Parametric Design Calculations Using Green’s Function to Determine Unique Source

The energy dependence of the current incident on a macrocell can in principle be determined if the Green's function and the interior flux due to the total current are known. The Green's function is the flux within some portion of the macrocell due to a unit source in each energy group. We have demonstrated that the appropriate solution for the current is obtained for the higher energy groups in a fast reactor example. However, the lower energy groups are very sensitive to the downscattering and the solution even led to negative values for the incident partial current in some energy groups, which is not physical. In this particular example, the preliminary design study was insensitive to the incident current of the lower energy groups. For problems where the lower groups are important, it would seem prudent to abandon the exact solution and use a weighted least squares solution. Such a weighted least squares solution could assign importance for obtaining nearly the exact solution for as many energy groups as possible, while simultaneously making slight adjustments in the higher energy currents to obtain downscatter contributions that will approximately preserve the flux in the lower energy groups.