Calculation of extrapolation distances by low order Chebyshev polynomial approximation of transport equation in slab geometry

In this study, the problem of extrapolated end point has been studied in one-speed neutron transport equation with isotropic scattering by using the Chebyshev polynomial approximation which is called TN method. Assuming neutrons of one speed, extrapolated end point are calculated for the uniform finite slab using Mark and Marshak type vacuum boundary conditions. It is shown that low order TN method gives very good results of low order spherical harmonics approximation and diffusion theory for extrapolation of the flux of neutrons leaking from the medium. We present an alternative method which is similar to P1 method to calculate the extrapolation distances z0. Moreover, we prefer new solution of transport equation in one-dimensional slab geometry.