The Methods and Applications of Monte Carlo in Low Energy (≲ 20 MeV) Neutron-Photon Transport (MORSE). Part I: Methods

Abstract

The Monte Carlo solution of the Boltzmann transport equation differs considerably from other standard numerical solutions such as discrete ordinates.^1,2 The discrete ordinate solution usually provides a rather complete description of the particle fluxes in all of phase space (spatial coordinates, x, y, z; angular direction, u_x, v_y, w_z; time, t; energy, E; etc.) in contrast to the Monte Carlo solution which usually only provides information about certain regions of the phase space. The Monte Carlo method utilizes random sampling from the physical probability distributions which describe what happens to the individual particles. For example, by sampling from ${e^{ - {\Sigma _T}x}}$ where Σ_T is the total interaction cross section, one knows how far the particle travels before interacting, and from the ratio Σ_i/Σ_T, where $\mathop \Sigma \limits_{j = 1}^n {\Sigma _j} = {\Sigma _T}$, what is the probability that the ith interaction will occur. The analysis of what happens to these particles constitutes the solution, that is, do the particles escape from the system, are they captured, how many particles cross a given boundary, etc.