Verification of analytic energy moments for the one-dimensional energy dependent neutron diffusion equation with MCNP5 and Attila-7.1.0

The energy dependent neutron diffusion equation (EDNDE) is converted into a moment equation which is solved analytically for the 1-D problem of a bare sphere of pure 235U. The normalized moments 0–5 generated analytically are compared to normalized energy moments, from Monte Carlo N Particle 5 version 1.40 (MCNP5) and Attila-7.1.0-beta version (Attila). The analytic normalized neutron energy moments, fall between the results from MCNP5 (lower bound) and Attila (upper bound) and are accurate compared to MCNP5 neutron energy moments when error in this Monte Carlo simulation are considered. The error range is from 0% to 14%. The Attila moments are less accurate when compared to MCNP5 than the analytical moments derived in this work. The method of moments is shown to be a fast reliable method, compared to either Monte Carlo methods (MCNP5) or 30 multi-energy group methods (Attila).

► Derived normalized energy moments with energy dependent neutron diffusion equation.
► Compared analytic energy moments 0–5 for a 100% 235U sphere with MCNP5 and Attila.
► Neutron energy moments from each method match expected physical intuition.
► Results of analytic moments are within 0–14% of MCNP5 moments.