Modified Chebyshev polynomial (U N ) approximation in the neutron transport theory and computation of critical half thicknesses

Abstract

Abstract A general theoretical scheme for the UN method and the evolution of a general eigenvalue spectrum are described. The applicability of UN method to one dimensional slab geometry neutron transport problems is discussed. The eigenvalue spectrum is calculated for isotropic scattering with different values of the parameter c, the mean number of secondary neutrons per collision, known as the fundamental eigenvalue. Then the critical slab problem has been studied. The critical half thicknesses are computed for different values of c. For the solution, Mark and Marshak boundary conditions are used. Results are obtained for both, UN and PN approximations for comparison.