A theoretical derivation of the Condensed History Algorithm

Abstract

Although the Condensed History Algorithm is a successful and widely-used Monte Carlo method for solving electron transport problems, it has been derived only by an ad-hoc process based on physical reasoning. In this paper we show that the Condensed History Algorithm can be justified as a Monte Carlo simulation of an operator-split procedure in which the streaming, angular scattering, and slowing-down operators are separated within each time step. Different versions of the operator-split procedure lead to (O([Delta]s) and O([Delta]s2) versions of the method, where [Delta]s is the path-length step. Our derivation also indicates that higher-order versions of the Condensed History Algorithm may be developed.