Solution of the critical thickness problem for one-speed neutrons in a slab with forward-backward scattering using Chebyshev polynomials approximation

In this thesis, the critical thickness problem in one-speed, one-dimensional and time-dependent neutron transport equation with isotropic scattering will be investigated. First, the neutron angular flux will be conventionally expanded in a series of second kind of the Chebyshev polynomials with their well-known properties. The isotropic scattering kernel with the combination of forward and backward scattering will be chosen for the neutrons in a uniform finite slab. Later, the time-dependent transport equation will be reduced to a time-independent form with a reasonable approach and then the critical thicknesses will be computed for various time decay constants and the scattering parameters. Some of the results obtained from this study will be compared with the results existed in literature and thus the availability and the applicability of the method used in this study will be discussed.