Using the Schwinger Variational Functional for the Solution of Inverse Transport Problems

A new iterative inverse method for gamma-ray transport problems is presented. The method, based on a novel application of the Schwinger variational functional, is developed as a perturbation problem in which the current model (in the iterative process) is considered the initial, unperturbed system, and the actual model is considered the perturbed system. The new method requires the solution of a set of uncoupled one-group forward and adjoint transport equations in each iteration. Four inverse problems are considered: determination of (a) interface locations in a multilayer source/shield system, (b) the isotopic composition of an unknown source (including inert elements), (c) interface locations and the source composition simultaneously, and (d) the composition of an unknown layer in the shield. Only the first two problems were actually solved in numerical one-dimensional (spherical) test cases. The method worked well for the unknown interface location problem and extremely well for the unknown source composition problem. Convergence of the method was heavily dependent on the initial guess.