Reliable Method for Fission Source Convergence of Monte Carlo Criticality Calculation with Wielandt's Method

Abstract

A new algorithm of Monte Carlo criticality calculations for implementing Wielandt's method, which is one of acceleration techniques for deterministic source iteration methods, is developed, and the algorithm can be successfully implemented into MCNP code. In this algorithm, part of fission neutrons emitted during random walk processes are tracked within the current cycle, and thus a fission source distribution used in the next cycle spread more widely. Applying this method intensifies a neutron interaction effect even in a loosely-coupled array where conventional Monte Carlo criticality calculation methods have difficulties, and a converged fission source distribution can be obtained with fewer cycles. Computing time spent for one cycle, however, increases because of tracking fission neutrons within the current cycle, which eventually results in an increase of total computing time up to convergence. In addition, statistical fluctuations of a fission source distribution in a cycle are worsened by applying Wielandt's method to Monte Carlo criticality calculations. However, since a fission source convergence is attained with fewer source iterations, a reliable determination of convergence can easily be made even in a system with a slow convergence. This acceleration method is expected to contribute to prevention of incorrect Monte Carlo criticality calculations.

KEYWORDS:

• Monte Carlo method
• criticality calculation
• eigenvalue problem
• fixed source problem
• Wielandt's method