A comparative study of different tracklength biassing schemes

Abstract

Tracklength biassing is employed in Monte Carlo Radiation Transport to obtain, within reasonable computer time, statistically reliable estimates of neutron and gamma transmission through thick shields. The material cross section of the shield medium is multiplied by a factor ‘ a’ so that the particle tracks toward the shield exit are stretched. Dependence of this factor on μ—the cosine of the angle between the particle direction and a direction toward the shield exit is considered by expressing a = a( b, μ) where b is the biassing parameter. Three schemes with (1) a( μ) = constant for μ ⩾ 0 and unity otherwise (2) a( μ) = 1 − bμ and (3) a( μ) = exp(− bμ) are considered in this paper and their relative merits are studied, analytically on a notional slab shield problem. It is found that the ‘exponential’ scheme has superior variance reduction characteristics and is also more efficient from the point of view of computer time requirements, compared to the other two schemes. The ‘linear’ scheme leads to greater variance reduction compared to ‘constant’ biassing scheme but is found to be less efficient. The improvement in the simulation under ‘constant’ biassing seems to be mainly through reduction obtained in the mean number of free flights to escape whereas under the ‘linear’ and ‘exponential’ schemes it is due to their inherent better variance reduction characteristics.