutron Transport

Ruixian Fang, Dan G. Cacuci

Nuclear Science and Engineering / Volume 198 / Number 8 / August 2024 / Pages 1682-1737

Computer Code Abstract / dx.doi.org/10.1080/00295639.2023.2255725

Received:May 12, 2023
Accepted:August 26, 2023
Published:June 14, 2024

This work presents a software module called 4th-Order-SENS, which enables the efficient computation of exactly obtained expressions for all sensitivities, up to and including the 4th order, of a functional of the particle flux (e.g., the leakage of particles out of a body) with respect to nuclear parameters (total, scattering, and fission cross sections; nu, chi, sources; and number densities) for systems modeled by the neutron transport equation. The 4th-Order-SENS module implements the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Linear Systems (nth-CASAM-L), which is the only practically implementable methodology for obtaining the exact expressions of arbitrarily high-order sensitivities of model responses to model parameters, for response-coupled forward/adjoint large-scale linear systems. In addition to presenting the equations that are solved to obtain the 1st-order through 4th-order sensitivities, this work also describes the components of the module 4th-Order-SENS, including the user interface, input file, output files, and several independent code verification capabilities using symmetries and/or finite-difference formulas. The 4th-Order-SENS module is written in Python and Fortran and runs on Linux platforms. Several illustrative applications involving fixed-source problems in one-dimensional spherical and slab geometries are also presented.