Abstract
The eigenvalue spectrum is studied for one-speed neutrons in a slab with forward and backward scattering. First, the transport equation describing the interaction of neutrons in a system with general geometry is given. Then, the scattering function in transport equation is chosen as the forward-backward-isotropic (FBI) scattering model. The resultant transport equation is solved using the Legendre polynomials expansion (PN method) and the Chebyshev polynomials of second kind expansion (UN method) in neutron angular flux. Then, the PN and UN moments of the equations are obtained using the properties of the Legendre and the Chebyshev polynomials of the second kind. Finally, the eigenvalues for various values of the collision and scattering parameters are calculated using different orders of the presented methods and they are given in the tables for comparison.
Highlights
The criticality problem of a multiplying system is among the important problems in calculations of the neutron transport theory
Since these polynomials are in the same family, i.e. Jacobi polynomials, the second kind of Chebyshev polynomials approximation (UN method) was used in criticality and diffusion length calculations for isotropic and anisotropic scattering in vacuum and reflecting boundary conditions
Before starting to apply the UN method to the problem, in order to establish a benchmark list for the comparison of the results, first the conventional PN method is applied to the transport equation for the solution of the problem
Summary
The criticality problem of a multiplying system is among the important problems in calculations of the neutron transport theory. The Legendre polynomials are the most widely used ones in the angular part of the neutron angular flux This technique is known as the PN method in literature. Since these polynomials are in the same family, i.e. Jacobi polynomials, the second kind of Chebyshev polynomials approximation (UN method) was used in criticality and diffusion length calculations for isotropic and anisotropic scattering in vacuum and reflecting boundary conditions. From those studies, it was observed that compatible results have been obtained in all cases [5,6,7,8,9]. The researchers in all areas may be interested in the solution algorithm followed in this study to apply it to their problems and an alternative method can be added to the literature
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