Exact weight cancellation in Monte Carlo eigenvalue transport problems

TL;DR

This paper introduces an exact weight cancellation method for Monte Carlo eigenvalue problems in nuclear reactor physics, enabling convergence with negative weights where traditional methods fail.

Contribution

It presents a novel, exact 3D weight cancellation algorithm that ensures convergence in Monte Carlo eigenvalue calculations with negative weights.

Findings

The algorithm successfully converges on the physical eigenstate.

It handles negative weights effectively in complex 3D problems.

Demonstrated on a realistic reactor physics case.

Abstract

Random walks are frequently used as a model for very diverse physical phenomena. The Monte Carlo method is a versatile tool for the study of the properties of systems modelled as random walks. Often, each walker is associated with a statistical weight, used in the estimation of observable quantities. Weights are typically assumed to be positive; nonetheless, some applications require the use of positive and negative weights or complex weights, and often pose particular challenges with convergence. In this paper, we examine such a case from the field of nuclear reactor physics, where the negative particle weights prevent the power iteration algorithm from converging on the sought fundamental eigenstate of the Boltzmann transport equation. We demonstrate how the use of weight cancellation allows convergence on the physical eigenstate. To this end, we develop a novel method to perform weight cancellation in an exact manner, in three spatial dimensions. The viability of this algorithm is then demonstrated on a reactor physics problem.