Analytic Treatment of Source Photon Emission Times to Reduce Noise in Implicit Monte Carlo Calculations

Statistical uncertainty is inherent to any Monte Carlo simulation of radiation transport problems. In space-angle-frequency independent radiative transfer calculations, the uncertainty in the solution is entirely due to random sampling of source photon emission times. We have developed a modification to the Implicit Monte Carlo algorithm that eliminates noise due to sampling of the emission time of source photons. In problems that are independent of space, angle, and energy, the new algorithm generates a smooth solution, while a standard implicit Monte Carlo solution is noisy. For space- and angle-dependent problems, the new algorithm exhibits reduced noise relative to standard implicit Monte Carlo in some cases, and comparable noise in all other cases. The improvements are limited to short time scales; over long time scales, noise due to random sampling of spatial and angular variables tends to dominate the noise reduction from the new algorithm.