U1 and P1 approximations to neutron transport equation for diffusion length calculation

Abstract

U-1 and P-1 approximations are used for the calculation of asymptotic relaxation length in one-dimensional neutron transport equation. The approximation methods are applied to anisotropic neutron transport equation with backward and forward scattering. The methods are based on the series expansion of the neutron angular flux in terms of the Chebyshev polynomials of second kind and Legendre polynomials. By applying the first order approximation to the transport equation, asymptotic relaxation lengths are calculated. Numerical results obtained from both methods are compared with each other.