Approximate Models for Neutral Particle Transport in Ducts with Wall Migration

Abstract

The problem of monoenergetic neutral particle transport in a duct with wall migration for various shielding materials is treated using an approximate one-dimensional model and a Monte Carlo-based multivariate logistic regression model. The one-dimensional model is a third-order approximation in a hierarchy of approximations derived by a weighted residual procedure that accounts for wall migration by means of a kernel density. Physical constants required for the one-dimensional model—scattering probability (c) and the average distance traveled in walls (d) — are calculated using MCNP’s PTRAC and a corresponding parsing code. Numerical results for the one-dimensional model are based on a discrete ordinates solution and compared to MCNP. The logistic regression models are developed using the R language in statistical computing for three explanatory variables— duct radius (r), length (L), and shield thickness plus inner radius (S)— where each parameter is explored via univariate models. Data for the models is collected from MCNP via automated processes using Python and shell scripts. The logistic regression models lead to analytical expressions, which are evaluated by randomly dividing our data set into training and test sets, and calculating predictions.