Calculation of the diffusion lengths for one-speed neutrons in a slab with forward and backward scattering

Year 2018, Volume: 2 Issue: 3, 287 - 291, 15.12.2018

Hakan Öztürk , Ökkeş Ege

Abstract

The diffusion lengths for
one-speed neutrons in a slab are calculated using the first kind of Chebyshev
polynomials approximation (T_N)
method. The scattering models are constituted in place of the scattering
function with an argument of the cosine of the neutron scattering angle.
Therefore, the forward-backward-isotropic (FBI) scattering model is used as the
scattering function in transport equation which describes the interaction and
the conservation of the neutrons throughout a system. In the solution
algorithm, first the neutron angular flux is expanded in terms of the Chebyshev
polynomials of first kind. After inserting this expansion in the transport
equation, the coupled differential equations are derived using the properties
of the Chebyshev polynomials of first kind. These equations are solved together
and then the diffusion equation is obtained by applying the first order
approximation (N = 1) which is known
as the diffusion approximation. Finally, the diffusion lengths for one-speed
neutrons are calculated for selected values of the collision, backward and
forward scattering parameters. The calculated diffusion lengths are given in
the tables together with the ones already obtained in literature in order to
indicate the applicability of the present method. The convenience and rapid
convergence of the present method with its easily executable equations can be
observed from the derived equations and the results in tables.

Keywords

Forward and backward scattering, Diffusion length, Slab geometry

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