Critical thickness problem for tetra-anisotropic scattering in the reflected reactor system

Abstract

Critical thicknesses are calculated in reflected systems for high-order anisotropic scattering by using neutron transport theory. The anisotropic systems are taken into account from isotropic to tetra-anisotropic scattering terms one by one. Neutron transport equation is solved by using the Legendre polynomial $\hbox {P}_{\mathrm {N}}$ method and then Chebyshev polynomial $\hbox {T}_{\mathrm {N}}$ method. The eigenfunctions and eigenvalues are calculated for different numbers of secondary neutrons (c) up to the ninth-order term in the iteration of the two methods. The Marshak boundary condition is applied to find critical thickness for the reflected reactor system. Thus, a wide-range critical thickness spectrum has been generated, depending on the number of secondary neutrons, anisotropic scattering coefficients and different range of reflection coefficients. Finally, the calculated critical thickness values are compared with those in the literature and it is observed that our results are in agreement with them.