A Numerical Solution of Low-Energy Neutron Boltzmann Equation

Abstract

A multigroup method using a straight ahead approximation is created to calculate low energy neutron fluence due to the elastic scattering of evaporation neutrons produced in interactions of high energy particles with target nuclei. This multigroup method is added to NASA Langley Research Center's HZETRN particle transport code. This new code is used to calculate the energy spectra of the neutron fluence in several different materials. The multigroup method is found to be an efficient way of calculating low energy neutron fluence in multiple atom materials as well as single atom materials. Comparisons to results produced by Monte Carlo methods show that the straight ahead multigroup method is accurate for larger depths but less accurate for small depths due to leakage at the boundary. For this reason, an improved multigroup method is created which propagates neutrons in two directions, forward and backward approximately accounting for the isotropic distribution of the evaporation source. This new multigroup method compares well with the Monte Carlo method at all depths. For this reason, the multigroup method is considered an accurate method which is highly computationally efficient for calculating low energy neutron fluence.