A method for deterministically calculating the population variances of Monte

Carlo particle transport calculations involving weight-dependent variance

reduction has been developed. This method solves a set of equations developed by

Booth and Cashwell [1979], but extends them to consider the weight-window variance reduction technique. Furthermore, equations that calculate the duration of a single history in an MCNP5 (RSICC version 1.51) calculation have been developed as well. The calculation cost, defined as the inverse figure of merit, of a Monte Carlo calculation can be deterministically minimized from calculations of the expected variance and expected calculation time per

history.The method has been applied to one- and two-dimensional multi-group and mixed

material problems for optimization of weight-window lower bounds. With the

adjoint (importance) function as a basis for optimization, an optimization mesh

is superimposed on the geometry. Regions of weight-window lower bounds

contained within the same optimization mesh element are optimized together with

a scaling parameter. Using this additional optimization mesh restricts the size

of the optimization problem, thereby eliminating the need to optimize each

individual weight-window lower bound.

Application of the optimization method to a one-dimensional problem, designed to

replicate the variance reduction iron-window effect, obtains a gain in

efficiency by a factor of 2 over standard deterministically generated weight

windows. The gain in two dimensional problems varies. For a 2-D block problem

and a 2-D two-legged duct problem, the efficiency gain is a factor of about 1.2.

The top-hat problem sees an efficiency gain of 1.3, while a 2-D 3-legged duct

problem sees an efficiency gain of only 1.05. This work represents the first attempt at deterministic optimization of Monte

Carlo calculations with weight-dependent variance reduction. However, the

current work is limited in the size of problems that can be run by the amount of

computer memory available in computational systems. This limitation results

primarily from the added discretization of the Monte Carlo particle weight

required to perform the weight-dependent analyses. Alternate discretization

methods for the Monte Carlo weight should be a topic of future investigation.

Furthermore, the accuracy with which the MCNP5 calculation times can be

calculated deterministically merits further study.