Calculating α Eigenvalues of One-Dimensional Media with Monte Carlo

Abstract

This paper presents results from the application of a Monte Carlo Markov Transition Rate Matrix Method to calculate forward and adjoint α eigenvalues and eigenfunctions of one-speed slabs, and perform eigenfunction expansion to approximate the time-dependent flux response to user-defined sources. The formulation of this method relies on the interpretation that the operator in the adjoint α-eigenvalue problem describes a continuous-time Markov process, i.e., elements of this operator are rates defining particles transitioning among the position-energy-direction phase space. A forward Monte Carlo simulation tallies these elements for a discretized phase space, using careful bookkeeping during the random walk. We compare calculated eigenvalues and eigenfunctions to those obtained by the Green's Function Method for multiplying and non-multiplying multi-region slabs.

Keywords:

• α eigenvalues
• Monte Carlo methods
• neutron transport