A probability-conserving cross-section biasing mechanism for variance reduction in Monte Carlo particle transport calculations

TL;DR

This paper introduces a probability-conserving biasing mechanism for Monte Carlo particle transport that adjusts reaction cross sections and track weights to reduce variance without distorting key results, enabling more efficient simulations of rare events.

Contribution

It presents a novel theory and sample implementation for cross section biasing in Geant4 that conserves probability and maintains result accuracy across a wide range of bias factors.

Findings

Allows cross section scaling by factors over 10^4 without result distortion

Maintains energy deposition and coincidence rates despite biasing

Applicable for both increased and decreased cross section scenarios

Abstract

In Monte Carlo particle transport codes, it is often important to adjust reaction cross sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analogous Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross section change. This makes it possible to increase the cross section of nuclear reactions by factors exceeding 10^4 (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful, for example, in problems that involve computation of particle penetration deep into a target, such as occurs in atmospheric showers or in shielding.