On the Well-Posedness of Green's Function Reconstruction via the Kirchhoff-Helmholtz Equation for One-Speed Neutron Diffusion
This addresses the problem of real-time neutron flux monitoring for nuclear reactor operators, though it appears incremental as it focuses on mathematical validation rather than new practical implementation.
This work tackles the problem of reconstructing neutron flux distribution in nuclear reactors using ex-core detector measurements by demonstrating the well-posedness of a data-driven Green's function approximation via the Kirchhoff-Helmholtz equation. The result establishes the existence and uniqueness of the Green's function inferred from sampled data, ensuring the reliability of the proposed reconstruction method.
This work presents a methodology for reconstructing the spatial distribution of the neutron flux in a nuclear reactor, leveraging real-time measurements obtained from ex-core detectors. The Kirchhoff-Helmholtz (K-H) equation inherently defines the problem of estimating a scalar field within a domain based on boundary data, making it a natural mathematical framework for this task. The main challenge lies in deriving the Green's function specific to the domain and the neutron diffusion process. While analytical solutions for Green's functions exist for simplified geometries, their derivation of complex, heterogeneous domains-such as a nuclear reactor-requires a numerical approach. The objective of this work is to demonstrate the well-posedness of the data-driven Green's function approximation by formulating and solving the K-H equation as an inverse problem. After establishing the symmetry properties that the Green's function must satisfy, the K-H equation is derived from the one-speed neutron diffusion model. This is followed by a comprehensive description of the procedure for interpreting sensor readings and implementing the neutron flux reconstruction algorithm. Finally, the existence and uniqueness of the Green's function inferred from the sampled data are demonstrated, ensuring the reliability of the proposed method and its predictions.