Criticality and time eigenvalues for one-speed neutrons in a slab with forward and backward scattering

Abstract

The combination of strongly forward and backward scattering with usual linearly anisotropic scattering has been studied for one-speed neutrons in infinite slabs with vacuum boundary conditions. For critical systems the criticality factor is given for two slab thicknesses and different degrees of the anisotropic scattering. The special case when the forward and backward scattering completely dominate over the 'ordinary' scattering is discussed in detail. The time decay of a neutron field in a moderator has also been studied. It is shown that the decay constant for thin slabs cannot exceed a certain limit determined by the degree of strongly forward and backward scattering.

Modified spherical harmonics method for one-speed transport equation with anisotropic scattering

“…With conventional notation [6], the starting linear transport equation for neutrons of one speed can be written as…”

“…When the forward and backward scattering completely dominate over the 'ordinary' scattering (the extreme case) or the thickness of the slab approaches to zero, the angular distribution is very strongly peaked along the direction parallel to the slab surface, one has to take high-order functions into account for the highly peaked angular flux. The standard N P method is thus inadequate for this type of problem [1,6]. D. C. Sahni has solved the problem by combining the N S method, integral equation method and eigenvalue method [6].…”

“…The standard N P method is thus inadequate for this type of problem [1,6]. D. C. Sahni has solved the problem by combining the N S method, integral equation method and eigenvalue method [6]. To the best knowledge of the present author there is currently no article on completely calculating various combinations of the scattering parameters including the extreme case.…”

Numerical results for the transport equation with strongly anisotropic scattering in a slab

“…The transport equation with forward and backward scattering was first introduced by Fermi (see Williams, 1985) and later extended by Williams (1966), Inönü (1973) and Sahni et al (1992) providing greater flexibility in representing realistic scattering cross sections (see the comments of Davison and Sykes, 1958). Although, these kernels were introduced for modeling of neutron transport, they have also been used in radiative transfer problems.…”

“…For instance, Spiga and Vestrucci (1981) developed a semi-analytical algorithm to calculate the critical total flux of the transport operator. Sahni et al (1992) applied discrete ordinates S N combined with the Carlvik's method to compute the eigenvalues of this operator. Ganapol and Kornreich (1996) simulated the scalar flux by their Green's function method.…”