Time–eigenvalue calculations in multi-region Cartesian geometry using Green’s functions

• Published in: Annals of nuclear energy Vol. 32; no. 9; pp. 964 - 985
• Main Authors: Kornreich, Drew E., Parsons, D. Kent
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-06-2005
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2005.02.004

We have continued the progression of providing benchmark-quality eigenvalue calculations in multi-region Cartesian geometry by reformulating the effective multiplication equations to calculate time eigenvalues. As with effective multiplication eigenvalues, there are few benchmark-quality solutions for time–eigenvalue calculations in multi-region multiplying systems, especially for systems that have divergent temporal neutron populations. The purpose of this paper is to describe the reformulations required and to add benchmark-quality calculations for several test problems. Green’s functions are used to model a multi-region, one-group, isotropically scattering, multiplying system in Cartesian geometry to obtain boundary flux values for a time–eigenvalue search and subsequent eigenfunction calculation. As usual with multi-region Cartesian systems, the solution is facilitated using (1) Placzek’s lemma, which allows us to consider a multi-region system one region at a time as an infinite medium, and (2) the calculation of the Green’s function solution for a nonphysical infinite multiplying medium.