title: Estimation of flux distributions with Monte Carlo functional expansion tallies.
abstract: Monte Carlo methods provide a powerful technique for estimating the average radiation flux in a volume (or across a surface) in cases where analytical solutions may not be possible. Unfortunately, Monte Carlo simulations typically provide only integral results and do not offer any further details about the distribution of the flux with respect to space, angle, time or energy. In the functional expansion tally (FET) a Monte Carlo simulation is used to estimate the functional expansion coefficients for flux distributions with respect to an orthogonal set of basis functions. The expansion coefficients are then used in post-processing to reconstruct a series approximation to the true distribution. Discrete event FET estimators are derived and their application in estimating radiation flux or current distributions is demonstrated. Sources of uncertainty in the FET are quantified and estimators for the statistical and truncation errors are derived. Numerical results are presented to support the theoretical development.
authors.affiliation: Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109, USA. dgrieshe@umich.edu
authors.forename: David P
authors.initials: DP
authors.lastname: Griesheimer
authors.forename: William R
authors.initials: WR
authors.lastname: Martin
authors.forename: James Paul
authors.initials: JP
authors.lastname: Holloway
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D009010:Monte Carlo Method; D009716:Numerical Analysis, Computer-Assisted; D011829:Radiation Dosage; D011835:Radiation Protection / Q000379:methods*; D011874:Radiometry / Q000379:methods*; D012542:Scattering, Radiation; D012984:Software