A probabilistic study of the influence of parameter uncertainty on solutions of the neutron transport equation

The influence of uncertainty in the scattering and absorption cross sections on the solution of the neutron transport equation is studied using polynomial chaos theory. The uncertainty is defined by means of uniform and log-uniform probability distributions. By expanding the neutron flux in a series of polynomial chaos functions we may reduce the stochastic transport equation to a set of coupled deterministic equations, analogous to those that arise in multi-group neutron transport theory, with the effective multi-group transfer scattering coefficients containing information about the uncertainty. This procedure enables existing transport theory computer codes to be used, with little modification, to solve the problem. Applications are made to a transmission problem and a constant source problem in a slab. In addition, we also study the rod model for which exact analytical solutions are readily available. In all cases, numerical results in the form of mean, variance and sensitivity are given which illustrate how absorption and scattering cross section uncertainty influences the solution of the transport equation.