Estimation of a Fission Product Concentration Distribution in a Spherical Body from Surface Release Measurements

The diffusion of fission products (FPs) in reactor materials affects the nuclear source term. The diffusion coefficient itself is measured through various techniques. In the release method, it is of interest to know the initial distribution of the FPs in nuclear graphite or other materials from an exterior measurement like mass surface flux or cumulative mass release. In this paper, a Fredholm integral of the first kind is considered, relating the initial distribution to the cumulative release fraction of a diffusant from a spherically symmetric body. The Tikhonov regularization, conjugate gradient least-squares (CGLS) method, and algebraic reconstruction technique (ART) with nonnegativity and conserved mass constraints were compared to fractional release data from a simulated linear profile using data for Cs diffusion in a 0.32-cm sphere NBG-18 at 1090 K. The Tikhonov regularization was shown to provide a better estimation of the initial linear distribution than the CGLS and ART methods. The performance of the Tikhonov regularization was further examined with simulated constant, quartic, and exponential initial distributions. The Tikhonov regularization provided a reasonable recovery of the exponential profile, while the estimation of the linear, constant, and quartic profiles suffers from several issues.