Energy Dependent Source Reconstructions via Explicit Formulations of the Adjoint Particles Flux

Abstract

An analytical solution to the discrete ordinates approximation of the adjoint to the multigroup transport equation in one-dimensional slab geometry is developed in this work, in order to be used in source estimation problems. The solution is firstly tested in a source-detector problem, where explicit expressions are derived to approximate the absorption rate of particles of internal detectors. Noisy data generated from readings of internal detectors were then used, along with the adjoint formulation, in an iterative process to solve an energy-dependent inverse problem of source reconstruction in the cases of polynomials and piecewise constant sources. The approach is shown to be fast and accurate.

Keywords:

• Adjoint transport equation
• analytical methods
• inverse problems
• source-detector
• source estimation
• ADO method

Acknowledgments

The authors would like to thank CNPq and CAPES for partial financial support to this work.