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Criticality eigenvalues of the one-speed transport equation with strong forward—backward scattering -relationship with rod model

1998; Taylor & Francis; Volume: 27; Issue: 2 Linguagem: Inglês

10.1080/00411459808205812

1532-2424

D. C. Sahni, N.G. Sjöstrand,

Nuclear physics research studies

Abstract The one—speed neutron transport equation with strong forward and backward scattering (characterized by α and β) has been solved analytically for an infinite slab with a finite order Sn method. It is shown that the solution changes smoothly as c(α + β) passes unity. For a fixed criticality factor, c, a finite thickness is obtained both for α + β = 1/c and = 1. When the number of directions goes to infinity, the critical slab thickness vanishes at c(α + β) = 1. The total flux is then asymptotically given by a cosine function going to zero at the boundary. This is in contrast to the integral equation, which gives a different flux distribution. The results are supported by numerical calculations using the S4, S16 and S96 approximations.