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The Adjoint Discrete Ordinates Solution Applied to Direct and Inverse Neutral Particle X, Y-Geometry Source-Detector Problems

Solving the adjoint transport equation allows obtaining maps of the neutral-particle importance to an objective function, e.g., a detector response. In source-detector problems, the adjoint interior source is defined as the macroscopic absorption cross section of the material the detector is made of. Determining the intensity of a source of particles in each energy group (causes) is possible by solving an inverse source-detector problem, given the source location and the detector response (effects). In this work, we present the application of an adjoint technique to solve energy multigroup X,Y-geometry direct and inverse transport problems. In order to obtain the importance maps, we have extended the adjoint spectral Green's function constant-nodal (SGF*-CN) method to numerically solve energy multigroup adjoint transport problems in the discrete ordinates formulation. Described here are the methodology to obtain the discretized SGF*-CNequations and the adjoint partial one-node block inversion scheme used to iteratively solve these equations. We present numerical results to two test problems to illustrate the accuracy of the present methodology.