Stabilization Technique of Modified Power Iteration method for Monte Carlo Simulation of Neutron Transport Eigenvalue Problem

Abstract

The instability problem of the modified power method was studied. The modified power iteration method was proposed several years ago to obtain the first two eigenvalues and eigenfunctions, and it can accelerate the convergence of the first eigenvalue and eigenfunction by subtracting the second mode from the first mode. It has been tested with deterministic method that the convergence rate of the first eigenfunction is |k3|/k1 instead of |k2|/k1. However, there are some difficulties with the Monte Carlo implementation of the modified power iteration method. One difficulty is that both positive and negative weights should be maintained and some weight cancellation scheme should be applied to get the second eigenfunction. Another difficulty is that for some cases the Monte Carlo implementation of the modified power iteration method may be unstable if not sufficient number of histories is used, or it may result in wrong results. Some stabilization techniques are proposed in this work and the test results are presented.