Monte Carlo and Deterministic Solutions of the Forward Master Equation for Random Neutron Populations

摘要

The equilibrium neutron number probability distribution in subcritical systems has been investigated for several models of the induced and spontaneous fission multiplicity distribution by means of Monte Carlo simulation, analytical time-asymptotic solutions, and solving the recursive relation nu- merically. By drastically restricting the multiplicity emission spectrum for fission events by introducing the BFM, the recursive formulation and the Monte Carlo method were shown to agree with an analytically derived solution, permitting further model development. A well known approximate but closed form solution, namely the quadratic model, was shown to be unacceptably inaccurate for subcritical systems where the fission chains effectively do not overlap and the multiplet emission is substantially more prevalent than in a supercritical counterpart. We are currently extending this approach to obtain the equilibrium joint distribution of neutrons within the system and those that have leaked to explicitly represent the neutron PDF as observed by an external detector, allowing for experimental validation. We are also generalizing the Monte Carlo code to account for spatial dependence and multiple energy groups to provide benchmark solutions for approximate solutions to the backward Master equation with phase space dependence.