A Paradigm-Shifting Methodology for Sensitivity Analysis of Critical Multiplying Nuclear Systems

Dispensing with the traditional approach to solving the equations modeling multiplying critical nuclear systems as an eigenvalue system, this work proposes a new and comprehensive mathematical framework (C-Framework) that eliminates the need for solving eigenvalue problems when computing the forward and adjoint neutron flux distributions in critical reactors. Consequently, the C-Framework enables the mathematical and computational analysis of critical and noncritical multiplying systems, with or without external sources, in a unified manner. By eliminating the need for solving eigenvalue problems, the C-Framework also enables the use of more efficient numerical methods (than currently used) for computing the forward and adjoint neutron flux distributions in critical reactors. Furthermore, the C-Framework also enables the application of the Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM) as a replacement for the so-called generalized perturbation theory (GPT). The C-ASAM is much simpler to apply than the GPT, while not only yielding all of the results that the GPT can deliver, but also delivering results for all of the many—and not “GPT-allowable”—nonlinear responses of interest in reactor analysis that do not satisfy the very restrictive orthogonality relations required by the GPT’s underlying generalized adjoint equation. By dispensing with the need for solving eigenvalue problems involving the inversion of singular operators, the C-ASAM is vastly more general and more efficient than the GPT. These conclusions are underscored by exact analytical results presented for paradigm illustrative problems, which include problems that are solvable using the GPT (e.g., the system’s multiplication factor, ratios of reaction rates responses), and problems that are not solvable using the GPT (e.g., absolute reaction rates, equilibrium xenon concentration responses); all of these problems are shown to be solvable exactly and most efficiently within the C-ASAM framework.