TRANSFER-MATRIX TREATMENTS IN TRIMARAN-II, NONEQUALLY PROBABLE STEP-FUNCTION REPRESENTATION IN MULTIGROUP MONTE-CARLO

The coefficients of a truncated Legendre series are usually used in mu ltigroup cross-section sets to treat the angular distribution for a gr oup-to-group scattering event. Fine energy meshes and low-order Legend re expansions result in negative values in the corresponding multigrou p Legendre expansions; therefore, special transfer matrix treatments f or multigroup cross sections are needed.The difficulties of the trunca ted 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 r epresentation 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 cau se ray effects; the EPSF representation can eliminate ray effects, but it is not suitable for the treatment of the transfer matrix for mater ial mixtures, because both forward- and backward-peaked scattering are present in this kind of cross section. A new method, the nonequally p robable step function (NEPSF) representation, which combines the advan tages of both the discrete angle and EPSF representations, is introduc ed. It can eliminate ray effects and accurately preserve the moments. The conjugate gradient method, powerful for solving multidimensional m inimization problems, is used to obtain both the EPSF and NEPSF repres entations. A problem of neutron transmission in a hydrogenous material is used to compare the three representations. Comparisons of the TRIM ARAN-II results with the three representations to those of the TRIPOLI -4 pointwise cross-section Monte Carlo code are given.