Solution of the finite slab criticality problem using an alternative phase function with the second kind of Chebyshev polynomials

Abstract

The critical size of a finite homogenous slab is investigated for one-speed neutrons using the alternative phase function (AG, Anli-Gungor) in place of the scattering function of the transport equation. First of all, the neutron angular flux expanded in terms of the Chebyshev polynomials of second kind (U-N approximation) together with the AG phase function is applied to the transport equation to obtain a criticality condition for the system. Then, using various values of the scattering parameters, the numerical results for the critical half-thickness of the slab are calculated and they are tabulated in the tables together with the ones obtained from the conventional spherical harmonic (P-N) method for comparison. They can be said to be in good accordance with each other.