A kinetic theory of nonanalog Monte Carlo methods for penetrating radiation.

Abstract

A new Monte Carlo Boltzmann (MCB) equation is proposed to describe the behavior of nonanalog Monte Carlo particle transport simulations. The MCB equation has weight as one of its independent variables and describes the transport processes of the particles governed by a set of rules for the transition of space, velocity, and weight. For simulations of transmission current utilizing the exponential transform with angular biasing and a last event estimator, the weight moments of the solution of the MCB equation predict the score moments. The spatial and angle integration of the zeroth weight moment predicts the mean number of flights per history. Therefore, one can predict the efficiency of the simulations by calculating the figure of merit using the MCB equation. Simulations of transmission current utilizing geometric splitting and a last event estimator are also analyzed. The MCB equation can be also used to predict the mean number of various events. Its adjoint equation is formulated to predict the score moments. Simulations of a source-detector problem utilizing a track length estimator are analyzed. The adjoint integro-differential equation is directly formulated to predict the score moments. The ratio of the relative error of sample variance to the relative error of sample mean is investigated for various scattering ratios and source-detector distances. Numerical results are presented to validate the above theory.