Transfer Matrix Treatments in TRIMARAN-II, Nonequally Probable Step Function Representation in Multigroup Monte Carlo

• Published in: Nuclear science and engineering 1998-10, Vol.130 (2), p.226-238
• Main Authors: Mao, Li, Both, J. P., Nimal, J. C.
• Format: Article
• Language: English
• Subjects: Classical transport; Exact sciences and technology; Function theory, analysis; Integral equations; Mathematical methods in physics; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Transport processes
• ISSN: 0029-5639; 1943-748X
• DOI: 10.13182/NSE98-A2002

The coefficients of a truncated Legendre series are usually used in multigroup cross-section sets to treat the angular distribution for a group-to-group scattering event. Fine energy meshes and low-order Legendre expansions result in negative values in the corresponding multigroup Legendre expansions; therefore, special transfer matrix treatments for multigroup cross sections are needed. The difficulties of the truncated Legendre series representation in treating multigroup transfer are explained. In TRIMARAN-II, two existing standard methods, the equally probable step function (EPSF) representation and the discrete angle representation, which are based on preservation (at least approximately) of the first moments, are studied. The discrete angle representation has the advantage of accurately preserving the moments, but it may cause ray effects; the EPSF representation can eliminate ray effects, but it is not suitable for the treatment of the transfer matrix for material mixtures, because both forward- and backward-peaked scattering are present in this kind of cross section. A new method, the nonequally probable step function (NEPSF) representation, which combines the advantages of both the discrete angle and EPSF representations, is introduced. It can eliminate ray effects and accurately preserve the moments. The conjugate gradient method, powerful for solving multidimensional minimization problems, is used to obtain both the EPSF and NEPSF representations. A problem of neutron transmission in a hydrogenous material is used to compare the three representations. Comparisons of the TRIMARAN-II results with the three representations to those of the TRIPOLI-4 pointwise cross-section Monte Carlo code are given.