Using the Schwinger inverse method for solutions of inverse transport problems in two-dimensional cylindrical geometries

The Schwinger method for solving inverse transport problems is applied to the problems of interface location identification, shield material identification, source isotope weight fraction identification, and material mass density identification (separately) in multilayered two-dimensional cylindrical gamma radiation source/shield systems. The method is iterative and estimates unknown interface locations, source isotope weight fractions, and material densities directly, while the unknown shield material is identified by estimating its total macroscopic gamma-ray cross sections. The energies of discrete gamma-ray lines emitted by the source are assumed to be known, while the unscattered flux of the lines is assumed to be measured at points external to the system. In numerical test cases, the Schwinger method correctly identifies the unknowns when the same deterministic ray-tracing code is used for both the parameter estimation process and simulation of the measured data. With realistic simulation of the measured data using a Monte Carlo code, the method produces more ambiguous results for interface location, shield material identification, and material density identification. The method works well for source weight fraction identification with measured data simulated by Monte Carlo. In addition to the application to more realistic (two-dimensional) problems, this paper extends previous work on the Schwinger inverse method by using surface formulas for unknown interface locations, automatic correction attempts for violated constraints, and ray-tracing instead of discrete-ordinates for transport calculations.