Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport

Abstract

Criticality type eigenvalues of the one-speed transport equation in a homogeneous slab with anisotropic scattering and Marshak boundary conditions are considered. The connection between the transport equations for a critical and for a time-decaying system is established, and thus the time-dependent equation is reduced to the stationary one. Variation of the size of the time-dependent system with anisotropic scattering is studied numerically. Calculations for different combinations of the scattering parameters and the selected values of the time decay constant using the method are reported. Results are discussed and compared with those already obtained using various methods available in the literature.

TN approximation on the critical size of time-dependent, one-speed and one-dimensional neutron transport problem with anisotropic scattering

“…Therefore, when the neutron flux density in a pulsed neutron experiment decays exponentially it is possible to remove the time dependence from the neutron flux and to get a stationary one in transport theory. The time eigenvalues of many systems can be determined by calculating the critical size of those systems in stationary condition [1,2].…”

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

“…The problem of anisotropy and its effects on the size of the system is one of the most important problems of transport theory. Many methods for computing transport equations have been proposed, such as the spherical harmonics ( N P ) method [1,2] and the discrete ordinates ( N S ) method [3,4,5]. 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.…”