A Response Matrix Method for Slab-Geometry Discrete Ordinates Adjoint Calculations in Energy-Dependent Neutral Particle Transport

Abstract

Presented here is an application of the Response Matrix (RM${}^{†}$) method for adjoint discrete ordinates (S${}_{\mathrm{N}}$) problems in slab-geometry applied to energy-dependent neutral particle transport problems. The RM${}^{†}$ method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree with the numerical values obtained from the analytical solution of the energy multigroup adjoint S${}_{\mathrm{N}}$ equations. The main contribution of this work is to analyze the application of the RM${}^{†}$ method to problems where it is required to solve the energy multigroup adjoint S${}_{\mathrm{N}}$ equations multiple times. This is the case of two classes of problems that can be taken care of through the adjoint technique: (i) source-detector problems; and (ii) the estimation of interior neutron source distributions that drive a subcritical system at a prescribed power density level. The efficiency (speed and accuracy) of the RM${}^{†}$ code is compared to the conventional Diamond Difference code.

Keywords:

• Adjoint transport problems
• discrete ordinates
• energy multigroup
• slab-geometry

Acknowledgments

The authors also would like to express their gratitude to the support of Conselho Nacional de Desenvolvimento Científico – Brasil (CNPq) – and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro – Brasil (FAPERJ).

Additional information

Funding

This study was financed in part by the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro – Brasil (FAPERJ) – and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.