GEOMETRIC SENSITIVITY ANALYSIS USING MONTE CARLO TECHNIQUES

A method is developed to perform calculations for the sensitivities of integral quantities to geometric parameters using Monte Carlo techniques. This method has been incorporated into a widely used Monte Carlo code for neutron and photon transport. The method is particularly useful when changes in integral quantities are required for small perturbations in surface parameters.; The technique involved in calculating geometric sensitivities includes the usual weight adjustment based on the probability of the track occurring in the unperturbed and perturbed cases due to an infinitesimal perturbation of the geometric surface. This weight adjustment is then applied to all the relevant results of interest. In addition to this term, there are two other terms in the expression for sensitivity which account for the possible effects of scattering in the infinitesimal volume in space caused by a small perturbation of a surface. The first of these represents scattering in the perturbed case and the second the scattering in the unperturbed case. Weights are assigned to these two tracks and their contributions to various results are determined by separate tracking.; The method is very powerful and versatile and represents a potentially useful extension to the Monte Carlo method. Sensitivities of integral quantities of interest to several surfaces can be simultaneously determined. Using these sensitivities and performing uncertainty analysis for small surface perturbations actual changes in tallies can be determined with excellent precision. The effects of surface perturbations can be determined in an individual or cumulative manner. These features make this method vastly superior to the alternate method of performing individual runs for the perturbed and unperturbed cases. Not only will these separate runs be much more expensive but they will also probably never achieve the required precision in the results. The results have been compared with those obtained using a one dimensional discrete ordinates transport code where the perturbed and unperturbed cases were run independently. The geometric sensitivity analysis method was found to work well within the limits of first order perturbation theory and promises to be of great assistance in the design and analysis of nuclear systems.