A “Transport” Condensed History Method

Abstract

“Condensed history” methods [1–4] are Monte Carlo electron transport simulation algorithms in which the cumulative effects of multiple electron collisions are approximated in a single “step” of (user-specified) path length s₀. This “step,” often chosen to be many mean free paths, is the distance that each Monte Carlo electron travels between “collisions”. Many current condensed history methods utilize a splitting routine over the range 0 ≤ s ≤ S₀. For example, the PENELOPE method [3] splits each step into two substeps; one with length ξS₀ and one with length (1 — ξ)s₀, where ξ is a random number from 0 < ξ < 1. A simpler method was proposed earlier by Berger [1], who suggested that the two substeps should have equal length s₀/2. Because condensed history methods approximate the physical transport process, solutions of condensed history simulations contain both statistical errors and a truncation error - which is presumably proportional to some power of the path length s₀. Also, because condensed history schemes are not equivalent to transport schemes, they contain features that lead to difficulties in some practical calculations. Most notably, it is not always easy to move condensed history Monte Carlo particles accurately across a material interface. For example, as a Monte Carlo particle approaches an interface, the PRESTA method in EGS2 considers a sequence of smaller steps, until the particle is almost traveling in an analog mode [4]. After the particle passes through the interface, the steps are gradually increased back to s₀.