Convergence of the second eigenfunction in Monte Carlo power iteration

The conditions of convergence in a modified Monte Carlo power iteration method to generate the eigenfunction with the second largest criticality eigenvalue, which was originally proposed by Booth, have been defined with a different approach. In this work, the first and second eigenvectors composed of two volume-integrated fission source intensities defined in two-partitioned regions are used for deriving the convergence conditions. The conditions of convergence as shown by Booth are found to be true in the limit of a small amplitude of the first eigenfunction. Following the method that uses two estimates of the second eigenvalue defined in two-partitioned regions, a new method for removing the fundamental mode eigenfunction from the fission source distributions has been developed. Because of the explicit removal of the first eigenfunction, the validity of this method is convincing as a technique for obtaining the second eigenfunction. Although this method needs the first eigenfunction and eigenvalue, and the subtraction of the first eigenfunction from the fission source distribution, it has the advantage that the adjoint mode calculation which is in general difficult for continuous energy Monte Carlo codes is not required.