Application of the Chebyshev polynomial (TN and UN) approximation to reflected slab geometry in the neutron transport equation and computation of critical half thicknesses

Abstract

The transport of one-speed neutrons has been studied in isotropically scattering slab using ultraspherical polynomial approximation whose sub-cases are spherical harmonics approximation and Chebyshev polynomial approximation of first and second kind with reflective boundaries. An integral equation for the total flux has been derived and solved numerically for different values of c and reflection coefficients. In the solution, Marshak type vacuum boundary conditions were used. The critical thicknesses obtained by the Chebyshev polynomial method are in good agreement with literature values. Computations were made by using the T-N, U-N and P-N approximations for comparison.