Track 4: basic nuclear science variance reduction for Monte Carlo criticality simulations. 4. Numerical Demonstration of Source Convergence Issues in Monte Carlo Eigenvalue Simulations

Obtaining results is clearly the ultimate objective of Monte Carlo numerical simulations and analyses, but ascertaining reliability of these results is equally important and sometimes more difficult to achieve. This is a special concern in eigenvalue Monte Carlo simulations because the possibility of significantly underestimating the eigenvalue is real. In this paper, we introduce a series of test problems and utilize them to demonstrate and clarify some of the source convergence issues. It is anticipated that this analysis will help to improve the diagnostics of Monte Carlo eigenvalue simulations. Monte Carlo is potentially the most accurate method for modeling particle transport since it allows detailed geometry representation and use of point-wise cross sections. However, its statistical nature introduces additional concerns related to the reliability of results. Essentially, since both the results and their variance are estimated within the same numerical simulation, the latter may be largely underestimated, and the actual results may be far from the apparent ones. In this paper, we focus on eigenvalue simulations, leaving aside specific challenges of fixed source simulations. Monte Carlo eigenvalue simulations are indispensable in achieving accurate modeling of nonstandard critical and subcritical systems. For example, reference analyses of novel reactor designs and complex subcritical configurations may be performed using this method. In either case, it is necessary to ensure that numerical results on criticality, or on the subcritical margin, are reliable. Monte Carlo eigenvalue simulations essentially follow neutrons through generations (cycles, batches), the fundamental mode is approached through these iterations, and the initial (transient) cycles are discarded. If the source distribution has not converged to the fundamental mode, the eigenvalue estimate may be significantly inaccurate. Moreover, because of size and intercorrelation of batches, necessity of renormalization, and the statistical nature of these simulations, different biases are introduced that make robust diagnostics very difficult. Of additional concern is the possibility that all regions with fissile material are not properly sampled. In this case, a large eigenvalue underestimate is possible. These and related issues have been previously identified and analyzed. The specific objective of this paper is to introduce simple test problems, yet with all the main features of actual simulations; to examine source convergence problems; and to use the results of the simulations to support development of robust diagnostic techniques that would help identify false source convergence. The MCNP computer code is utilized for simulations; however, the conclusions should remain valid in general for eigenvalue Monte Carlo eigenvalue simulations. Test problems were defined suitable for examining issues related to source convergence in Monte Carlo eigenvalue simulations. A series of numerical simulations was performed, and their results will be employed to formulate improved diagnostic methods for identifying or preventing false source convergence. (authors)